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1. Completeness And Categoricity: Frege, Godel And Model Theory - History And Philo Frege s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such http://www.informaworld.com/smpp/621611201-69746491/content~content=a776180580~d

Skip over navigation HOME ABOUT US CONTACT US ... LIBRARIANS Search in entire site Publication Names ISSN/ISBNs Subject Names Author Names Title/Kwds/Abstract or Explore informaworld Journals eBooks Reference Works Allied Health Anthropology Area Studies Arts Behavioral Sciences Bioscience Built Environment Chemistry Communication Studies Computer Science Cultural Studies Dentistry Development Studies Earth Sciences Education Arena Ergonomics Food Science Geography History Law Literature, Language and Linguistics Medicine Pharmaceutical Science Philosophy Physics Religion Social Work Toxicology Urban Studies Browse Publications A-Z Browse ... Got a Voucher? Username: Password: athens sso forgotten password? hide Session timed out - new session started. You may need to sign in again. [ hide message informaworld HOME SEARCH BROWSE Issues List ... Related articles first prev toc next last Download Citation Recommend Mark Alert Link Print hide Please choose the type of alert you would like: Citation Alert New citations of this Article will trigger an alert New Issue Alert New issues of History and Philosophy of Logic will trigger an alert iFirst Alert New iFirst articles in History and Philosophy of Logic will trigger an alert Note: To be alerted to new content in all related publications, please click on one of the subject areas below and select

2. 03Cxx 03C35 Categoricity and completeness of theories; 03C40 Interpolation, preservation, 03C62 Models of arithmetic and set theory See also 03Hxx http://www.ams.org/msc/03Cxx.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 Model theory 03C05 Equational classes, universal algebra [See also 03C07 Basic properties of first-order languages and structures 03C10 Quantifier elimination, model completeness and related topics 03C13 Finite structures [See also 03C15 Denumerable structures 03C20 Ultraproducts and related constructions 03C25 Model-theoretic forcing 03C30 Other model constructions 03C35 Categoricity and completeness of theories 03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 03C55 Set-theoretic model theory 03C57 Effective and recursion-theoretic model theory [See also 03C60 Model-theoretic algebra [See also 03C62 Models of arithmetic and set theory [See also 03C64 Model theory of ordered structures; o-minimality 03C65 Models of other mathematical theories 03C68 Other classical first-order model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators [See also 03C85 Second- and higher-order model theory 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

3. 03Cxx 03C35, Categoricity and completeness of theories. 03C40, Interpolation, preservation, definability. 03C45, Classification theory, stability and related http://www.impan.gov.pl/MSC2000/03Cxx.html

Model theory Equational classes, universal algebra [See also Basic properties of first-order languages and structures Quantifier elimination, model completeness and related topics Finite structures [See also Denumerable structures Ultraproducts and related constructions Model-theoretic forcing Other model constructions Categoricity and completeness of theories Interpolation, preservation, definability Classification theory, stability and related concepts Models with special properties (saturated, rigid, etc.) Properties of classes of models Set-theoretic model theory Effective and recursion-theoretic model theory [See also Model-theoretic algebra [See also Models of arithmetic and set theory [See also Model theory of ordered structures; o-minimality Models of other mathematical theories Other classical first-order model theory Logic on admissible sets Other infinitary logic Logic with extra quantifiers and operators [See also Second- and higher-order model theory Nonclassical models (Boolean-valued, sheaf, etc.) Abstract model theory Applications of model theory [See also None of the above, but in this section

4. HeiDOK 03C35 Categoricity and completeness of theories ( 0 Dok. ) 03C40 Interpolation, preservation, definability ( 0 Dok. ) 03C45 Classification theory http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03C&anzahl

5. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection theories Categoricity and completeness of 03C35 theories categories and 18Cxx theories classical field 70Sxx theories existence 49Jxx http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_58.htm

textbooks, tutorial papers, etc.) # instructional exposition ( textbooks, tutorial papers, etc.) # instructional exposition ( textbooks, tutorial papers, etc.) # instructional exposition ( textbooks. textbook use in the classroom # analysis of textbooks, development and evaluation of texture th and 16th centuries, renaissance # 15 th centuries, renaissance # 15th and 16 th century # 17 th century # 18 th century # 19 th century # 20 th problem and ramifications) # theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16 theorem # Hilbertian fields; Hilbert's irreducibility theorem proving (deduction, resolution, etc.) theorem, asphericity # Dehn's lemma, sphere theorem, loop theorem, loop theorem, asphericity # Dehn's lemma, sphere theorem. polynomials. finite sums) # elementary algebra (variables, manipulation of expressions. binomial theorems # $L^p$-limit theorems # abstract inverse mapping and implicit function theorems # algebraic dependence theorems # analytic algebras and generalizations, preparation

6. John Corcoran Homepage Future Research on Ancient theories of Communication and Reasoning, ibid. . A note on Categoricity and completeness, History and Philosophy of Logic 2 http://www.acsu.buffalo.edu/~corcoran/pubs.htm

Welcome to the homepage of John Corcoran Contact Information Curriculum Vitae Courses Contact me ... via email Complete List of Publications: (Last updated October 2004) I. Articles II. Abstracts III. Books (editor) IV. Miscellaneous ... Printable list of publications (PDF), or see Taylor and Francis Online Journals (sign-in required). PDF requires free Acrobat Reader software. I. Articles: MR indicates review in Mathematical Reviews available at MathSciNet (login required) J indicates available at JSTOR (with online link, login required). G indicates available at Google by entering John Corcoran plus the complete title (with online link). J Three Logical Theories, Philosophy of Science Logical Consequence in Modal Logic: Natural Deduction in S5 (co-author G. Weaver), Notre Dame Journal of Formal Logic Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and the Stratification of Language

7. List KWIC DDC And MSC Lexical Connection Categoricity and completeness of theories 03C35 categories Abelian 18Exx categories accessible and locally presentable 18C35 http://www.mi.imati.cnr.it/~alberto/dml_11_05.htm

Boolean functions Boolean programming Boolean rings) # Boolean algebras ( Boolean rings, measure algebras # measures on Boolean-valued models # other aspects of forcing and Boolean-valued, sheaf, etc.) # nonclassical models ( bootstrap, jackknife and other resampling methods bordism and cobordism theories, formal group laws Borel, analytic, projective, etc. sets) # descriptive set theory (topological aspects of bornologies and related structures; Mackey convergence, etc. botanic sciences boundaries # dynamics of phase boundaries # geometric and analytic invariants on weakly pseudoconvex boundaries of domains # CR$ manifolds as boundary # method of contraction of the boundary behavior boundary behavior (theorems of Fatou type, etc.) boundary behavior of holomorphic functions boundary behavior of holomorphic functions # global boundary behavior of power series, over-convergence boundary data, parameters # dependence of solutions of PDE on initial and boundary element methods boundary element methods boundary element methods boundary element methods boundary element methods boundary layers # turbulent boundary problems for PDE # free boundary regularity of mappings boundary theory boundary theory # ideal boundary theory # Martin boundary uniqueness of mappings boundary value and inverse problems boundary value and inverse problems boundary value problems boundary value problems boundary value problems boundary value problems boundary value problems # linear boundary value problems # multipoint

8. Sachgebiete Der AMS-Klassifikation: 00-09 deductive systems 03B25 Decidability of theories and sets of sentences, 03C35 Categoricity and completeness of theories 03C40 Interpolation, 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

9. Department Of Mathematics, University Of Illinois At Urbana-Champaign Systems of formal proofs and the completeness theorem. Basic elements of model theory (completeness of theories, Categoricity, quantifier elimination) and http://www.math.uiuc.edu/ResearchAreas/logic/exams.html

Logic: Exams Logic Comprehensive Exam Logic Preliminary Exam Thesis and Final Examination Logic Comprehensive Exam Before you decide to take the comprehensive exam in Mathematical Logic check out the overall structure of the comprehensive exam system. Syllabus The Comprehensive Exam in Mathematical Logic may contain problems in the following topics: Syntax and semantics of propositional logic and first order logic. Compactness theorem. Systems of formal proofs and the completeness theorem. Basic elements of model theory (completeness of theories, categoricity, quantifier elimination) and examples such as dense linear orderings, vector spaces, algebraically closed fields, and simple fragments of arithmetic. Incompleteness theorem and related topics, including: basic properties of computable functions, relations and functions representable in a theory, undecidability of various systems of arithmetic, undecidability of pure first order logic, and decidability of certain other theories. S uggestions from a student who passed Make sure you know the topics above.

10. The Development Of Mathematical Logic From Russell To Tarski: 1900-1935 | Richar 1.2 Peano s school on the logical structure of theories, 4. 1.3 Hilbert on axiomatization, 8. 1.4 completeness and Categoricity in the work of Veblen and http://www.ucalgary.ca/~rzach/papers/history.html

@import "/rzach/misc/drupal.css"; @import "http://www.ucalgary.ca/templates2/styles/uofc-level-c.css"; @import "/rzach/files/rzach/custom_colors/uofc_c_v7.css"; Skip to Headline Skip to Navigation Skip to Content Skip to Sidebar UofC Navigation Prospective Students Current Students Alumni Community Search UofC: IT MY U OF C Contacts Richard Zach Site Navigation Primary links Home Research Teaching CV ... LogBlog Research and Publications History of Logic Kurt G¶del and computability theory Hilbert's "Verungl¼ckter Beweis," the first epsilon theorem, and consistency proofs The Development of Mathematical Logic from Russell to Tarski: 1900-1935 ... Other Logic Search Navigation search The Development of Mathematical Logic from Russell to Tarski: 1900-1935 Source Leila Haaparanta, ed., The History of Modern Logic . New York and Oxford: Oxford University Press, to appear. 178 pp. (with Paolo Mancosu and Calixto Badesa) Abstract The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, L¶wenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth.

11. Springer Online Reference Works Based on predicate calculus various logicomathematical theories have been and questions of Categoricity and completeness of classes of models. http://eom.springer.de/m/m062660.htm

Encyclopaedia of Mathematics M Article referred from Article refers to Mathematical logic, symbolic logic The branch of mathematics concerned with the study of mathematical proofs and questions in the foundation of mathematics. Historical sketch. The idea of constructing a universal language for the whole of mathematics, and of the formalization of proofs on the basis of such a language, was suggested in the 17th century by G. Leibniz . But not until the middle of the 19th century did there appear the first scientific work on the algebraization of Aristotelean logic ( G. Boole , A. de Morgan ). After G. Frege ) and C. Peirce ) put the logic of predicates, variables and quantifiers into the language of algebra, it became possible to apply this language to questions in the foundations of mathematics. On the other hand, the creation of non-Euclidean geometry in the 19th century K. Weierstrass R. Dedekind and G. Cantor , and G. Peano ). In this connection, Peano created a more suitable symbolic representation for the language of logic. Afterwards, this language was perfected in the joint work of B. Russell

12. UC Berkeley - Department Of Philosophy “From the DeductiveNomological Model to Unification theories of Explanation” Mexico City, “On completeness and Categoricity of Deductive Systems” http://philosophy.berkeley.edu/people/page/7

Paolo Mancosu Talks Invited talks since 2004 1/17/2004, Feferman Symposium, Stanford University, “Tarski on models and logical consequence”, 1/30/2004, Mathematics in the Humanities Series, Stanford University, “The varieties of mathematical explanation”, 3/5/2004, Workshop on Methodology of Pure and Applied Mathematics, Laguna Beach, “Visualization in Logic and Mathematics”. 4/23/ 2004, Logic Colloquium, UCLA, Los Angeles, “Tarski on models and logical consequence”, 5/21/2004, Congr¨s d’histoire des sciences et des techniques, Poitiers, “Tendences actuelles en histoire et philosophie des math©matiques aux USA”. 5/27/2004, College de France, Paris, “Logic, mathematics and the finiteness of the world: the discussion between Tarski and Carnap in 1941”. 6/16/2004, Maison Suger, Paris, Colloque “Fondements et justification des pratiques en math©matiques, “The varieties of mathematical explanation” 8/27/2004, University of Uppsala, Sweden, International Workshop “Logicism, Intuitionism, Formalism: What has become of them?”, “Predicativity: Problems and Prospects,” 9/2/2004, Mathematics Department, Uppsala University, “Tarski on models and logical consequence”

13. Faculty Of Science -Department Of MACS-Course Synopses FirstOrder axiomatics theories. Consistency and satisfiability of Sets formula. Consistency, completeness and Categoricity of First-Order theories. http://www.nul.ls/faculties/science/macs_gsynopses.htm

V isitors Contacts Sitemap Feedback ... Students Affairs Department of MACS - Graduate Course Synopses PM 561 - Abstract Algebra: ( 6 c.h) 1. Ordered sets: Example from mathematics, computer science and social science. Diagrams, Maps between ordered sets. The Duality principle. Maximal and minimal elements; top and bottom. Building new ordered sets. 2. Lattices and complete lattices: Lattices as ordered sets. Complete lattices chain condition and completeness. Completions (Dedekind-MacNeille completion). 3. CPOS. Algebraic lattices and domains: Directed joins and algebraic closure operators. CPOS (complete partial ordered sets) Finiteness, algebraic lattices and domains. Information systems. 4. Ideals and filters: Ideals and filters. Prime ideals, maximal ideal and ultrafilters. The existence of prime ideals, maximal ideals and ultrafilters. 5. Representation theory: Representation by lattices of sets. The prime ideal space (Stone’s representation theorem for Boolean algebra). Priestley’s representation theorem for distributive lattice.

14. PlanetMath: Vaught's Test Keywords, model theory, logic AMS MSC, 03C35 (Mathematical logic and foundations Model theory Categoricity and completeness of theories) http://planetmath.org/encyclopedia/VaughtsTest.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Vaught's test (Theorem) Let be a first order language , and let be a set of -sentences with no finite models which is -categorical for some . Then is complete "Vaught's test" is owned by Evandar view preamble View style: HTML with images page images TeX source See Also: -categorical Keywords: model theory, logic Attachments: proof of Vaught's test (Proof) by Evandar Log in to rate this entry. view current ratings Cross-references: finite first order language This is version 4 of Vaught's test , born on 2002-08-29, modified 2002-09-04. Object id is , canonical name is VaughtsTest Accessed 1660 times total. Classification: AMS MSC (Mathematical logic and foundations :: Model theory :: Categoricity and completeness of theories) Pending Errata and Addenda None.

15. STATE UNIVERSITY COLLEGE AT BUFFALO Isomorphism and Categoricity. c. Decidability. 6. theories with equality MAT 431 MATHEMATICAL LOGIC Validity, deducibility, and completeness in http://math.buffalostate.edu/~math/courses/undergraduate/mat 431.html

STATE UNIVERSITY COLLEGE AT BUFFALO Department of Mathematics Request for Course I. Number and title of course MAT 431 - Mathematical Logic II. Reasons for addition to the present curricula A. The course, an extension of MAT 270. will consist of topics in mathematical logic not covered in courses presently offered. B. The course should enable the student to better appreciate the axiomatic method in mathematics. C. The course provides a study of formal systems in contrast to informal systems which is the usual way topics in all other mathematics courses are presented. D. The course should help prepare the student for more formally structured graduate mathematics courses. E. While other courses may emphasize skills and knowledge in special areas of mathematics, this course allows the student to understand the abstract nature and structure of all of mathematics. III. Major objectives of the course A. To acquaint the student with a basic knowledge of mathematical logic. B. To help the student better understand the precise roles of set theory and quantification logic in mathematics in providing a uniform language and basis for all of mathematics. C.

16. General General Mathematics Mathematics For Nonmathematicians model completeness and related topics Finite structures See also 68Q15, constructions Categoricity and completeness of theories Interpolation, http://amf.openlib.org/2001/msc2000.xsd

17. UoY - CS - AIG completeness and Categoricity in RegionBased theories of Space This means that the entailments provable in the RCC theory are only those that hold in a http://www.cs.york.ac.uk/aig/seminars/96.php

AI Group: Seminars held in 2005 March 11th Formal reasoning in the Z notation using the CADiZ toolset Ian Toyn University of York Abstract The Z notation is used for formal specifications of systems. CADiZ is a set of tools for manipulating Z specifications. It extends an existing document preparation system (troff/latex/word) with a type-checker for the mathematical paragraphs of a specification and a browser based on a document previewing tool. Having established this effective browsing interface, some reasoning abilities have been added that are accessed through the same user interface. The result is a theorem prover whose user interface is superior, but whose reasoning abilities are as yet inferior, compared to most good theorem provers. This seminar will take the form of an on-line demonstration of CADiZ using a portable computer linked to a video projector. April 11th A Topological Transition Based Logic for the Qualitative Motion of Objec ts Andre Trudel Jodrey School of Computer Science, Acadia University, Nova Scotia, Canada Abstract We present a spatio-temporal ontology suitable for representing and reasoning about the qualitative motion of rigid bodies. This simple ontology provides a uniform treatment of motion in one, two, and three dimensional space. A succinct axiomatization is provided capturing the ontology. This first order logic is based on the transition of topological relations between objects.

18. Steve Awodey S. Awodey and H. Forssell, Theory and Applications of Categories 15(5), CT 2004, Categoricity and completeness 19th century axiomatics to 21st century http://www.andrew.cmu.edu/~awodey/

Steve Awodey Associate Professor Department of Philosophy Carnegie Mellon University Research Areas Category Theory Logic Philosophy of Mathematics History of Logic and Analytic Philosophy Research Connections: Algebraic Set Theory Logic of Types and Computation New book, now available! Category Theory , Oxford Logic Guides, Oxford University Press, 2006 Click here for more information. Selected Current Preprints An outline of algebraic set theory. S. Awodey, January 2006. Algebraic models of theories of sets and classes. S. Awodey, H. Forssell, M. Warren, June 2006. Relating topos theory and set theory via categories of classes. S. Awodey, C. Butz, A. Simpson, T. Streicher, June 2003. Sheaf toposes for realizability. S. Awodey and A. Bauer, (2002), forthcoming in: Archive for Mathemtical Logic Continuity and logical completeness [ps] [pdf]. S. Awodey, December 2000. Selected Publications Algebraic models of intuitionistic theories of sets and classes. S. Awodey and H. Forssell, Theory and Applications of Categories 15(5), CT 2004, pp. 147163 (2004).

19. JSTOR 2000-2001 Spring Meeting Of The Association For Symbolic Logic Speakers and topics in the Reverse Mathematics and Computability Theory . 2 S. AWODEY and E.H. RECK, completeness and Categoricity 19th century http://links.jstor.org/sici?sici=1079-8986(200109)7:3<413:2SMOTA>2.0.CO;2-W

20. Model Theory - Wikipedia, The Free Encyclopedia edit Elimination of quantifiers and model completeness . edit Categoricity. If T is a first order theory in the language L and is a cardinal, http://en.wikipedia.org/wiki/Model_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Model theory From Wikipedia, the free encyclopedia Jump to: navigation search This article discusses model theory as a mathematical discipline and not the term mathematical model which is used informally in other parts of mathematics and science. In mathematics model theory is the study of (classes of) mathematical structures such as groups fields graphs or even models of set theory using tools from mathematical logic . Model theory has close ties to algebra and universal algebra This article focuses on finitary first order model theory of infinite structures. The model theoretic study of finite structures (for which see finite model theory ) diverges significantly from the study of infinite structures both in terms of the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages. Contents The role of model theory The areas of model theory Universal algebra Finite model theory ... Axiomatizability, elimination of quantifiers, and model-completeness

21. Equivalence Of Strong Completeness And Categoricity - Sci.logic | Google Groups ~F so T adjoin F is an inconsistent theory. Now, strong completeness implies Categoricity Again, if F is a theorem then you re done. http://groups.google.bs/group/sci.logic/msg/8ebc7f1227d3dc1a

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Equivalence of Strong completeness and categoricity The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful William Boshuck View profile More options Jul 27 1992, 12:25 pm Newsgroups: sci.logic From: bosh @triples.math.mcgill.ca (William Boshuck) Date: Tue, 28 Jul 92 02:52:11 GMT Local: Mon, Jul 27 1992 10:52 pm Subject: Re: Equivalence of Strong completeness and categoricity Reply to author Forward Print View thread ... Find messages by this author @cenatls.cena.dgac.fr (Jean-Marc Alliot) writes: The proof which answers question 1) depends on something called the deduction theorem which, in turn gives an answer to the second question. The deduction theorem says that for a theory T and formulas F,G, that the following inferences (both top to bottom and bottom to top) are valid under consideration) In some treatments of logic, this is

22. FOM: The Blind Spot About Theory-completeness And Categoricity I have been researching the origins of logicians grasp of the concepts of theorycompleteness and Categoricity, and have uncovered what I regard as an http://cs.nyu.edu/pipermail/fom/1997-December/000548.html

FOM: the blind spot about theory-completeness and categoricity Neil Tennant neilt at hums62.cohums.ohio-state.edu Tue Dec 16 11:22:32 EST 1997 Previous message: FOM: Reply to Machover on Conclusiveness addendum Next message: FOM: the blind spot about theory-completeness and categoricity Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... tennant.9 at osu.edu ) I shall send you hard copy when the paper is ready. Those with whom I have already been corresponding and to whom a copy has been promised need not reply! The current, tentative title is 'Mathematics: Intuition and Structure'. As you will be able to tell from the above acknowledgements, I really do not think this paper would have come about without the stimulation and resources provided by fom. So season's greetings, tinged with gratitude, to Steve, for getting it all going! Previous message: FOM: Reply to Machover on Conclusiveness addendum Next message: FOM: the blind spot about theory-completeness and categoricity Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

23. Model Theory | Mathematical Institute - University Of Oxford The concepts of completeness and Categoricity will be studied and some more advanced technical notions, up to elements of modern stability theory, http://www.maths.ox.ac.uk/courses/mfocs/model-theory

@import "/modules/aggregator/aggregator.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/./sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/cck/content.css"; @import "/sites/all/modules/drutex/drutex.css"; @import "/sites/all/modules/event/event.css"; @import "/sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/date/date.css"; @import "/sites/all/modules/cck/fieldgroup.css"; @import "/sites/all/themes/maths/style.css"; Skip navigation Locator: Home » View Model Theory Main Home Prospective Students Current Students Teaching Staff ... About Us Departmental Members Login Username: Password: Model Theory HT View course material Number of lectures: 16 HT Lecturer(s): Boris Zilber Course Description Recommended Prerequisites This course presupposes basic knowledge of First Order Predicate Calculus up to and including the Soundness and Completeness Theorems. Also a familiarity with (at least the statement of) the Compactness Theorem would also be desirable. The course deepens student’s understanding of the notion of a mathematical structure and of the logical formalism that underlies every mathematical theory, taking B1 Logic as a starting point. Various examples emphasise the connection between logical notions and practical mathematics.

24. IngentaConnect Towards Completeness: Husserl On Theories Of Manifolds 18901901 Towards completeness Husserl on theories of manifolds 18901901 shows that Husserl meant by definiteness what is today called `Categoricity . http://www.ingentaconnect.com/content/klu/synt/2007/00000156/00000002/00000008

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Towards completeness: Husserl on theories of manifolds 1890-1901 Author: Hartimo, Mirja Source: Synthese , Volume 156, Number 2, May 2007 , pp. 281-310(30) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: Husserl's notion of definiteness, i.e., completeness is crucial to understanding Husserl's view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel's `principle of permanence'. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic Keywords: Early Husserl Definiteness Completeness Theories of manifolds Document Type:

25. Category Theory > Alphabetically Sorted, Complete Bibliography (Stanford Encyclo Awodey, S. Reck, E. R., 2002, completeness and Categoricity I. Baianu, I. C., 1987, Computer Models and Automata Theory in Biology and Medecine , http://plato.stanford.edu/entries/category-theory/bib.html

Cite this entry Search the SEP Advanced Search Tools ... Stanford University Supplement to Category Theory Alphabetically Sorted, Complete Bibliography Adamek, J. et al Abstract and Concrete Categories: The Joy of Cats , New York: Wiley. Adamek, J. et al ., 1994, Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press. Annals of Mathematics and Artificial Intelligence Journal of Symbolic Logic History and Philosophy of Logic History and Philosophy of Logic Awodey, S., 1996, "Structure in Mathematics and Logic: A Categorical Perspective", Philosophia Mathematica Awodey, S., 2004, "An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism", Philosophia Mathematica Awodey, S., 2006, Category Theory , Oxford: Clarendon Press. n -Categories and the Algebra of Opetopes", Advances in Mathematics Higher Category Theory , Contemporary Mathematics, Baez, J., 1997, "An Introduction to n -Categories", Category Theory and Computer Science , Lecture Notes in Computer Science, Baianu, I. C., 1987, "Computer Models and Automata Theory in Biology and Medecine", in Witten, Matthew, Eds.

26. Publications In Logic Fundamentals of Stability Theory, SpringerVerlag, 1988, XIII+ 447 pages. Categoricity and generalized model completeness, (withG. Ahlbrandt), Z. Math. http://www.math.uic.edu/~jbaldwin/pmodel.html

Publications in Logic John T. Baldwin On strongly minimal sets, (with A. H. Lachlan), J. SymbolicLogic 36 (1971), 79-96. Alpha T is finite for aleph-one categorical T, Trans.Amer. Math. Soc. 181 (1973), 37-51. Almost strongly minimal theories I, J. Symbolic Logic 37(1972), 481-493. Almost strongly minimal theories II, J. Symbolic Logic 37(1972), 657-660. The number of automorphisms of a model of an aleph-onecategorical theory, Fund. Math., (1) 83 (1973), 1-6. On universal Horn theories categorical in some infinitepower, (with A. H. Lachlan), Algebra Universalis (fasc. 1) 3 (1973),98-111. A sufficient condition for a variety to have the amalgamationproperty, Colloq. Math. (fasc. 2) XXVIII (1973), 81-83. A "natural" theory without a prime model, (with A. Blass,D.W. Kueker and A.M.W. Glass), Algebra Universalis (fasc. 2)3 (1973), 152-155. A topology for the space of countable models of a first ordertheory, (with J. M. Plotkin), Z. Math. Logik Grundlag.Math. 20 (1974) 173-178. Atomic compactness and aleph-one categorical Horntheories, Fund. Math. LXXXII (1975), 7-9. Conservative extensions and the two cardinal theoremfor stable theories, Fund. Math. LXXXVIII (1975), 7-9.

27. Historia Matematica Mailing List Archive: [HM] Categorical Systems concepts and methods in model theory, universal algebra and category theory that cover completeness for Categoricity appeared as a consequence of http://sunsite.utk.edu/math_archives/.http/hypermail/historia/oct99/0042.html

[HM] Categorical systems Carlos Cesar de Araujo carlos.cesar@taskmail.com.br 10 Oct 99 18:58:47 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Antreas P. Hatzipolakis: "Re: [HM] An Italian archive" Previous message: Antreas P. Hatzipolakis: "Re: [HM] Pick's Theorem" Next in thread: Luigi Borzacchini: "Re: [HM] Categorical systems" As Zach [1] recently pointed out (p.353), "The history of the concept(s) of completeness of an axiomatic system has yet to be written". Be that as it may, there is no doubt that one starting point here is Hilbert's "axiom of completeness". Note that "completeness" is first used by him to name just an axiom and not a PROPERTY OF an axiom system. "Completeness" in this latter sense (and in many forms) would be very much investigated by Hilbert himself and his collaborators in the 1920s. Zach [1] is right when he remarks (p.353) that "one of the roots of completeness as a property of axiom systems is the completeness axiom that Hilbert introduced in" [2].

28. UCR Faculty Directory: Individual Listing completeness and Categoricity, Part II 20th Century Metalogic to 21st The Development of Metamathematics and Proof Theory (with Jeremy Avigad), http://www.facultydirectory.ucr.edu/cgi-bin/pub/public_individual.pl?faculty=181

29. Completeness » SlideShare ANDREJKO completeness. Slide 10 COMPLETNESS Categoricity COMPLETE theories THEOREM Let be an L theory. Suppose for some L for all M, http://www.slideshare.net/andrejko/completeness/

Uploading Slideshare.net (beta) Home My Slidespace Upload Community ... Slidecasts Post: Download file close addthis_url = location.href; addthis_title = document.title; addthis_pub = 'slideshare'; All Comments Comments on Slide 1 Add a comment All comments Add a comment on Slide 1 If you have a SlideShare account, login to comment; else you can comment as a guest Embed Video? Just include the embed code in the comment! We support embeds from Youtube, Google Videos, BlipTV, Metacafe, DailyMotion, Viddler and several other approved sites only Are you human? (Sorry for asking) Enter the text in the image (Cannot see the image? Reload image Showing 1-50 of ( more Completeness From: andrejko , 4 months ago embed ( Stats Share this slideshow Tags No tags to display Groups Not added to any group Privacy Info New! This slideshow is Public Embed in your blog Embed ( wordpress.com Related Slideshows Decidability from: andrejko views Completeness from: andrejko views Compactness from: andrejko views ZF from: andrejko views Ordinal Cardinals from: andrejko views Basic S and L : The existence of an S-space under MA...

30. Course Number Generalized Functions, Theory of Distribution, Green Functions and Boundary Value . of Models Categoricity in Power, Element Types, Model completeness, http://math.korea.ac.kr/www_old/english version/curriculum/graduate_courses.html

Graduate Courses Course Number Title Course Description IA 501 Algebra I Group, Ring, Field, Vector Space, Structure of Ring, Abelian Group IA 502 Algebra II Real Number Field, Lebesque Measure, Lebesque Measurable Function, Lebesque Integration, Differentiation and Integration, Space of Measurable Functions IA 503 Topology I Topological Space, Identification Topology, Connectiveness, Separation, Metric Space IA 504 Geometry Curve, Surface, Shape Operator, Surface Geometry, Riemann Geometry IA 505 Probability I Relationship between Probability and Real Analysis, Law of Large Number, Conditional Expectation, Martingale, Ergodic Theory IA 506 Applied Mathematics I Generalized Functions, Theory of Distribution, Green Functions and Boundary Value Problems, Fourier Transformation IA 507 Complex Analysis Conformal Mapping, Application of conformal Mapping, Schwarz-Christoffel Transformation, Poisson Integration Formula, Analytic Continuation IA 601 Algebra II Noetherian Ring and Abelian Group, Primary Decomposition, Localization and Tensor Product, Local Ring, Completeness

31. Logic Seminars 1997-98 Effective completeness theorem; model completeness and decidability. September 4, 1997 Computable Categoricity and degree spectra. January 29, 1998 http://www.math.cornell.edu/~shore/sem978.html

Logic Seminars September 2, 1997 Suman Ganguli, Cornell University Effective completeness theorem; model completeness and decidability September 4, 1997 Reed Solomon, Cornell University Computable presentations of structures of low degree September 9, 1997 Robert Milnikel, Cornell University Omitting types and decidability September 11, 1997 Joe Miller, Cornell University Avoidable algebraic sets in Euclidean space September 16, 1997 Robert Milnikel, Cornell University Omitting types and decidability II September 18, 1997 Joe Miller, Cornell University Avoidable algebraic sets in Euclidean space II September 23, 1997 Robert Milnikel, Cornell University Omitting types and decidability September 25, 1997 Denis Hirschfeldt , Cornell University The Baldwin-Lachlan theorem September 30, 1997 Robert Milnikel , Cornell University Omitting types and decidability II October 5, 1997 Denis Hirschfeldt, Cornell University The Baldwin-Lachlan theorem II October 7, 1997 Richard Shore, Cornell University Decidable prime models October 16, 1997

32. Tree Structure Of LoLaLi Concept Hierarchy Updated On 2004624 219 completeness of theories . . . . 235 saturation . 218 Categoricity g . . . . 220 definability . . . . 226 interpolation . 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)