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1. JSTOR Effectively Retractable Theories And Degrees Of Undecidability We identify a sentence with its Godel number so that we speak of 0 sets of . degrees OF Undecidability 601 resulting sequence of sentences, say do, d~,. http://links.jstor.org/sici?sici=0022-4812(196912)34:4<597:ERTADO>2.0.CO;2-3

2. 03Dxx Other Turing degree structures; 03D30 Other degrees and reducibilities; 03D35 Undecidability and degrees of sets of sentences; 03D40 Word problems, etc. http://www.ams.org/msc/03Dxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Computability and recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 03D10 Turing machines and related notions [See also 03D15 Complexity of computation [See also 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section

3. List For KWIC List Of MSC2000 Phrases sentences decidability of theories and sets of 03B25 sentences Undecidability and degrees of sets of 03D35 separability 54D65 http://www.math.unipd.it/~biblio/kwic/msc/m-kl_11_48.htm

semigroupoids, semigroups, groups (viewed as categories) # groupoids, semigroups semigroups # $C$- semigroups # analysis on topological semigroups # commutative semigroups # integrated semigroups # inverse semigroups # mappings of semigroups # orthodox semigroups # regular semigroups # representations of general topological groups and semigroups # structure of topological semigroups # transformation groups and semigroups # varieties of semigroups and applications to diffusion processes # Markov semigroups and linear evolution equations # one-parameter semigroups and monoids # ordered semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions # almost periodic functions on groups and semigroups in $C^*$-algebras # derivations, dissipations and positive semigroups in automata theory, linguistics, etc. semigroups of linear operators # groups and semigroups of linear operators, their generalizations and applications # groups and semigroups of nonlinear operators semigroups of nonlinear operators # groups and semigroups of rings # semigroup rings, multiplicative

4. Mhb03.htm 03D28, Other Turing degree structures. 03D30, Other degrees and reducibilities. 03D35, Undecidability and degrees of sets of sentences http://www.mi.imati.cnr.it/~alberto/mhb03.htm

03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

5. Sachgebiete Der AMS-Klassifikation: 00-09 deductive systems 03B25 Decidability of theories and sets of sentences, reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html

Sachgebiete der AMS-Klassifikation: 00-09 nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen 01-XX 03-XX 04-XX 05-XX 06-XX 08-XX nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

6. MathNet-Mathematical Subject Classification 03D25, Recursively enumerable sets and degrees. 03D30, Other degrees; reducibilities. 03D35, Undecidability and degrees of sets of sentences http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

7. HeiDOK 03D35 Undecidability and degrees of sets of sentences ( 0 Dok. ) 03D40 Word problems, etc. ( 0 Dok. ) 03D45 Theory of numerations, effectively presented http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

8. DC MetaData For:The Halting Problem For Additive Machines Is Not Decidable By An 68Q10 Modes of computation 03D25 Recursively enumerable sets and degrees 03D35 Undecidability and degrees of sets of sentences 68Q65 Abstract data types; http://www.math-inf.uni-greifswald.de/preprints/shadow/06_4.rdf.html

The Halting Problem for Additive Machines is Not Decidable by an Additive Machine with the Rational Numbers as an Oracle Preprint series: Preprintreihe Mathematik 2006, 4 MSC 2000 68Q10 Modes of computation 03D25 Recursively enumerable sets and degrees 03D35 Undecidability and degrees of sets of sentences 68Q65 Abstract data types; algebraic specification 68Q17 Computational difficulty of problems Abstract We answer the question posed by Klaus Meer and Martin Ziegler in "Uncomputability below the Real Halting Problem" whether the set of rational numbers is strictly easier than the Halting Problem with respect to additive machines. We define a problem below the Halting Problem such that the set of rational numbers is strictly easier than the new problem. As a consequence, the set of rational numbers is strictly easier than the Halting Problem. This document is well-formed XML.

9. DC MetaData For: Decidability Of Code Properties See also {20M35, 03D35 Undecidability and degrees of sets of sentences We explore the borderline between decidability and Undecidability of http://www.mathematik.uni-halle.de/reports/shadows/00-11report.html

Decidability of Code Properties by H. Fernau, K. Reinhardt, L. Staiger Preprint series: 00-11, Reports on Computer Science The paper is published: in: Proc. Developments in Language Theory IV (G. Rozenberg and W. Thomas Eds.), World Scientific, Singapore 2000, 153 - 163. MSC 03D35 Undecidability and degrees of sets of sentences CR Abstract We explore the borderline between decidability and undecidability of the following question: Keywords: partially blind counter machines, prefix code, infix code, bifix code, deciphering delay, decidability Upload: Update: The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.

10. DC MetaData For: Decidability Of Chaos For Some Families Of Dynamical Systems MSC 2000 37C99 None of the above, but in this section 03D35 Undecidability and degrees of sets of sentences. Preprint Server. http://www.preprint.impa.br/Shadows/SERIE_A/2002/188.html

Preprint Série A 188/2002 Decidability of chaos for some families of dynamical systems Source file as Postscript Document (.ps) Portable Document Format (.pdf) Alexander Arbieto Carlos Matheus Keywords: Decidability, chaos, lyapunov exponents, SRB measues, topological entropy. Abstract: MSC 2000: 37C99 None of the above, but in this section 03D35 Undecidability and degrees of sets of sentences Preprint Server

11. J Logic Computation -- Sign In Page we shall consider not only sentences but also formulas with free .. On the structure of degrees of index sets. Algebra and Logic (1979) 18463–480. http://logcom.oxfordjournals.org/cgi/content/full/exm038v1

@import "/resource/css/hw.css"; @import "/resource/css/logcom.css"; Skip Navigation Oxford Journals Contact Us My Basket ... Volume 0, Number 2007 10.1093/logcom/exm038 This item requires a subscription* to Journal of Logic and Computation Online. * Please note that articles prior to 1996 are not normally available via a current subscription. In order to view content before this time, access to the Oxford Journals digital archive is required. If you would like to purchase short-term access you must have a personal account. Please sign in below with your personal user name and password or register to obtain a user name and password for free. Full Text Undecidability in the Homomorphic Quasiorder of Finite Labelled Forests Kudinov and Selivanov J Logic Computation. To view this item, select one of the options below: Sign In User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgot your user name or password? Purchase Short-Term Access Pay per View - If you would like to purchase short-term access you must have a personal account. Please sign in with your personal user name and password or register to obtain a user name and password for free. You will be presented with Pay per Article options after you have successfully signed in with a personal account.

12. General General Mathematics Mathematics For Nonmathematicians systems Decidability of theories and sets of sentences See also 11U05, 12L05, Undecidability and degrees of sets of sentences Word problems, etc. http://amf.openlib.org/2001/msc2000.xsd

13. 359/369 (Total 5522) NO 152 03E04 Ordered Sets And Translate this page See also 06B25, 08A50, 20F10, 68R15. 139, 03D35, Undecidability and degrees of sets of sentences. 138, 03D30, Other degrees and reducibilities http://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=359

14. Catálogo Translate this page Búsqueda por tema 03D35 - Undecidability and degrees of sets of sentences Martin Weese, Undecidable extensions of the theory of Boolean algebras http://catalis.uns.edu.ar/cgi-bin/catalis_pack_demo_devel/wxis?IsisScript=opac/x

15. 0 Top The TOP Concept In The Hierarchy. 1 Adverbial Modification 308 degrees of sets of sentences 309 effectively presented structure 31 329 thue system 33 unicorn 330 Undecidability 331 word problem 332 reference The http://staff.science.uva.nl/~caterina/LoLaLi/soft/ch-data/gloss.txt

16. Richard A. Shore: Publications On the AEsentences of alpha-recursion theory, in Generalized Recursion Theory II, . The theories of the T, tt and wtt r.e. degrees Undecidability and http://www.math.cornell.edu/~shore/publications.html

Richard A. Shore : Publications Curriculum Vitae Most of the documents below with electronic versions have been compiled for optimum viewing in PDF format. However, some papers (for various reasons) look grainy as PDF files. All the papers with electronic versions are, however, also available in postscript and DVI format. On large cardinals and partition relations, Journal of Symbolic Logic (1971), 305-308 (with E.M. Kleinberg). Weak compactness and square bracket partition relations, Journal of Symbolic Logic (1972), 673-676 (with E.M. Kleinberg). Square bracket partition relations in L Fundamenta Mathematica Minimal alpha-degrees, Annals of Mathematical Logic Cohesive sets: countable and uncountable, Proceedings of the American Mathematical Society Sigma n sets which are Delta n -incomparable (uniformly), Journal of Symbolic Logic Splitting an alpha-recursively enumerable set, Transactions of the American Mathematical Society The recursively enumerable alpha-degrees are dense, Annals of Mathematical Logic The irregular and non-hyperregular alpha-r.e. degrees

17. Publication Of V.L. Selivanov On the structure of degrees of index sets. Algebra and Logic, 18, . Undecidability in the homomorphic quasiorder of finite labeled forests (joint with http://vseliv.nspu.ru/en/publ/part

Title page Curriculum vitae Publication Research Photoalbum Publication of V.L. Selivanov Papers refereed by journal standards 1. On computability of some classes of numberings. Prob. Methods and Cybernetics, v.12-13, Kazan University, Kazan,1976, 157170 (Russian). 2. On numberings of families of total recursive functions. Algebra and Logic, 15, N 2 (1976), 205226 (Russian, there is an English translation). 3. Two theorems on computable numberings. Algebra and Logic, 15, N 4 (1976), 484 (Russian, there is an English translation). 4. Numberings of canonically computable families of finite sets. Sib. Math. J., 18, N 6 (1977), 13731381 (Russian, there is an English translation). 5. On index sets of classes of numberings. Prob. Methods and Cybernetics, v.14, Kazan University, Kazan,1978, 90103 (Russian). 6. On index sets of computable classes of finite sets. In: Algorithms and Automata, Kazan University, Kazan,1978, 9599 (Russian). 7. Some remarks on classes of recursively enumerable sets. Sib. Math. J., 19, N 1 (1978), 109115. 8. On the structure of degrees of index sets. Algebra and Logic, 18, N 4 (1979), 286299.

18. CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC Robert Soare, /Recursively Enumerable sets and degrees/, Springer. The famous incompleteness, Undecidability and undefinability results of Godel and http://logic.cmu.edu/pal-courses-s05.txt

19. Tree Structure Of LoLaLi Concept Hierarchy Updated On 2004624 330 Undecidability . . . . 328 theory of numerations . 308 degrees of sets of sentences . . . . 319 recursive equivalence type . http://remote.science.uva.nl/~caterina/LoLaLi/soft/ch-data/tree.txt

Tree structure of LoLaLi Concept Hierarchy Updated on 2004:6:24, 13:16 In each line the following information is shown (in order from left to right, [OPT] indicates information that can be missing): Type of relation with the parent concept (see below for the legend) [OPT] Id of the node Name of the node Number of children, in parenthesis [OPT] + if the concept is repeated somehwere [OPT] (see file path.txt for the list of repeated nodes) LEGEND: SbC Subclass Par Part-of Not Notion Res Mathematical results His historical view Ins Instance Uns Unspecified top (4) g . 87 computer science (4) g . . 191 logic (1) (31) + g . . . Par 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 198 proof theory (22) g . . . . SbC 503 sequent calculus . . . . . Not 484 structural rules . . . . 289 interpretation . . . . 282 constructive analysis . . . . 295 recursive ordinal . . . . 287 Goedel numbering . . . . 288 higher-order arithmetic . . . . 281 complexity of proofs . . . . 294 recursive analysis . . . . Res 292 normal form theorem . . . . 297 second-order arithmetic . . . . SbC 110 natural deduction (2) + g . . . . . Not 482 hypothetical reasoning + . . . . . Not 483 normalization . . . . 290 intuitionistic mathematics . . . . 286 functionals in proof theory . . . . 298 structure of proofs g . . . . 283 constructive system . . . . 291 metamathematics . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . 296 relative consistency . . . . Not 284 cut elimination theorem g . . . . 293 ordinal notation . . . . 285 first-order arithmetic . . . . SbC 485 proof nets . . . SbC 475 first order logic (4) g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . Par 476 first order language g . . . . . Not 477 fragment (3) g . . . . . . SbC 479 finite-variable fragment g . . . . . . SbC 480 guarded fragment g . . . . . . SbC 478 modal fragment g . . . . . . . Not 470 standard translation + g . . . . 511 SPASS g . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . 193 computability theory . . . SbC 167 temporal logic (2) + g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 495 substructural logic . . . SbC 200 relevance logic + . . . . 108 entailment + . . . Res 180 Lindstroem's theorem + . . . SbC 481 linear logic . . . 526 variable g . . . . SbC 517 free variable + g . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . SbC 125 feature logic + . . . . 75 unification + . . . 197 model theory (29) . . . . 237 set-theoretic model theory . . . . 11 universal algebra + . . . . 225 infinitary logic . . . . 217 admissible set . . . . 234 recursion-theoretic model theory . . . . 239 ultraproduct . . . . 227 logic with extra quantifiers . . . . SbC 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . 219 completeness of theories . . . . 235 saturation . . . . 222 equational class . . . . 238 stability . . . . 233 quantifier elimination . . . . 221 denumerable structure . . . . 228 model-theoretic algebra . . . . 236 second-order model theory . . . . 230 model of arithmetic . . . . 218 categoricity g . . . . 220 definability . . . . 226 interpolation . . . . SbC 454 first order model theory . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . 231 nonclassical model (2) . . . . . 246 sheaf model . . . . . 245 boolean valued . . . . 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . 232 preservation . . . . 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 229 model-theoretic forcing . . . . 224 higher-order model theory . . . . Par 493 correspondence theory . . . . 223 finite structure . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . SbC 156 modal logic (13) + g . . . . Ins 512 S4 . . . . 488 modes . . . . 486 frame (2) . . . . . SbC 487 frame constraints . . . . Par 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . SbC 213 doxastic logic g . . . . Not 489 accessability relation + . . . . Par 471 modal language (2) g . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 490 boolean operators . . . . SbC 211 alethic logic g . . . . SbC 212 deontic logic (3) g . . . . . SbC 521 standard deontic logic g . . . . . SbC 523 two-sorted deontic logic g . . . . . SbC 522 dyadic deontic logic g . . . . Par 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . Par 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . SbC 214 epistemic logic g . . . . Not 462 model (4) + . . . . . SbC 464 finite model g . . . . . SbC 466 image finite model . . . . . . Res 467 Hennessy-Milner theorem g . . . . . Par 463 valuation g . . . . . SbC 465 tree model g . . . 194 computational logic (2) . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . SbC 192 combinatory logic g . . . Par 199 recursive function theory . . . 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . SbC 168 lambda calculus (4) g . . . . 170 application . . . . 172 lambda operator . . . . 169 abstraction . . . . 171 conversion . . . 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 367 semantics 367 (8) g . . . . 371 truth conditional semantics . . . . 373 truth table . . . . SbC 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . 85 functional completeness + . . . . 370 satisfaction . . . . 369 material implication g . . . . 368 assignment . . . . Not 372 truth function + g . . . Par 201 set theory (24) + g . . . . 398 set-theoretic definability . . . . Not 391 iota operator . . . . 384 determinacy . . . . 387 fuzzy relation . . . . Not 385 filter . . . . 389 generalized continuum hypothesis . . . . 386 function (3) g . . . . . 482 hypothetical reasoning + . . . . . 509 functional application . . . . . 508 functional composition . . . . Not 394 ordinal definability . . . . Not 107 consistency + . . . . 397 set algebra . . . . 399 Suslin scheme . . . . SbC 383 descriptive set theory g . . . . 388 fuzzy set g . . . . 378 borel classification g . . . . SbC 380 combinatorial set theory . . . . Not 390 independence . . . . 381 constructibility . . . . 396 relation g . . . . 377 axiom of choice g . . . . 392 large cardinal . . . . Not 395 ordinal number . . . . 393 Martin's axiom . . . . 382 continuum hypothesis g . . . . Not 379 cardinal number . . . Par 216 abstract model theory + . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . 178 compactness + . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . Par 196 foundations of theories . . . 195 constraint programming . . Not 88 software (2) . . . 104 database + g . . . . 105 query g . . . 275 programming language (3) . . . . 190 semantics 190 (8) + g . . . . . 356 denotational semantics . . . . . 119 domain theory g . . . . . . 120 domain . . . . . 360 program analysis . . . . . 359 process model . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 357 operational semantics . . . . . 358 partial evaluation . . . . . 355 algebraic semantics . . . . 276 syntax 276 . . . . 277 prolog g . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . Par 34 artificial intelligence (5) g . . . Par 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . 191 logic (1) (31) + g . . . . Par 53 automated reasoning (25) + . . . . . 35 belief revision . . . . . . 76 update . . . . . 67 nonmonotonic reasoning . . . . . 63 mathematical induction . . . . . 71 rewrite system (3) . . . . . . 350 termination . . . . . . 348 confluence . . . . . . 349 critical pair . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . . . . 68 paramodulation . . . . . Not 72 skolemisation . . . . . 65 model checking . . . . . 55 clause 55 (2) . . . . . . 80 horn clause g . . . . . . 79 Gentzen clause . . . . . 74 uncertainty . . . . . 75 unification + . . . . . 57 connection graph procedure . . . . . 64 metatheory . . . . . 61 literal . . . . . 58 connection matrix . . . . . 81 clause 81 . . . . . . SbC 82 relative clause . . . . . 69 reason extraction . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . Res 60 Herbrand's theorem . . . . . 56 completion . . . . . . 86 Knuth Bendix completion . . . . . 73 theorem prover (3) . . . . . . 427 Bliksem g . . . . . . 428 Boyer-Moore theorem prover . . . . . . 429 SPASS g . . . . . 66 narrowing . . . . . 62 logic programming g . . . . . 54 answer extraction . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Par 198 proof theory (22) g . . . . . SbC 503 sequent calculus . . . . . . Not 484 structural rules . . . . . 289 interpretation . . . . . 282 constructive analysis . . . . . 295 recursive ordinal . . . . . 287 Goedel numbering . . . . . 288 higher-order arithmetic . . . . . 281 complexity of proofs . . . . . 294 recursive analysis . . . . . Res 292 normal form theorem . . . . . 297 second-order arithmetic . . . . . SbC 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . 290 intuitionistic mathematics . . . . . 286 functionals in proof theory . . . . . 298 structure of proofs g . . . . . 283 constructive system . . . . . 291 metamathematics . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . 296 relative consistency . . . . . Not 284 cut elimination theorem g . . . . . 293 ordinal notation . . . . . 285 first-order arithmetic . . . . . SbC 485 proof nets . . . . SbC 475 first order logic (4) g . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . Par 476 first order language g . . . . . . Not 477 fragment (3) g . . . . . . . SbC 479 finite-variable fragment g . . . . . . . SbC 480 guarded fragment g . . . . . . . SbC 478 modal fragment g . . . . . . . . Not 470 standard translation + g . . . . . 511 SPASS g . . . . . Par 515 quantification (4) + . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . 193 computability theory . . . . SbC 167 temporal logic (2) + g . . . . 435 type theory (2) + . . . . . 433 type . . . . . . 434 type shifting . . . . . Not 23 polymorphism + g . . . . 495 substructural logic . . . . SbC 200 relevance logic + . . . . . 108 entailment + . . . . Res 180 Lindstroem's theorem + . . . . SbC 481 linear logic . . . . 526 variable g . . . . . SbC 517 free variable + g . . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . . SbC 125 feature logic + . . . . . 75 unification + . . . . 197 model theory (29) . . . . . 237 set-theoretic model theory . . . . . 11 universal algebra + . . . . . 225 infinitary logic . . . . . 217 admissible set . . . . . 234 recursion-theoretic model theory . . . . . 239 ultraproduct . . . . . 227 logic with extra quantifiers . . . . . SbC 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . 219 completeness of theories . . . . . 235 saturation . . . . . 222 equational class . . . . . 238 stability . . . . . 233 quantifier elimination . . . . . 221 denumerable structure . . . . . 228 model-theoretic algebra . . . . . 236 second-order model theory . . . . . 230 model of arithmetic . . . . . 218 categoricity g . . . . . 220 definability . . . . . 226 interpolation . . . . . SbC 454 first order model theory . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . 231 nonclassical model (2) . . . . . . 246 sheaf model . . . . . . 245 boolean valued . . . . . 201 set theory (24) + g . . . . . . 398 set-theoretic definability . . . . . . Not 391 iota operator . . . . . . 384 determinacy . . . . . . 387 fuzzy relation . . . . . . Not 385 filter . . . . . . 389 generalized continuum hypothesis . . . . . . 386 function (3) g . . . . . . . 482 hypothetical reasoning + . . . . . . . 509 functional application . . . . . . . 508 functional composition . . . . . . Not 394 ordinal definability . . . . . . Not 107 consistency + . . . . . . 397 set algebra . . . . . . 399 Suslin scheme . . . . . . SbC 383 descriptive set theory g . . . . . . 388 fuzzy set g . . . . . . 378 borel classification g . . . . . . SbC 380 combinatorial set theory . . . . . . Not 390 independence . . . . . . 381 constructibility . . . . . . 396 relation g . . . . . . 377 axiom of choice g . . . . . . 392 large cardinal . . . . . . Not 395 ordinal number . . . . . . 393 Martin's axiom . . . . . . 382 continuum hypothesis g . . . . . . Not 379 cardinal number . . . . . 232 preservation . . . . . 216 abstract model theory + . . . . . . 254 quantifier (5) + g . . . . . . . Not 516 bound variable + g . . . . . . . His 514 Frege on quantification + g . . . . . . . Not 517 free variable + g . . . . . . . His 513 Aristotle on quantification + . . . . . . . Not 301 scope . . . . . . . . 351 scoping algorithm . . . . . 229 model-theoretic forcing . . . . . 224 higher-order model theory . . . . . Par 493 correspondence theory . . . . . 223 finite structure . . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . . Not 83 completeness (2) + g . . . . . SbC 84 axiomatic completeness . . . . . SbC 85 functional completeness + . . . . SbC 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 194 computational logic (2) . . . . Not 183 operator (4) + g . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . SbC 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 518 truth-funcional operator (2) g . . . . . . SbC 252 iff g . . . . . . SbC 253 negation . . . . . Not 525 arity g . . . . SbC 192 combinatory logic g . . . . Par 199 recursive function theory . . . . 361 formal semantics (10) + g . . . . . 365 property theory . . . . . 240 Montague grammar (4) . . . . . . 243 sense 243 (4) g . . . . . . . 203 meaning relation (5) . . . . . . . . 205 hyponymy g . . . . . . . . 204 antonymy g . . . . . . . . 207 synonymy g . . . . . . . . . 149 intensional isomorphism + . . . . . . . . 206 paraphrase g . . . . . . . . 108 entailment + . . . . . . . 375 metaphor g . . . . . . . 376 metonymy g . . . . . . . 374 literal meaning . . . . . . 244 sense 244 g . . . . . . 241 meaning postulate . . . . . . 242 ptq g . . . . . . . 300 quantifying in . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . 353 truth (4) + . . . . . . 431 truth definition g . . . . . . 432 truth value . . . . . . 372 truth function + g . . . . . . 430 truth condition . . . . . 362 dynamic semantics . . . . . 363 lexical semantics . . . . . 366 situation semantics (2) g . . . . . . 402 partiality . . . . . . 400 situation . . . . . . . 401 scene . . . . . Not 507 compositionality . . . . . 364 natural logic + . . . . . Par 515 quantification (4) + . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . SbC 168 lambda calculus (4) g . . . . . 170 application . . . . . 172 lambda operator . . . . . 169 abstraction . . . . . 171 conversion . . . . 38 knowledge representation (20) + g . . . . . 152 frame (1) . . . . . 104 database + g . . . . . . 105 query g . . . . . 165 situation calculus . . . . . 167 temporal logic (2) + g . . . . . 166 temporal logic (1) g . . . . . 93 concept formation . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 154 logical omniscience . . . . . 162 rule-based representation . . . . . 157 predicate logic + g . . . . . 159 procedural representation . . . . . 161 representation language . . . . . 156 modal logic (13) + g . . . . . . Ins 512 S4 . . . . . . 488 modes . . . . . . 486 frame (2) . . . . . . . SbC 487 frame constraints . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . SbC 213 doxastic logic g . . . . . . Not 489 accessability relation + . . . . . . Par 471 modal language (2) g . . . . . . . Par 210 modal operator (2) + g . . . . . . . . SbC 472 diamond g . . . . . . . . SbC 473 box g . . . . . . . 490 boolean operators . . . . . . SbC 211 alethic logic g . . . . . . SbC 212 deontic logic (3) g . . . . . . . SbC 521 standard deontic logic g . . . . . . . SbC 523 two-sorted deontic logic g . . . . . . . SbC 522 dyadic deontic logic g . . . . . . Par 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Par 457 modal model theory (7) + . . . . . . . SbC 215 Kripke semantics + g . . . . . . . . Not 489 accessability relation + . . . . . . . Not 461 generated submodel g . . . . . . . 462 model (4) + . . . . . . . . SbC 464 finite model g . . . . . . . . SbC 466 image finite model . . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . . Par 463 valuation g . . . . . . . . SbC 465 tree model g . . . . . . . Not 459 disjoint union of models g . . . . . . . 455 homomorphism (2) + g . . . . . . . . SbC 456 bounded homomorphism g . . . . . . . . SbC 468 bounded morphism . . . . . . . Not 469 expressive power g . . . . . . . . Not 470 standard translation + g . . . . . . . Not 460 bisimulation g . . . . . . SbC 214 epistemic logic g . . . . . . Not 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . 97 context (2) . . . . . . 99 context dependence . . . . . . 98 context change . . . . . 160 relation system . . . . . 153 frame problem g . . . . . 92 concept analysis . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 163 script . . . . . 145 idea g . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 164 semantic network g . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Par 367 semantics 367 (8) g . . . . . 371 truth conditional semantics . . . . . 373 truth table . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 85 functional completeness + . . . . . 370 satisfaction . . . . . 369 material implication g . . . . . 368 assignment . . . . . Not 372 truth function + g . . . . Par 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . Par 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 178 compactness + . . . . His 177 aristotelean logic (2) + g . . . . . Par 39 syllogism g . . . . . Par 513 Aristotle on quantification + . . . . Par 196 foundations of theories . . . . 195 constraint programming . . . 40 planning . . . Not 36 classification . . . Not 37 heuristic g . . Par 89 theory of computation (4) g . . . Par 127 formal language theory (10) g . . . . 128 categorial grammar + . . . . . SbC 528 combinatorial categorial grammar . . . . 131 context free language g . . . . 130 Chomsky hierarchy g . . . . 134 phrase structure grammar . . . . 129 category . . . . 135 recursive language + g . . . . 137 unrestricted language g . . . . 136 regular language . . . . 132 context sensitive language g . . . . 133 feature constraint . . . Par 302 recursion theory (31) g . . . . 306 complexity of computation . . . . 330 undecidability . . . . 328 theory of numerations . . . . 309 effectively presented structure . . . . 314 isol . . . . 307 decidability (2) g . . . . . 474 tree model property g . . . . . 504 subformula property . . . . 322 recursively enumerable degree . . . . 331 word problem . . . . 327 subrecursive hierarchy . . . . 315 post system . . . . 324 recursively enumerable set . . . . 320 recursive function . . . . 318 recursive axiomatizability . . . . 329 thue system . . . . 325 reducibility . . . . 304 automaton . . . . 310 formal grammar . . . . 326 set recursion theory . . . . 303 abstract recursion theory . . . . 323 recursively enumerable language . . . . 305 axiomatic recursion theory . . . . 135 recursive language + g . . . . 313 inductive definability . . . . 316 recursion theory on admissible sets . . . . Not 52 Turing machine + . . . . 308 degrees of sets of sentences . . . . 319 recursive equivalence type . . . . 312 higher type recursion theory . . . . 317 recursion theory on ordinals . . . . 321 recursive relation . . . . 311 hierarchy . . . Par 185 computational logic (1) (8) g . . . . 190 semantics 190 (8) + g . . . . . 356 denotational semantics . . . . . 119 domain theory g . . . . . . 120 domain . . . . . 360 program analysis . . . . . 359 process model . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 357 operational semantics . . . . . 358 partial evaluation . . . . . 355 algebraic semantics . . . . 189 reasoning about programs . . . . 53 automated reasoning (25) + . . . . . 35 belief revision . . . . . . 76 update . . . . . 67 nonmonotonic reasoning . . . . . 63 mathematical induction . . . . . 71 rewrite system (3) . . . . . . 350 termination . . . . . . 348 confluence . . . . . . 349 critical pair . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . . . . 68 paramodulation . . . . . Not 72 skolemisation . . . . . 65 model checking . . . . . 55 clause 55 (2) . . . . . . 80 horn clause g . . . . . . 79 Gentzen clause . . . . . 74 uncertainty . . . . . 75 unification + . . . . . 57 connection graph procedure . . . . . 64 metatheory . . . . . 61 literal . . . . . 58 connection matrix . . . . . 81 clause 81 . . . . . . SbC 82 relative clause . . . . . 69 reason extraction . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . Res 60 Herbrand's theorem . . . . . 56 completion . . . . . . 86 Knuth Bendix completion . . . . . 73 theorem prover (3) . . . . . . 427 Bliksem g . . . . . . 428 Boyer-Moore theorem prover . . . . . . 429 SPASS g . . . . . 66 narrowing . . . . . 62 logic programming g . . . . . 54 answer extraction . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Not 83 completeness (2) + g . . . . . SbC 84 axiomatic completeness . . . . . SbC 85 functional completeness + . . . . 188 program verification (4) . . . . . 274 mechanical verification . . . . . 269 invariant + . . . . . 273 logic of programs . . . . . 43 assertion (2) + . . . . . . 45 imperative assertion . . . . . . 44 declarative assertion . . . . 435 type theory (2) + . . . . . 433 type . . . . . . 434 type shifting . . . . . Not 23 polymorphism + g . . . . 186 program construct (5) . . . . . 265 functional construct . . . . . 267 program scheme . . . . . 266 object oriented construct . . . . . 264 control primitive . . . . . 268 type structure . . . . 187 program specification (5) . . . . . 271 pre-condition . . . . . 269 invariant + . . . . . 272 specification technique . . . . . 43 assertion (2) + . . . . . . 45 imperative assertion . . . . . . 44 declarative assertion . . . . . 270 post-condition . . . Par 48 automata theory (4) . . . . Not 52 Turing machine + . . . . 50 linear bounded automaton . . . . 49 finite state machine g . . . . 51 push down automaton . 173 linguistics (13) g . . Par 446 descriptive linguistics g . . . 142 grammar (5) g . . . . Not 519 derivation g . . . . 452 grammatical constituent g . . . . . 121 ellipsis g . . . . . . 122 antecedent of ellipsis . . . . 444 linguistic unit (3) g . . . . . SbC 440 word (5) g . . . . . . 28 anaphor (2) g . . . . . . . 30 antecedent of an anaphor . . . . . . . 29 anaphora resolution . . . . . . 278 pronoun (2) g . . . . . . . 280 pronoun resolution . . . . . . . 279 demonstrative g . . . . . . 138 function word (2) g . . . . . . . SbC 139 determiner g . . . . . . . SbC 441 modifier g . . . . . . . . 445 adjective (4) g . . . . . . . . . 4 predicative position . . . . . . . . . 1 adverbial modification g . . . . . . . . . 3 intersective adjective . . . . . . . . . 2 graded adjective . . . . . . 442 content word g . . . . . . 425 term (2) g . . . . . . . 426 singular term g . . . . . . . 260 plural term (2) g . . . . . . . . 261 collective reading . . . . . . . . 262 distributive reading . . . . . SbC 500 quantified phrases + . . . . . SbC 115 discourse (3) g . . . . . . 116 discourse particle . . . . . . 118 discourse representation theory g . . . . . . 117 discourse referent . . . . 144 syntax 144 (2) g . . . . . 453 logical syntax g . . . . . . 12 algebraic logic (10) + . . . . . . . 6 boolean algebra + . . . . . . . . SbC 7 boolean algebra with operators . . . . . . . 17 post algebra . . . . . . . 15 Lukasiewicz algebra . . . . . . . 14 cylindric algebra g . . . . . . . 8 lattice + g . . . . . . . 18 quantum logic . . . . . . . 10 relation algebra + . . . . . . . 13 categorical logic . . . . . . . 16 polyadic algebra . . . . . . . 19 topos . . . . . 423 syntactic category (3) g . . . . . . 447 part of speech g . . . . . . SbC 249 noun (2) g . . . . . . . SbC 251 proper name . . . . . . . SbC 250 mass noun g . . . . . . SbC 438 verb g . . . . . . . SbC 439 perception verb . . . . 143 sentence g . . 443 linguistic geography g . . Not 502 discontinuity . . Par 361 formal semantics (10) + g . . . 365 property theory . . . 240 Montague grammar (4) . . . . 243 sense 243 (4) g . . . . . 203 meaning relation (5) . . . . . . 205 hyponymy g . . . . . . 204 antonymy g . . . . . . 207 synonymy g . . . . . . . 149 intensional isomorphism + . . . . . . 206 paraphrase g . . . . . . 108 entailment + . . . . . 375 metaphor g . . . . . 376 metonymy g . . . . . 374 literal meaning . . . . 244 sense 244 g . . . . 241 meaning postulate . . . . 242 ptq g . . . . . 300 quantifying in . . . 254 quantifier (5) + g . . . . Not 516 bound variable + g . . . . His 514 Frege on quantification + g . . . . Not 517 free variable + g . . . . His 513 Aristotle on quantification + . . . . Not 301 scope . . . . . 351 scoping algorithm . . . 353 truth (4) + . . . . 431 truth definition g . . . . 432 truth value . . . . 372 truth function + g . . . . 430 truth condition . . . 362 dynamic semantics . . . 363 lexical semantics . . . 366 situation semantics (2) g . . . . 402 partiality . . . . 400 situation . . . . . 401 scene . . . Not 507 compositionality . . . 364 natural logic + . . . Par 515 quantification (4) + . . . . Not 516 bound variable + g . . . . His 514 Frege on quantification + g . . . . Not 517 free variable + g . . . . His 513 Aristotle on quantification + . . Not 20 ambiguity (7) g . . . SbC 27 syntactic ambiguity . . . SbC 25 semantic ambiguity + g . . . SbC 22 lexical ambiguity g . . . SbC 21 derivational ambiguity . . . SbC 24 pragmatic ambiguity . . . SbC 26 structural ambiguity . . . 23 polymorphism + g . . 510 frameworks (7) . . . 535 LFG . . . 128 categorial grammar + . . . . SbC 528 combinatorial categorial grammar . . . 530 TAG . . . 532 DRT . . . 529 GB . . . 534 HPSG . . . 531 dynamic syntax . . 506 linguistic phenomena . . Not 174 language acquisition g . . Par 450 pragmatics (2) g . . . 403 speech act (5) g . . . . 408 statement (2) g . . . . . 112 description (2) g . . . . . . SbC 114 indefinite description . . . . . . SbC 113 definite description . . . . . 409 indicative statement . . . . 405 indirect speech act . . . . 406 performative . . . . 407 performative hypothesis . . . . 404 illocutionary force . . . 100 conversational maxim (3) g . . . . 103 implicature + g . . . . 102 cooperative principle . . . . 101 conversational implicature g . . 499 syntax and semantic interface + . . Par 175 semantics 175 (16) g . . . 25 semantic ambiguity + g . . . Not 123 extension g . . . . 124 extensionality g . . . 334 referent g . . . Not 332 reference (2) g . . . . 333 identity puzzle . . . . 335 referential term . . . . . SbC 336 anchor . . . Not 263 presupposition g . . . . 103 implicature + g . . . Not 146 indexicality . . . . 147 indexical expression g . . . Par 41 aspect . . . . 42 aspectual classification . . . SbC 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . Not 501 coordination . . . Not 353 truth (4) + . . . . 431 truth definition g . . . . 432 truth value . . . . 372 truth function + g . . . . 430 truth condition . . . Not 354 underspecification (2) . . . . 437 quasi-logical form . . . . 436 monotonic semantics . . . 499 syntax and semantic interface + . . . Par 46 attitude . . . . SbC 47 propositional attitude . . . . . Not 299 belief . . . Not 500 quantified phrases + . . . Not 148 intension (3) g . . . . 149 intensional isomorphism + . . . . 151 intensionality . . . . 150 intensional verb . . . 31 animal (3) g . . . . SbC 33 unicorn . . . . SbC 32 donkey . . . . SbC 352 rabbit . . Par 496 syntax 496 (2) g . . . Par 498 word order . . . Par 497 movement . . Par 140 language generation . . . 141 reversibility . 202 mathematics (5) g . . Not 527 algebra 2 g . . 191 logic (1) (31) + g . . . Par 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 198 proof theory (22) g . . . . SbC 503 sequent calculus . . . . . Not 484 structural rules . . . . 289 interpretation . . . . 282 constructive analysis . . . . 295 recursive ordinal . . . . 287 Goedel numbering . . . . 288 higher-order arithmetic . . . . 281 complexity of proofs . . . . 294 recursive analysis . . . . Res 292 normal form theorem . . . . 297 second-order arithmetic . . . . SbC 110 natural deduction (2) + g . . . . . Not 482 hypothetical reasoning + . . . . . Not 483 normalization . . . . 290 intuitionistic mathematics . . . . 286 functionals in proof theory . . . . 298 structure of proofs g . . . . 283 constructive system . . . . 291 metamathematics . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . 296 relative consistency . . . . Not 284 cut elimination theorem g . . . . 293 ordinal notation . . . . 285 first-order arithmetic . . . . SbC 485 proof nets . . . SbC 475 first order logic (4) g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . Par 476 first order language g . . . . . Not 477 fragment (3) g . . . . . . SbC 479 finite-variable fragment g . . . . . . SbC 480 guarded fragment g . . . . . . SbC 478 modal fragment g . . . . . . . Not 470 standard translation + g . . . . 511 SPASS g . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . 193 computability theory . . . SbC 167 temporal logic (2) + g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 495 substructural logic . . . SbC 200 relevance logic + . . . . 108 entailment + . . . Res 180 Lindstroem's theorem + . . . SbC 481 linear logic . . . 526 variable g . . . . SbC 517 free variable + g . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . SbC 125 feature logic + . . . . 75 unification + . . . 197 model theory (29) . . . . 237 set-theoretic model theory . . . . 11 universal algebra + . . . . 225 infinitary logic . . . . 217 admissible set . . . . 234 recursion-theoretic model theory . . . . 239 ultraproduct . . . . 227 logic with extra quantifiers . . . . SbC 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . 219 completeness of theories . . . . 235 saturation . . . . 222 equational class . . . . 238 stability . . . . 233 quantifier elimination . . . . 221 denumerable structure . . . . 228 model-theoretic algebra . . . . 236 second-order model theory . . . . 230 model of arithmetic . . . . 218 categoricity g . . . . 220 definability . . . . 226 interpolation . . . . SbC 454 first order model theory . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . 231 nonclassical model (2) . . . . . 246 sheaf model . . . . . 245 boolean valued . . . . 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . 232 preservation . . . . 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 229 model-theoretic forcing . . . . 224 higher-order model theory . . . . Par 493 correspondence theory . . . . 223 finite structure . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . SbC 156 modal logic (13) + g . . . . Ins 512 S4 . . . . 488 modes . . . . 486 frame (2) . . . . . SbC 487 frame constraints . . . . Par 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . SbC 213 doxastic logic g . . . . Not 489 accessability relation + . . . . Par 471 modal language (2) g . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 490 boolean operators . . . . SbC 211 alethic logic g . . . . SbC 212 deontic logic (3) g . . . . . SbC 521 standard deontic logic g . . . . . SbC 523 two-sorted deontic logic g . . . . . SbC 522 dyadic deontic logic g . . . . Par 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . Par 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . SbC 214 epistemic logic g . . . . Not 462 model (4) + . . . . . SbC 464 finite model g . . . . . SbC 466 image finite model . . . . . . Res 467 Hennessy-Milner theorem g . . . . . Par 463 valuation g . . . . . SbC 465 tree model g . . . 194 computational logic (2) . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . SbC 192 combinatory logic g . . . Par 199 recursive function theory . . . 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . SbC 168 lambda calculus (4) g . . . . 170 application . . . . 172 lambda operator . . . . 169 abstraction . . . . 171 conversion . . . 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 367 semantics 367 (8) g . . . . 371 truth conditional semantics . . . . 373 truth table . . . . SbC 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . 85 functional completeness + . . . . 370 satisfaction . . . . 369 material implication g . . . . 368 assignment . . . . Not 372 truth function + g . . . Par 201 set theory (24) + g . . . . 398 set-theoretic definability . . . . Not 391 iota operator . . . . 384 determinacy . . . . 387 fuzzy relation . . . . Not 385 filter . . . . 389 generalized continuum hypothesis . . . . 386 function (3) g . . . . . 482 hypothetical reasoning + . . . . . 509 functional application . . . . . 508 functional composition . . . . Not 394 ordinal definability . . . . Not 107 consistency + . . . . 397 set algebra . . . . 399 Suslin scheme . . . . SbC 383 descriptive set theory g . . . . 388 fuzzy set g . . . . 378 borel classification g . . . . SbC 380 combinatorial set theory . . . . Not 390 independence . . . . 381 constructibility . . . . 396 relation g . . . . 377 axiom of choice g . . . . 392 large cardinal . . . . Not 395 ordinal number . . . . 393 Martin's axiom . . . . 382 continuum hypothesis g . . . . Not 379 cardinal number . . . Par 216 abstract model theory + . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . 178 compactness + . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . Par 196 foundations of theories . . . 195 constraint programming . . 424 system g . . Par 5 algebra 1 (8) g . . . 8 lattice + g . . . SbC 6 boolean algebra + . . . . SbC 7 boolean algebra with operators . . . 11 universal algebra + . . . 77 category theory + g . . . . 78 bottom . . . SbC 9 Lindenbaum algebra . . . 10 relation algebra + . . . 12 algebraic logic (10) + . . . . 6 boolean algebra + . . . . . SbC 7 boolean algebra with operators . . . . 17 post algebra . . . . 15 Lukasiewicz algebra . . . . 14 cylindric algebra g . . . . 8 lattice + g . . . . 18 quantum logic . . . . 10 relation algebra + . . . . 13 categorical logic . . . . 16 polyadic algebra . . . . 19 topos . . . Par 491 algebraic principles . . . . SbC 492 residuation . . 176 mathematical logic (12) g . . . Res 180 Lindstroem's theorem + . . . 77 category theory + g . . . . 78 bottom . . . 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . 181 logical constants . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . Not 178 compactness + . . . Res 520 Goedel's 2nd incompleteness theorem (1931) g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 184 symbolic logic (18) g . . . . SbC 412 dynamic logic . . . . 420 partial logic . . . . SbC 413 fuzzy logic g . . . . 200 relevance logic + . . . . . 108 entailment + . . . . SbC 419 paraconsistent logic . . . . 416 intermediate logic . . . . 125 feature logic + . . . . . 75 unification + . . . . 157 predicate logic + g . . . . 364 natural logic + . . . . SbC 422 propositional logic g . . . . SbC 410 boolean logic g . . . . SbC 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . SbC 418 many-valued logic g . . . . SbC 417 intuitionistic logic g . . . . SbC 421 probability logic . . . . 411 conditional logic . . . . SbC 414 higher-order logic . . . . 415 inductive logic . 258 philosophy (3) g . . Par 524 philosophy of language g . . Par 259 logic 259 (2) g . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . 449 proposition (2) g . . . . 448 contradiction g . . . . . 255 paradox (2) g . . . . . . 256 liar paradox g . . . . . . 257 semantic paradox . . . . 94 conditional statement (2) . . . . . 95 antecedent . . . . . 96 counterfactual g . . Par 208 metaphysics g . . . 209 common sense world g

20. Hilary Putnam Bibliography “Decidability and Essential Undecidability.” Journal of Symbolic Logic 22.1 (March 1957) . “degrees of Unsolvability of Constructible sets of Integers. http://www.pragmatism.org/putnam/

A Bibliography of Publications by Hilary Putnam Books [For tables of contents of these books, see below in the chronological listing of all publications] The Meaning of the Concept of Probability in Application to Finite Sequences . Ph.D. dissertation, University of California, Los Angeles, 1951. New York: Garland, 1990. Philosophy of Mathematics: Selected Readings . Edited with Paul Benacerraf. Englewood Cliffs, N.J.: Prentice-Hall, 1964. 2nd ed., Cambridge: Cambridge University Press, 1983. Philosophy of Logic . New York: Harper and Row, 1971. London: George Allen and Unwin, 1972. Mathematics, Matter and Method Philosophical Papers , vol. 1. Cambridge: Cambridge University Press, 1975. 2nd. ed., 1985. Mind, Language and Reality Philosophical Papers , vol. 2. Cambridge: Cambridge University Press, 1975. Meaning and the Moral Sciences . London: Routledge and Kegan Paul, 1978. Reason, Truth, and History . Cambridge: Cambridge University Press, 1981. Realism and Reason Philosophical Papers , vol. 3. Cambridge: Cambridge University Press, 1983. Methodology, Epistemology, and Philosophy of Science: Essays in Honour of Wolfgang Stegmüller

21. Springer Online Reference Works Both natural and programming languages can be viewed as sets of sentences, that is, finite strings of elements from some basic vocabulary. http://eom.springer.de/F/f040850.htm

Encyclopaedia of Mathematics F Article referred from Article refers to Formal languages and automata Both natural and programming languages can be viewed as sets of sentences, that is, finite strings of elements from some basic vocabulary. The notion of a language introduced below is very general. It certainly includes both natural and programming languages and also all kinds of nonsense languages one might think of. Traditionally, formal language theory is concerned with the syntactic specification of a language rather than with any semantic issues. A syntactic specification of a language with finitely many sentences can be given, at least in principle, by listing the sentences. This is not possible for languages with infinitely many sentences. The main task of formal language theory is the study of finitary specifications of infinite languages. The basic theory of computation, as well as of its various branches, such cryptography Turing machine Automaton, finite Grammar, formal ... Automata, theory of An alphabet is a finite non-empty set. The elements of an alphabet

22. Computability Theory Post asked whether there is an intermediate c.e. degree and this was solved by Friedberg and .. We define Rosser sentences and show their Undecidability. http://caltechmacs117b.wordpress.com/

Computability Theory Goodstein sequences July 27, 2007 by andrescaicedo Will Sladek, a student at Caltech, wrote an excellent introductory paper on incompleteness in PA, The termite and the tower . While Will was working on his paper, I wrote a short note, Goodstein’s function Posted in Undecidability and incompleteness Unsolvable problems - Lecture 3 March 12, 2007 by andrescaicedo At the beginning of the course we built (recursively in ) two incomparable sets A,B . It follows that A and B  have degrees intermediate between and . The construction required that we fixed finite initial segments of A and B  during an inductive construction and so it is not clear whether they are c.e. or not. (A c.e. construction would add elements to a set and we would not have complete control on what is kept out of the set). Post asked whether there is an intermediate c.e. degree and this was solved by Friedberg and Muchnik using what is now called a finite injury priority construction. We show this construction; again, 2 incomparable sets A and B are built and the construction explicitly shows they are c.e. This implies they are not recursive and have degree strictly below

23. 1. Computability And Randomness Higher Randomness Notions And The theory of the polynomial manyone degrees of recursive sets is undecidable (with K.Ambos-Spies). STACS 92, Lecture Notes in Computer Science 577, http://www.cs.auckland.ac.nz/~nies/onlinepapers.html

1. Computability and Randomness Higher randomness notions and their lowness properties (with Chitat Chong and Liang Yu). Israel J. Math, To appear Eliminating concepts. To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. Lowness for Computable Machines (with Rod Downey, Noam Greenberg and Nenad Mikhailovich). To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. A lower cone in the wtt degrees of non-integral effective dimension (with Jan Reimann). To appear in Proc. of the IMS workshop on computational aspects of infinity, Singapore. Non-cupping and randomness. Proc. Amer. Math. Soc. 135 (2007), no. 3, 837844. (with Rod Downey, Rebecca Weber, and Liang Yu). Journal of Symbolic logic 71( 3), 2006, pp. 1044-1052. Randomness via effective descriptive set theory (with Greg Hjorth). J. London Math Soc Nies 75 (2): 495-508. Calibrating randomness. Bull. Symb. Logic. 12 no 3 (2006) 411-491 (with Downey, Hirschfeldt and Terwijn). Randomness and computability: Open questions (with Joe Miller). Bull. Symb. Logic. 12 no 3 (2006) 390-410.

24. Mathematical Preprints By Steffen Lempp The Pi3theory of the enumerable Turing degrees is undecidable, with andré Nies .. in terms of congruences and effective conjunctions of Pi01-sentences. http://www.math.wisc.edu/~lempp/papers/list.html

Mathematical Preprints by Steffen Lempp (The preprints are listed by research area, within research area in alphabetical order of coauthor(s).) Research Areas Classical Computability Theory Computably enumerable degrees Lattice embeddings into the c. e. degrees Decidability of fragments of theories of the c. e. degrees ... Lecture Notes and Ph. D. Thesis Classical Computability Theory Computably enumerable degrees Lattice embeddings into the c. e. degrees Lattice embeddings into the r. e. degrees preserving and 1 , with Klaus Ambos-Spies and Manuel Lerman (published in Journal of the London Mathematical Society, 1994, ps download of paper Abstract: We show that a finite distributive lattice can be embedded into the r. e. degrees preserving least and greatest element iff the lattice contains a join-irreducible noncappable element. Lattice embeddings into the r. e. degrees preserving 1 , with Klaus Ambos-Spies and Manuel Lerman (published in "Logic and Philosophy of Science: Papers from the 9th International Congress of Logic, Methodology, and Philosophy of Science", 1994, ps download of paper , jpg download of Diagram 1 in preparation) Abstract: We show that the two nondistributive five-element lattices, M

25. North Texas Logic Conference Logic, 1997 proved the Undecidability of the firstorder theory of the enumeration degrees of the 02-sets. A closer analysis of their proof shows that http://www.math.unt.edu/logic/ntlc/ntlc.html

North Texas Logic Conference October 8 th th UNT Logic Schedule Abstracts Future Directions ... Transportation Schedule All talks will be held in GAB 105. The official program can be found here Friday, October 8 Saturday, October 9 Sunday, October 10 Morning Session: Morning Session: Morning Session: Andreas Blass Julia Knight Steffen Lempp Ilijas Farah ... Benedikt Loewe Break For Lunch Break For Lunch Break For Lunch Afternoon Session: Afternoon Session: Afternoon Session: Dan Mauldin Reed Solomon Millican Lecture Ted Slaman Denis Hirschfeldt Peter Cholak Peter Komjath ... Future Directions Contributed Talks Thomas Kent Alexander Raichev Bart Kastermans Ross Bryant ... Charles Boykin Dinner Trail Dust Abstracts Becker Title: Cocycles Abstract: This talk is a contribution to the descriptive set theory of Polish group actions. Like much of the recent research in this field, it is concerned with a known theorem about locally compact groups and with the question of whether or to what extent the result generalizes to arbitrary Polish groups. The theorem in question is Mackey's Cocycle Theorem: Every almost cocycle is equivalent to a strict cocycle. This question is relevant to the foundations of quantum mechanics. Blass Title: Abstract State Machines and Choiceless Polynomial Time Abstract: Choiceless polynomial time is a complexity class of decision problems whose instances are finite structures. The polynomial-time computations here are not permitted to use an ordering of the input structure (or, what amounts to the same thing, arbitrary choices), but parallelism and rich data structures are allowed. The underlying computational framework is given by Gurevich's abstract state machines, to which I'll provide a brief introduction. Then I'll discuss what can (and what cannot) be computed in choiceless polynomial time, particularly when it is augmented by an oracle for cardinality. My work in this area is joint with Yuri Gurevich and Saharon Shelah.

26. Studia Informatica AbstractThe degree of Undecidability of nonmonotonic logic is investigated. arithmetical but not recursively enumerable sets of sentences definable by http://www.studiainformatica.ii.ap.siedlce.pl/volume.php?id=7

27. Olivier Finkel The stretching theorem for local sentences expresses a remarkable reflection . Undecidability of Topological and Arithmetical Properties of Infinitary http://www.logique.jussieu.fr/www.finkel

Olivier Finkel Équipe Modèles de Calcul et Complexité Laboratoire de l'Informatique du Parallélisme et Institut des Systèmes Complexes CNRS et ENS LYON 46 Allée d'Italie 69364 Lyon Cedex 07 FRANCE E-Mail: Olivier.Finkel_at_ens-lyon.fr Thèmes de Recherche Théorie des Modèles des Formules Locales Complexité Descriptive Théorie des Modèles Finis Omega Langages Rationnels, Algébriques, Localement Finis Relations Rationnelles Infinitaires Propriétés Topologiques des Omega Langages Machines Finies Stratégies Gagnantes dans les Jeux Infinis Automates et Langages Temporisés Automates Cellulaires Research Areas Model Theory of Local Sentences Descriptive Complexity Finite Model Theory Regular, Context Free, and Locally Finite Omega Languages Infinitary Rational Relations Topological Properties of Omega Languages Finite Machines Winning Strategies in Infinite Games Timed Automata and Timed Languages Cellular Automata Publications Journal papers Conference papers Thesis Habilitation ... Some talks Journal papers Langages de Büchi et Omega Langages Locaux Comptes Rendus de l' Académie des Sciences , t. 309, Série I, p. 991-995, 1989.

28. Boolos Bibliography (with Hilary Putnam) degrees of unsolvability of constructible sets of Extremely undecidable sentences. Journal of Symbolic Logic 47 (1982) 191196. http://web.mit.edu/philos/www/facultybibs/boolos_bib.html

George Boolos: List of Publications 1. (with Hilary Putnam) "Degrees of unsolvability of constructible sets of integers." Journal of Symbolic Logic 2. "Effectiveness and natural languages." In S. Hook, ed., Language and Philosophy . New York University Press, 1969. 3. "On the semantics of the constructible levels." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 4. "A proof of the Löwenheim-Skolem theorem." Notre Dame Journal of Formal Logic 5. "The iterative conception of set." Journal of Philosophy 68 (1971) 215-231. Reprinted in Logic, Logic, and Logic and in Benacerraf, P. and Putnam, H., eds. Philosophy of Mathematics: Selected Readings , second ed. Cambridge: Cambridge University Press, 1984, pp. 486-502. 6. "A note on Beth's theorem." Bulletin de l'Academie Polonaise des Sciences 7. "Arithmetical functions and minimization." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 8. "Reply to Charles Parsons' 'Sets and classes' (1974)" First published in Logic, Logic, and Logic

29. Sentence Modeling And Parsing Parsing is the process of discovering analyses of sentences, that is, consistent sets of relationships between constituents that are judged to hold in a http://cslu.cse.ogi.edu/HLTsurvey/ch3node8.html

Next: 3.7 Robust Parsing Up: 3 Language Analysis and Previous: 3.5 Semantics 3.6 Sentence Modeling and Parsing Fernando Pereira The complex hidden structure of natural-language sentences is manifested in two different ways: predictively , in that not every constituent (for example, word) is equally likely in every context, and evidentially , in that the information carried by a sentence depends on the relationships among the constituents of the sentence. Depending on the application, one or the other of those two facets may play a dominant role. For instance, in language modeling for large-vocabulary connected speech recognition , it is crucial to distinguish the relative likelihoods of possible continuations of a sentence prefix , since the acoustic component of the recognizer may be unable to distinguish reliably between those possibilities just from acoustic evidence . On the other hand, in applications such as machine translation or text summarization , relationships between sentence constituents, such as that a certain noun phrase is the direct object of a certain verb occurrence, are crucial evidence in determining the correct translation or summary. Parsing is the process of discovering analyses of sentences, that is, consistent sets of relationships between constituents that are judged to hold in a given sentence, and, concurrently, what the constituents are, since constituents are typically defined inductively in terms of the relationships that hold between their parts.

30. Computability Complexity Logic Book Reduction concepts and degrees of unsolvability. 114 Reduction concepts (theorem of Post), index sets (theorem of Rice and Shapiro, Sncomplete program http://www.di.unipi.it/~boerger/cclbookcontents.html

Studies in Logic and the Foundations of Mathematics, vol. 128, North-Holland, Amsterdam 1989, pp. XX+592. CONTENTS Graph of dependencies XIV Introduction XV Terminology and prerequisites XVIII Book One ELEMENTARY THEORY OF COMPUTATION 1 Chapter A. THE MATHEMATICAL CONCEPT OF ALGORITHM 2 PART I. CHURCH'S THESIS 2 1. Explication of Concepts. Transition systems, 2 Computation systems, Machines (Syntax and Semantics of Programs), Turing machines. structured (Turing- and register-machine) programs (TO, RO). 2. Equivalence theorem, 26 LOOP-Program Synthesis for primitive recursive functions. 3. Excursus into the semantics of programs. 34 Equivalence of operational and denotational semantics for RM-while programs, fixed-point meaning of programs, proof of the fixed-point theorem. 4*. Extended equivalence theorem. Simulation of 37 other explication concepts: modular machines, 2-register machines, Thue systems, Markov algorithms, ordered vector addition systems (Petri nets), Post calculi (canonical and regular), Wang's non-erasing half-tape machines, word register machines. 5. Church's Thesis 48

31. Annals Of Pure And Applied Logic Decidable and undecidable prime theories in infinitevalued logic On Sigma1 and Pi1 sentences and degrees of Interpretability. by Per Lindström v. http://wotan.liu.edu/docis/dbl/apuapl/index.html

The Digital Librarian's Digital Library search D O CIS  Do cuments in  C omputing and I nformation  S cience Home Journals and Conference Proceedings Annals of Pure and Applied Logic On gaps under GCH type assumptions by:  Moti Gitik v. 119 i. 1-3 p. 1 - 18 Thue trees by:  Jerzy Marcinkowski, Leszek Pacholski v. 119 i. 1-3 p. 19 - 59 Apartness spaces as a framework for constructive topology by:  Douglas S. Bridges, Luminita Dediu v. 119 i. 1-3 p. 61 - 83 Delta20 - categoricity in Boolean algebras and linear orderings by:  Charles F. D. McCoy v. 119 i. 1-3 p. 85 - 120

32. DBLP: André Nies 2 Klaus AmbosSpies, André Nies The Theory of the Polynomial Many-One degrees of Recursive sets is Undecidable. STACS 1992 209-218 http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/n/Nies:Andr=eacute=.ht

List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Pavel Semukhin : Finite Automata Presentable Abelian Groups. LFCS 2007 EE Bakhadyr Khoussainov Sasha Rubin ... Frank Stephan : Automatic Structures: Richness and Limitations CoRR abs/cs/0703064 EE Wolfgang Merkle Joseph S. Miller ... Frank Stephan : Kolmogorov-Loveland randomness and stochasticity. Ann. Pure Appl. Logic 138 EE Santiago Figueira Frank Stephan : Lowness Properties and Approximations of the Jump. Electr. Notes Theor. Comput. Sci. 143 EE Wolfgang Merkle Joseph S. Miller ... Frank Stephan : Kolmogorov-Loveland Randomness and Stochasticity. STACS 2005 EE Frank Stephan : Lowness for the Class of Schnorr Random Reals. SIAM J. Comput. 35 EE Bakhadyr Khoussainov Sasha Rubin ... Frank Stephan : Automatic Structures: Richness and Limitations. LICS 2004 EE Electr. Notes Theor. Comput. Sci. 84 EE ... Frank Stephan : Trivial Reals. Electr. Notes Theor. Comput. Sci. 66 EE Rodney G. Downey Denis R. Hirschfeldt ... Douglas A. Cenzer Classes. J. Symb. Log. 66 Rodney G. Downey J. Comput. Syst. Sci. 60 Andrea Sorbi : Structural Properties and Sigma Enumeration Degrees.

33. Publications - Timothy Hinrichs Logicians frequently use axiom schemata to encode (potentially infinite) sets of sentences with particular syntactic form. In this paper we examine a http://logic.stanford.edu/~thinrich/publications.htm

Refereed Proceedings Hinrichs, T. L., Genesereth, M. R. Extensional Reasoning CADE Workshop on Empirically Successful Automated Reasoning in Large Theories (ESARLT) July 2007 Relational databases are one of the most industrially successful applications of logic in computer science, built for handling massive amounts of data. The power of the paradigm is clear both because of its widespread adoption and theoretical analysis. Today, automated theorem provers are not able to take advantage of database query engines and therefore do not routinely leverage that source of power. Extensional Reasoning is an approach to automated theorem proving where the machine automatically translates a logical entailment query into a database, a set of view definitions, and a database query such that the entailment query can be answered by answering the database query. This paper discusses the framework for Extensional Reasoning, describes algorithms that enable a theorem prover to leverage the power of the database in the case of axiomatically complete theories, and discusses theory resolution for handling incomplete theories. Hinrichs, T. L., Genesereth, M. R.

34. Logic Colloquium 2003 Older results typically showed the two quantifier level decidable and the third undecidable. We examine the situation for the r.e. degrees, the degrees http://www.helsinki.fi/lc2003/titles.html

Main Awards Registration Accommodation ... ASL Speakers and Titles Tutorial speakers Michael Benedikt Model Theory and Complexity Theory Bell Labs, Lisle, USA. E-mail: benedikt@research.bell-labs.com ABSTRACT: This tutorial concentrates on links between traditional (infinitary) model theory and complexity theory. We begin with an overview of the `classical' connection between complexity theory and finite model theory, giving quickly the basic results of descriptive complexity theory. /We then discuss several ways of generalizing this to take account a fixed infinite background structure. We will start by giving the basics of complexity theory parameterized by a model (algebraic complexity over an arbitrary structure). We then cover results characterizing first-order theories of models via the complexity of query problems (embedded finite model theory). Finally, time permitting, we will look at abstractions of descriptive complexity theory to take into account a background structure. Stevo Todorcevic Set-Theoretic Methods in Ramsey Theory C.N.R.S. - UMR 7056, Paris, France.

35. Atlas: Victoria International Conference 2004 - Abstracts The set of Krandom strings has long been known to be undecidable. It is shown that the Turing degrees of Schnorr-random sets are those of Martin-Loef http://atlas-conferences.com/cgi-bin/abstract/select/camo-01?session=1

36. Abstracts Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all http://www.impan.gov.pl/~kz/Abstracts.html

8. Undecidability and concatenation pdf We consider the problem stated by Andrzej Grzegorczyk in ``Undecidability without arithmetization'' (Studia Logica 79(2005)) whether certain weak theory of concatenation is essentially undecidable. We give a positive answer for this problem. 7. The Intended Model of Arithmetic. An Argument from Tennenbaum's Theorem pdf We present an argument that allows to determine the intended model of arithmetic using some cognitive assumptions and the assumptions on the structure of natural numbers. Those assumptions are as follows: the psychological version of the Church thesis, computability of addition and multiplication and first order induction. We justify the thesis that the notion of natural number is determined by 6. Coprimality in finite models pdf We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard of addition and multiplication on indices of prime numbers. of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004

37. Lawrence S. Moss: Articles The Undecidability of Iterated Modal Relativization, with Joseph S. Miller Traditional syllogisms involve sentences of the following simple forms All X http://www.indiana.edu/~iulg/moss/aarticles.htm

Abstract Data Types Abstract State Machines Coalgebra Grammars ... Situation Theory Abstract Data Types Final Algebras, Cosemicomputable Algebras, and Degrees of Unsolvability , with Jose Meseguer and Joseph A. Goguen. Theoretical Computer Science 110, (1992), 267-302. Also appears in D.H. Pitt, et al (eds.), Conference on Category Theory and Computer Science, Springer LNCS 283, 1987, 158-181. The theme of this paper is the interaction between recursion-theoretic and algebraic properties of abstract data types. We show that any "algebra with semicomputable inequality which has a nonunit computable $V$-behaviour has a final algebra specification by a finite set of equations and possibly using additional function symbols. For any computable algebra there is a finite set of equations specifying it under both the initial and final algebra semantics. All recursively enumerable degrees of unsolvability arise both in final and initial algebras." (My quotes here are not from the paper, but instead from the summary on by H. Jürgensen on Math Reviews). Generalization of Final Algebra Semantics by Relativization , with Satish R. Thatte. In M. Main, et al (eds.)

38. AUTHOR INDEX Single matrices for the operations of both types contain two sets of designated values one of possible values (degrees of truth) for the premisses, http://www.filozof.uni.lodz.pl/bulletin/v331.html

BULLETIN OF THE SECTION OF LOGIC TABLE OF CONTENTS 1. George TOURLAKIS and Francisco KIBEDI, A Modal Extension of First Order Classical Logic, Part II [Abstract] [DVI] 2. Katsumi SASAKI and Shigeo OHAMA, A Sequent System of the Logic R for Rosser Sentences [Abstract] [DVI] 3. Alexej P. PYNKO, Sequential Calculi for Many-valued Logics with Equality Determinant [Abstract] [DVI] 4. F.A.DORIA and N.C.A.da COSTA, On Set Theory as a Foundation for Computer Science [Abstract] [DVI] 5. Szymon FRANKOWSKI, Formalization of a Plausible Inference [Abstract] [DVI] 6. Andrei KOUZNETSOV, Deduction Chains and DC-like Decision Procedure for Guarded Logic [Abstract] [DVI] ABSTRACTS 1. George TOURLAKIS and Francisco KIBEDI, A Modal Extension of First Order Classical Logic, Part II We define the semantics of the modal predicate logic introduced in Part I and prove its soundness and strong completeness with respect to appropriate structures. These semantical tools allow us to give a simple proof that the main conservation requirement articulated in Part I, Section 1, is met as it follows directly from Theorem 5.1 below. Section numbering is consecutive to that of Part I.

39. Let S Be The Set Of All Sets That Don't Contain Themselves. Does S Contain Itsel The comment by KK in this metafilter thread (the one this sentence is . For instance, the angles of a triangle in a flat plane always add to 180 degrees, http://www.metafilter.com/44614/Let-S-be-the-set-of-all-sets-that-dont-contain-t

skip to main content MetaFilter AskMeFi Projects ... New User Tags: self-reference self reference paradox var federated_media_section = ''; Advertise here: Contact FM Let S be the set of all sets that don't contain themselves. Does S contain itself? August 27, 2005 5:08 AM Subscribe This link, which you are no longer looking at, will take you to a pretty cool essay. posted by Citizen Premier (48 comments total) This is not the first comment of this very good post, which I enjoyed immensely. posted by iconomy at 5:52 AM on August 27 This is not the second comment where I say something totally inreverent and everybody ignores me. I think this post is qUite good too. (wasn't there a legendary thread in which we did this forever?) posted by wheelieman at 6:15 AM on August 27 I don't have a comment, I just wanted to say how much I enjoyed this link. posted by Jatayu das at 6:19 AM on August 27 By reading this comment, you are not reading Metafilter posted by Dukebloo at 6:25 AM on August 27 I'm not going to mention in what order, numerically-speaking, this fifth comment falls. I'm not going to comment at all, actually. Just wanted to press home the point, once again, that I really enjoyed the link. posted by iconomy at 6:40 AM on August 27 No commenting allowed in this thread.

40. All About Oscar The theory had the revolutionary aspect of treating infinite sets as Thus, the existence of undecidable sentences in each such theory points out an http://www.britannica.com/oscar/print?articleId=109532&fullArticle=true&tocId=24

41. M. E. Szabo: The Collected Works Of Gerhard Gentzen In this context he constructs an infinite set of sentences that has no . This refers to a small portion of Godel s 1931 paper on Undecidability. http://mathgate.info/cebrown/notes/szabo.php

The Omega Group TPS A higher-order theorem proving system This page was created and is maintained by Chad E Brown M. E. Szabo. The Collected Works of Gerhard Gentzen . North-Holland Publishing Company, 1969. Introduction Investigations into Logical Deduction (1934) Introduction: At age 22 in 1932, Gentzen submitted the paper #1: "On the Existence of Independent Axiom Systems for Infinite Sentence Systems." He introduces a system of the propositional calculus as a sequent calculus based on Hertz's work. He modifies Hertz's "syllogism" rule to be Gentzen's "cut" rule. In this context he constructs an infinite set of sentences that has no independent set of axioms. He also shows that all "linear" sentence systems do have an independent axiomatization. Tarski introduced the semantic notion of logical consequence in 1936. Gentzen had developed this idea (for propositional logic) in #1. Gentzen's natural deduction system in #3 [1935, see below] provides a formalization of the notion of consequence in the sense first used by Bolzano (which was introduced by Bolzano over a hundred years earlier and is analogous to Tarski's notion).

42. 2007-08 UCI Catalogue: Social Sciences Introduction to sentence logic, including truth tables and natural deduction; . 205C Undecidability and Incompleteness (4). Formal theory of effective http://www.editor.uci.edu/07-08/ss/ss.10.htm

DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE 721 Social Science Tower; (949) 824-1520 Jeffrey A. Barrett, Department Chair Graduate Program Courses The Department of Logic and Philosophy of Science (LPS) brings together faculty and students interested in a wide range of topics loosely grouped in the following areas: general philosophy of science; philosophy of the particular sciences; logic, foundations and philosophy of mathematics; and philosophy of mathematics in application. LPS enjoys strong cooperative relations with UCI's Department of Philosophy; in particular, the two units jointly administer a single graduate program which offers the Ph.D. in Philosophy. LPS also has strong interconnections with several science departments, including Mathematics and Physics, as well as the School of Biological Sciences, the Donald Bren School of Information and Computer Sciences, the Departments of Cognitive Sciences and Economics, and the graduate concentration in Mathematical Behavioral Sciences. Graduate Program Faculty Aldo Antonelli: Logic, philosophy of mathematics, history of analytic philosophy

43. Peter Suber, "Non-Standard Logics" Would it be interesting to make these sets undecidable? Logics that deal with the truth of conditional sentences, particularly in the subjunctive mood. http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm

A Bibliography of Non-Standard Logics Peter Suber Philosophy Department Earlham College Categorical logic ... Non-standard logics in general In the kinds of non-standard logics included, this bibliography aims for completeness, although it has not yet succeeded. In the coverage of any given non-standard logic, it does not at all aim for completeness. Instead it aims to include works suitable as introductions for those who are already familiar with standard first-order logic. Looking at these non-standard logics gives us an indirect, but usefully clear and comprehensive idea of the usually hazy notion of "standardness". In standard first-order logics: Wffs are finite in length (although there may be infinitely many of them). Rules of inference take only finitely many premises. There are only two truth-values, "truth" and "falsehood". Truth-values of given proposition symbols do not change within a given interpretation, only between or across interpretations. All propositional operators and connectives are truth-functional. "p ~p" is provable even if we do not have p or ~p separately; that is, the principle of excluded middle holds.

44. Godel's Theorem@Everything2.com It proved difficult to construct a theory of sets which outruled such objects . To prove that an undecidable sentence existed, Godel needed to find a http://everything2.com/index.pl?node_id=23136

45. EULER Record Details Of course $\cup$ is definable in ${\cal D}$, but many interesting degreetheoretic results are expressible as $\Sigma_2$-sentences in the language of ${\cal http://www.emis.de/projects/EULER/detail?ide=1993jocksigm2theuppe&matchno=11&mat

46. George Boolos - Wikipedia, The Free Encyclopedia 1982, Extremely undecidable sentences, Journal of Symbolic Logic 47 191196. 1987c (with Vann McGee), The degree of the set of sentences of http://en.wikipedia.org/wiki/George_Boolos

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; George Boolos From Wikipedia, the free encyclopedia Jump to: navigation search For the 19th-century British mathematical logician of a similar name, see George Boole George Boolos Born September 4 New York New York U.S. Died May 27 Cambridge Massachusetts U.S. George Stephen Boolos September 4 New York City May 27 ) was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology Contents Life Work See also Books ... edit Life Boolos graduated from Princeton University in 1961 with an A.B. in mathematics Oxford University awarded him the B.Phil in 1963. In 1966, he obtained the first Ph.D. in philosophy ever awarded by the Massachusetts Institute of Technology , under the direction of Hilary Putnam . After teaching three years at Columbia University , he returned to MIT in , where he spent the rest of his career until his death from cancer A charismatic speaker well-known for his clarity and wit, he once delivered a lecture (1994a) giving an account of G¶del's second incompleteness theorem , employing only words of one syllable. At the end of his viva

47. ICALP'07: Accepted Papers - Track B The Undecidability result holds also for the simulation of twolabel BPP processes. . bound on the length of the local sentence in terms of the original. http://icalp07.ii.uni.wroc.pl/acceptl-trackb.html

ICALP 2007 34th International Colloquium on Automata, Languages and Programming Colocated with LICS 2007, LC 2007, and PPDP 2007 Overview Call for Papers Program Committee ... Submissions (closed) Accepted papers short list, alphabetic list with abstracts Online proceedings (NEW!) ... Other events in July in Wrocà ‚aw List of accepted papers (In order of appearance) Invited Lectures Track A: Algorithms, Automata, Complexity and Games Track B: Logic, Semantics and Theory of Programming Track C: Security and Foundations of Cryptography Track B: Logic, Semantics and Theory of Programming Modular Algorithms for Heterogeneous Modal Logics Lutz Schr¶der and Dirk Pattinson State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and an algorithmic description to a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided that this is the case for the components. By instantiating the general framework to concrete cases, we obtain PSPACE decision procedures for a wide variety of structurally different logics, describing e.g. Segala systems and games with uncertain information.

48. FOM: Midwest Model Theory Meeting Another way to look at this is to look at the Pi0-1 sentence. There is an old theorem of mine about Undecidability in dynamics of semilinear maps that http://cs.nyu.edu/pipermail/fom/1999-November/003475.html

FOM: Midwest Model Theory Meeting Harvey Friedman friedman at math.ohio-state.edu Mon Nov 8 09:14:45 EST 1999 Previous message: FOM: Formal Z and R/lengths of proofs Next message: FOM: Re: Midwest Model Theory Meeting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: Formal Z and R/lengths of proofs Next message: FOM: Re: Midwest Model Theory Meeting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

49. Abstracts For Publications Of Prof. J. Maurice Rojas Computational Arithmetic Geometry I sentences Nearly in the Polynomial We consider the averagecase complexity of some otherwise undecidable or open http://www.math.tamu.edu/~rojas/abstracts.html

Abstracts for Maurice 's Mathematical Papers (You can click HERE to see a list with downloadable files and further bibliographic information, but without abstracts.) New Complexity Bounds for Certain Real Fewnomial Zero Sets, (by Joel Gomez, Andrew Niles, and J. Maurice Rojas) Extremal Real Algebraic Geometry and A-Discriminants (by Alicia Dickenstein, J. Maurice Rojas, Korben Rusek, and Justin Shih) From Quantum to Algebraic Complexity via Sparse Polynomials (by Sean Hallgren, Bjorn Poonen, and J. Maurice Rojas) A deep problem which remains open is the relation between the complexity classes NP and BQP. Toward understanding this question, we present a natural computational problem that (as an underlying parameter is varied) interpolates between these two famous complexity classes. More precisely, let UNIFEAS_p denote the problem of deciding whether a univariate polynomial f, with integer coefficients, has a p-adic rational root. Also let UNIFEAS_p(m) denote the analogous problem, restricted to sparse polynomials with m or fewer monomial terms. We show that (a) UNIFEAS_p(2) in BQP, (b) UNIFEAS_p in BQP implies that NP is in BQP. Curiously, the natural analogue of UNIFEAS_p over the real numbers is not even known to be NP-complete. Recent results on Carmichael numbers turn out to be useful in our proofs. A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes (by J. Maurice Rojas)

50. Information Typically, one points to the sentence This statement is unprovable as an leads to a logical contradiction (a formally undecidable proposition?). http://serendip.brynmawr.edu/local/scisoc/information/1july04.html

Information?: An Inquiry Tuesdays, 9:30-11 am Science Building, Room 227 Schedule On-line Forum Evolving Resource List For further information contact Paul Grobstein. Discussion Notes 1 July 2004 Participants: Al Albano (Physics), Doug Blank (Computer Science), Peter Brodfuehrer (Biology), Anne Dalke (English, Feminist and Gender Studies), Wil Franklin (Biology), Paul Grobstein (Biology), David Harrison (Linguistics, Swarthmore), Mark Kuperberg (Economics, Swarthmore), Jim Marshall (Computer Science, Pomona/Bryn Mawr), Liz McCormack (Physics), Lisa Meeden (Computer Science, Swarthmore), Eric Raimy (Linguistics, Swarthmore/Trico), Ed Segall (Edge Technical Associates), Jan Trembly (Alumnae Bulletin), George Weaver (Logic/Philosophy) Summary by Paul Grobstein presentation notes available Intending to lay a foundation for discussing Chaitin's work on randomness and algorithmic information theory, Jim laid out a sufficiently rich array of material on the history of logic and its connections to computer science (see first five sections of Jim's notes ) to fully occupy the group for this week. The conversation will continue on to Chaitin's work next week.