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 1. JSTOR Directions In Relevant Logic. The classical logic of relevant logicians. Pp. 8793. LARISA MAKSIMOVA. The nonexistence of finite characteristic matrices for Subsystems of Rt. Pp.http://links.jstor.org/sici?sici=0022-4812(199312)58:4<1466:DIRL>2.0.CO;2-4

 2. Encoding Two-valued Nonclassical Logics In Classical Logic 117 Renate A. Schmidt, EUnification for Subsystems of S4, Proceedings of the 9th International II, Extensions of classical logic, Synthese Library Vol.http://portal.acm.org/citation.cfm?id=778530

3. 03Bxx
03B05 classical propositional logic; 03B10 classical firstorder logic; 03B15 Higher-order logic and type theory; 03B20 Subsystems of classical logic
http://www.ams.org/msc/03Bxx.html

4. Connexive Logic (Stanford Encyclopedia Of Philosophy)
Systems of connexive logic are neither Subsystems nor extensions of classical logic. Connexive logics have a standard logical vocabulary and comprise
http://plato.stanford.edu/entries/logic-connexive/
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Connexive Logic
First published Fri Jan 6, 2006; substantive revision Tue Oct 10, 2006 A A A and A A but usually the underlying intuitions are expressed by requiring that certain schematic formulas are theorems: AT: ~(~ A ) and
A The first formula is often called Aristotle's Thesis And those who introduce the notion of connection say that a conditional is sound when the contradictory of its consequent is incompatible with its antecedent. (Sextus Empiricus, translated in Kneale and Kneale 1962, p. 129.) Boethius' Theses and which may be viewed (in addition with their converses) as capturing Chrysippus' idea: BT: ( A B B ) and
A B B Prior Analytics b 3, where it is explained that: [I]t is impossible that the same thing should be necessitated by the being and by the not-being of the same thing. I mean, for example, that it is impossible that B should necessarily be great since A is white and that B should necessarily be great since A is not white.

5. Brainstorms: Evolutionary Logic
Systems could become sparsely instantiated, leading to Subsystems that effectively In short, classical logic cannot deliver evolution because evolution
http://www.iscid.org/boards/ubb-get_topic-f-6-t-000171.html
 my profile search faq forum home ... Brainstorms Evolutionary Logic Author Topic: Evolutionary Logic William A. Dembski Member Member # 7 posted 27. September 2002 13:09 I recently posted a frivolous piece on "evolutionary logic" here Keying off this piece but taking evolutionary logic seriously, John Wilkins wrote the following serious response on talk.origins. (I would simply include the URL, but things are trickier with citing individual posts on newsgroups.) quote: This is something that I am actually interested in - evolutionary logic. It seems to me that it would have a number of nonstandard features: Instead of true or false, it would be a many valued logic and the value assigned would be "fitness". This could be a continuous or discrete scale. Fitness would not be a fully transitive property. Not only would it be contextual, but it would have something akin to a neo-Hebbian decay rate. It would be a logic that used Sorites predicates, AKA vague predicates. In a fully evolutionary system, the extension of a predicate would be specified by the external relations of the instances of the predicate with other instances in the system. Potential fitness would be defined in terms of these relations - fitness functions would not be absolute or fixed. Neither would fitness functions have a single value over time, and they may even be indiscernable (below the evaluative resolution of the system).

6. 03Bxx
03B05 classical propositional logic 03B10 classical firstorder logic 03B15 Higher-order logic and type theory 03B20 Subsystems of classical logic
http://www.emis.de/MSC2000/03Bxx.html
Version of December 15, 1998

7. 03Bxx
03B20, Subsystems of classical logic (including intuitionistic logic). 03B22, Abstract deductive systems. 03B25, Decidability of theories and sets of
http://www.impan.gov.pl/LIB/MSC/03Bxx.html

8. Mauro Ferrari
The circuit is described by formulas of classical logic and the delays of . we will give as examples some families of effective Subsystems of a wide
http://www.dicom.uninsubria.it/~ferram/publications/
Mauro Ferrari - Publications - By topic Indice
Intuitionistic and intermediate logics
M. Ferrari, C. Fiorentini, and G. Fiorino. On the complexity of the disjunction property in intuitionistic and modal logics. ACM, TOCL
Abstract
ACM Transactions on Computational Logic(TOCL)
M. Ferrari, C. Fiorentini, and G. Fiorino. A secondary semantics for second order intuitionistic propositional logic. Mathematical Logic Quarterly
Abstract
In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics.
M. Ferrari and C.Fiorentini. A proof-theoretical analysis of semiconstructive intermediate theories. Studia Logica
Abstract
In the 80's Pierangelo Miglioli, starting from motivations in the framework of Abstract Data Types and Program Synthesis, introduced semiconstructive theories, a family of ``large subsystems'' of classical theories that guarantee the computability of functions and predicates represented by suitable formulas. In general, the above computability results are guaranteed by algorithms based on a recursive enumeration of the theorems of the whole system. In this paper we present a family of semiconstructive systems, we call

9. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
logic) nonclassical logic (nonstandard 511.31 logic) Subsystems of classical logic (including intuitionistic 03B20 logic, Lambek calculus, BCK and BCI
http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_33.htm
 linear integral equations # systems of linear integral equations # systems of nonsingular linear integral equations # systems of singular linear logic and other substructural logics linear logic, Lambek calculus, BCK and BCI logics) # substructural logics (including relevance, entailment, linear mappings, matrices, determinants, theory of equation) # linear algebra. multilinear algebra. (vector spaces, linear models # generalized linear operators linear operators # equations and inequalities involving linear operators # equations with linear operators # general theory of linear operators # groups and semigroups of linear operators # special classes of linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) # functions whose values are linear operators as elements of algebraic systems # individual linear operators) # linear relations (multivalued linear operators, their generalizations and applications # groups and semigroups of linear operators, with operator unknowns # equations involving

 10. HeiDOK 03B15 Higherorder logic and type theory ( 0 Dok. ) 03B20 Subsystems of classical logic (including intuitionistic logic) ( 0 Dok.http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?anzahl=0&la=de&

11. 20th WCP: Sentential Falsehood Logic FL4
In other words, the laws of classical logic are valid for sentence ( S) , . Subsystems of FL4. LetÂs define three sublogics of FL4 that correspond to
http://www.bu.edu/wcp/Papers/Logi/LogiPavl.htm
 Logic and Philosophy of Logic Sentential Falsehood Logic FL4 Sergey Pavlov Institute of Philosophy RAS sergey.pavlov@usa.net ABSTRACT: In some philosophical conceptions, statements are valued as true, false, senseless (neither true nor false), or inconsistent. Falsehood logic FL4 makes it possible to operate correctly by such statements. Logic with falsehood operator FL4 is formulated. For FL4 metatheorems of consistency, deduction and completeness are fulfilled. Correlation between falsehood logic FL4 and four-valued Belnap’s logic and von Wright’s truth logic T"LM is considered. In FL4, the implication for Belnap’s logic is defined so that the truth-valued matrix of it is characterized for logic of tautological consequences E fde The construction of falsehood logic FL4 and its analysis answer the question about the use of truth and falsehood notions. In some philosophical conceptions statements are valued as true, false, senseless (neither true nor false), inconsistent. Falsehood logic FL4 makes it possible to operate correctly by such statements. The main principles of falsehood logic FL4 are as follows: 1. The notion of falsehood will be considered as applied only to sentences of the following form: "Sentence 'S' is false" (in symbols: '(

12. Fuzzy Logic
Fuzzy logic concept challenges the concept of classical logic. . household appliances, cameras, automobile Subsystems, and smart weapons. Fuzzy logic is
http://www.kurdishscientist.com/FuzzyLogic.htm
 Kurdish Scientist Searching for the Absolute Fact never ends Kurdish Scientist is sponsored by Support Committee for Higher Education in Iraqi Kurdistan, SCHEIK December 2007 OVER VIEW OF FUZZY LOGIC INTRODUCTION The concept of Fuzzy logic is not new. Fuzzy logic theory was introduced by Lofti A. Zadeh in the mid 1960s.Fuzzy logic is method used to solve the complex problems with maximum accuracy possible (examples digital camera stabilizer, Lift control systems etc). Fuzzy logic as opposed to binary (which has only two values) contains the values between and 1. Fuzzy logic can handle rough and inexact data (Clarify by Giving an Example). Classical (binary) logic uses the concept which is based on the logic that things can be expressed in binary terms 0s or 1s; in terms of Boolean algebra. Classical logic theory says that a thing belongs to only one set and can not be a member of another set, which means that a thing can have a value of either or 1 but canÂt be in between. When we say that fuzzy logic can handle inexact data, in this case this concept goes against the conventional (binary) logic theory. Fuzzy logic concept is based on more than two values which means that fuzzy logic can also handle data in between and 1. Fuzzy logic concept challenges the concept of classical logic. Unlike classical logic, Fuzzy logic allows partial membership in a set which means that an element can be a member of both sets.), values between and 1.

13. Phys. Rev. Lett. 82 (1999): Yuri F. Orlov - Origin Of Quantum Indeterminism...
Analysis of directly measurable Subsystems of quantum systems (i.e., prepared and arises in classical decisionmaking systems obeying classical logic.
 Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY Home Browse Search Members ... Help Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Phys. Rev. Lett. 82, 243 - 246 (1999) Previous article Next article Issue 2 View PDF (91 kB) or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Origin of Quantum Indeterminism and Irreversibility of Measurements Yuri F. Orlov Floyd R. Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853 Received 13 May 1998 Analysis of directly measurable subsystems of quantum systems (i.e., prepared and measured observable, parameters of symmetry transformations), based on the Einstein-Podolsky-Rosen definition of physical reality, shows that such subsystems cannot be deterministic. This effect is not specifically quantum: a physically different but mathematically similar situation arises in classical decision-making systems obeying classical logic. Direct consequences of this phenomenon are nonclassical behavior of probabilities and irreversibility of measurements (or decisions). URL: http://link.aps.org/abstract/PRL/v82/p243

14. Sachgebiete Der AMS-Klassifikation: 00-09
logic 03B05 classical propositional logic 03B10 classical firstorder logic 03B15 Higher-order logic and type-theory 03B20 Subsystems of classical logic
http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html
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

15. Reverse Mathematics - Wikipedia, The Free Encyclopedia
Reverse mathematics makes use of several Subsystems of second order arithmetic. because it is a theory in classical logic including the excluded middle.
http://en.wikipedia.org/wiki/Reverse_mathematics
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
Reverse mathematics
Jump to: navigation search Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as Ã¢ÂÂgoing backwards from the theorems to the axioms Ã¢ÂÂ rather than the usual direction (from the axioms to the theorems). This program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory . The goal of reverse mathematics, however, is to study ordinary theorems of mathematics rather than possible axioms for set theory. The program was founded by Harvey Friedman in his article "Some systems of second order arithmetic and their use" and abstracts "Systems of second order arithmetic with restricted induction" (I and II). The program was pursued by many researchers in mathematical logic. Stephen Simpson [1999] wrote the primary reference book on the subject.
edit General principles
The principle of reverse mathematics is the following: one starts with a framework language and a base theoryÃ¢ÂÂa core axiom systemÃ¢ÂÂthat is too weak to prove most of the theorems one might be interested in but still powerful enough to develop the definitions necessary to state the theorem. For example, in order to study the theorem Ã¢ÂÂEvery bounded sequence of

16. Publication Lists
Th. Coquand, Computational Content of classical logic, in A. Pitts and P. Dybjer . Applications of a representation theorem to Subsystems of arithmetics,
http://www.cs.chalmers.se/~makoto/sci9799body.html
Selected publications
• Th. Coquand, Computational Content of Classical Logic, in A. Pitts and P. Dybjer eds, Semantics and Logics of Computation , pp 33-78, Publications of the Newton Institute, 1997. [ compressed ps file
• B. NordstrÃ¶m, K. Petersson, and Jan M. Smith, Martin-LÃ¶f's Type Theory, to appear as a chapter in Handbook on Logic in Computer Science , Oxford University Press.
• Peter Dybjer, A general formulation of simultaneous inductive-recursive definitions in type theory, to appear in Journal of Symbolic Logic ps file
• Aarne Ranta, Type-Theoretical Grammer , ISBN 019853857X, Oxford University Press, 1994. [ OUP catalogue entry
• T. Tammet, Gandalf, Journal of Automated Reasoning , vol. 18, no. 2; pp 199-204, 1997. [ ps file In this section various kinds of publications resulting from the work of Programming Logic Group are presented. The following lists cover the period 1997-1999. They have been classified in Ph.D. and Licentiate theses (supervised by members of the group), monographs, refereed and nonrefereed papers. It is also worth remarking that our proof assistants ALF and Agda Alfa , avaiable via ftp, are now being used in several academic sites.
• 17. Kelly And Varela
Unlike classical logic, we do not lump together the contrasting and the nodes, Subsystems) which exhibit stability as a totality, and the parts are the
http://www.aippc.it/articles/aippc1.html
 CONSTRUCTS AND TRINITIES: KELLY AND VARELA ON COMPLEMENTARITY AND KNOWLEDGE (Centro di Psicologia e Psicoterapia Costruttivista, Roma, Italy) [Paper presented at the Seventh International Congress on Personal Construct Psychology , Memphis, TN, August 5th-9th, 1987] The paper is aimed at showing similarities and differences between the views of complementarity in relation to the creation and structure of cognitive systems held by George A. Kelly and Francisco J. Varela, both of them sharing a constructivist metatheory. Though operating in different times and in different fields (psychology and biology), their notions of construct and trinity, respectively, represent a similar departure from classical logic and dialectics, and lead to similar implications as to the problem of knowledge and the hierarchical structure of cognitive systems. Even if, because of their different views on the dependence/independence of reality from the observer's act of construing, Kelly's constructivism can be considered as trivial and Varela's constructivism as radical, the triviality of the former is questioned. Complementarity and the Problem of Knowledge Kelly's departure from classical logic: the construct Being a psychologist, Kelly paid primary attention to the individual rather than to the environment; and, being a revolutionary psychologist, he considered as the marks of individuality the personal ways of construing the world, rather than external stimuli, internal impulses, or personal biographies. In defining a construct as the only basis of any personal construction, Kelly (1955) departs from the notion of concept and from conventional logic by assuming that "the differences expressed by a construct are just as relevant as the likenesses. Unlike classical logic, we do not lump together the contrasting and the irrelevant. We consider the contrasting end of a construct to be both relevant and necessary [italics added] to the meaning of the construct." (p. 63).

18. LogBlog: October 2007 | Richard Zach | Philosophy | University Of Calgary
Classic logic papers, pt. 3 Normal derivability in classical logic some Subsystems of secondorder logic, slow-growing and fast-growing hierarchies
http://www.ucalgary.ca/~rzach/logblog/2007_10_01_archive.html
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19. IngentaConnect The Possibility Of Reconciling Quantum Mechanics With Classical P
as a collection of open classical Subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics.
http://www.ingentaconnect.com/content/klu/tamp/2006/00000149/00000003/00000151
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The possibility of reconciling quantum mechanics with classical probability theory
Author: Slavnov, D. Source: Theoretical and Mathematical Physics , Volume 149, Number 3, December 2006 , pp. 1690-1701(12) Publisher: Springer Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.

20. Variants Of Set Theory - MIMS
One possibility is to replace classical logic by intuitionistic logic. Various much weaker Subsystems seem to be more appropriate.
http://www.mims.manchester.ac.uk/research/logic/variants-set-theory.html
You are here: MIMS research mathematical logic MIMS RESEARCH IN LOGIC uncertain reasoning stuctures on categories of modules variants of classical set theory and applications logic seminars recent phd dissertations RELATED PAGES seminar series EPrints visitors SCHOOL OF MATHEMATICS ... postgraduate admissions
News
• MATHLOGAPS Marie Curie fellowships in Mathematical Logic
Research in Variants of Classical Set Theory and their Applications
Classical Axiomatic Set Theory, as formalised in ZFC; i.e. Zermelo Fraenkel set theory with the Axiom of Choice, has been used, through much of this century, as the foundational theory for modern pure mathematics. This central role for ZFC is based on the fact that all the mathematical objects needed can be coded in purely set theoretical terms and their properties can be proved from the ten or so axioms of ZFC. For various reasons many other systems of set theory have been studied by logicians and others. In Manchester three kinds of variants have received particular attention. These are
Constructive Set Theory
Instead of changing the non-logical axioms of axiomatic set theory so as to allow for non-well-founded sets or for non-sets of various kinds we may consider changing the logic. One possibility is to replace classical logic by intuitionistic logic. Provided that the non-logical axioms of axiomatic set theory are carefully formulated the resulting set theory has been called Intuitionistic Set Theory. Constructive Set Theory is intended to be a set theoretical approach to constructive mathematics. Intuitionistic Set Theory would seem to be too strong to be taken to be an axiomatic constructive set theory. Various much weaker subsystems seem to be more appropriate. In particular there has been a good deal of attention focused on an axiom system CZF.

21. MCS - Computer Science Seminars And Short Courses, 96-97
We look at various preservation theorems of classical logic (principally the LosTarski and verifying the major Subsystems of AMULET (address interface,
http://www.cs.le.ac.uk/seminars/archive/ComputerScience96-97.html
Computer Science Seminars, 96-97
Details are available for
Extended ML: a framework for specification and development of modular Standard ML programs.
Don Sannella (LFCS, Edinburgh University)

22. Main Text
Some axiomatic theories of truth and related Subsystems of secondorder arithmetic .. FefermanÂs axiomatization KF formulated in classical logic is an
http://users.ox.ac.uk/~sfop0114/abstracts.htm
 Abstracts Axiomatische Wahrheitstheorien , Akademie Verlag, Berlin, 1996 In this book I provide a technical survey of many axiomatic theories of truth as well as a survey of many semantical approaches to the paradoxes. Table of Contents I Grundlagen 1 Explikationen von Wahrheit 2 Das Kategorieproblem 3 Metamathematik der Wahrheit II Die Basistheorie 4 Rekursive Funktionen 5 Arithmetisierung 6 Beweistheoretische Reduktionen III Klassische Wahrheitstheorien 10 Wahrheit und arithmetische Komprehension IV Wahrheitsklassen 11 Nonstandardmodelle 12 Lachlans Theorem V Iterierte Wahrheitstheorien 15 Objekt- und Metasprachen 16 Tarski-Hierarchien 17 Definierbarkeit in Tarski-Hierarchien 18 Ein System iterierter Wahrheit 19 Unfundierte Hierarchien 20 Burges Hierarchien VI Typfreie Wahrheit 21 Selbstreferentielle Wahrheit 22 Einige Inkonsistenzen 23 Typfreie Tarski-Bikonditionale VII Kripkes Wahrheitstheorie und ihre Axiomatisierungen 24 Kripkes Wahrheitstheorie und Tarski-Hierarchien 25 Kripke-Feferman-Theorien 26 Supervaluation 27 Klassische symmetrische Wahrheit 28 Revisionssemantik und FS 29 Beweistheorie von FS IX Philosophische Aspekte 32 Paradoxien 33 Ontologische Reduktion Back Semantics and Deflationism , unpublished habilitation thesis, 2001 In this book a develop a deflationist approach to semantics where truth and reference are treated as logico-mathematical notions.

23. [Author] Alexander Sakharov [Title] Median Logic [AMS Subj-class
Author Alexander Sakharov Title Median logic AMS Subjclass 03B55 Intermediate logics 03B20 Subsystems of classical logic Abstract Median logic
http://www.mathsoc.spb.ru/preprint/2004/04-12.txt
 [Author] Alexander Sakharov [Title] Median logic [AMS Subj-class] 03B55 Intermediate logics 03B20 Subsystems of classical logic [Abstract] Median logic introduced here is a minimal intermediate logic that combines classical properties in its propositional part and intuitionistic properties for derivations not containing propositional symbols. A sequent calculus and other formulations are presented for median logic. Cut elimination is proven for the sequent calculus formulation. Constrained Kripke structures are introduced for modeling median logic. The extent of the disjunction and existence properties is investigated. [Keywords] intermediate logic, classical logic, intuitionistic logic, sequent calculus, cut elimination, Kripke structures, disjunction property, existence property [Comments] LaTeX, English, 20 pp. [Contact e-mail] alex@sakharov.net

24. Renate A. Schmidt: Publications
Together with B. Konev and S. Schulz (eds). Journal of Applied Nonclassical logic 16 (1-2). . E-Unification for Subsystems of S4. In Nipkow, T. (ed.
http://www.cs.man.ac.uk/~schmidt/publications/
Publications
Publications ordered by theme Current DBLP listing Scholar Google R ...
To appear
To appear
Special issue on Relations and Kleene Algebras in Computer Science. Together with G. Struth (eds). Journal of Logic and Algebraic Programming
Abstract
BiBTeX
Special issue on Empirically Successful Computerized Reasoning. Together with G. Sutcliffe and S. Schulz (eds). Journal of Applied Logic
Abstract
First-Order Resolution Methods for Modal Logics. Together with U. Hustadt. In Podelski, A. and Voronkov, A. and Wilhelm, R. (eds), Volume in memoriam of Harald Ganzinger. Lecture Notes in Artificial Intelligence , Springer. Invited overview paper.
Abstract
BiBTeX PDF
On Combinations of Propositional Dynamic Logic and Doxastic Modal Logics. Together with D. Tishkovsky. Journal of Logic, Language and Information
Abstract
BiBTeX Full text via Springer
Using Tableau to Decide Expressive Description Logics with Role Negation. Together with D. Tishkovsky. In Aberer, K. et al (eds), The Semantic Web, 6th International Semantic Web Conference, 2nd Asian Semantic Web Conference, ISWC 2007 + ASWC 2007, Busan, Korea, November 11-15, 2007. Lecture Notes in Computer Science , Vol. 4825, Springer, 438-451.

25. List KWIC DDC And MSC Lexical Connection
Subsystems of classical logic (including intuitionistic logic) 03B20 subtraction 513.212 subvarieties 14K12 success runs 519.84
http://www.mi.imati.cnr.it/~alberto/dml_11_50.htm
 structure theorems # general structure theory structure theory structure theory structure theory structure theory structure theory structure theory structure theory structure theory # characterization and structure theory # characterization and structure theory # general structure, canonical formalism, Cauchy problems) # Einstein's equations (general structure, classification of commutative topological algebras structure, classification of topological algebras structure, classification theorems structure; Euclidean algorithm; greatest common divisors # multiplicative structured objects in a category (group objects, etc.) structured programming structured surfaces and interfaces, coexistent phases structures # algebraic structures # associated Lie structures # asymptotic results on counting functions for algebraic and topological structures # basic properties of first-order languages and structures # combinatorial complexity of geometric structures # data structures # data structures # deformations of structures # deformations of analytic structures # deformations of complex structures # deformations of special (e.g. CR)

26. MPLA :: Graduate Program In Logic, Algorithms And Computation
Intersection types in classical logic. 5/12/03, F. Afrati, N.T.U.A. Finite axiomatizability of Subsystems of P. 29/3/02, F. Ferreira, University of
http://mpla.math.uoa.gr/seminars/
mpla.math.uoa.gr
Graduate Program in Logic, Algorithms and Computation. Old website
By Semester
• A. Tzouvaras University of Thessaloniki
On the consistency of NF E. Kranakis Carleton University (Ottawa)
The power of tokens: Rendezvous and symmetry detection for twomobile agents in a ring K. Potika N.T.U.A.
Boundary labeling problems
Petri net semantics for communicating agents D. Thilikos University of Athens
Graph searching in a crime wave (joint work with D. Richerby) Y. Moschovakis
Borel determinacy A. Kechris Caltech
Set theory and dynamical systems E. Zachos N.T.U.A.
Hierarchies of complexity classes
top
• K. Yamazaki Gunma University (Japan).
Relationships between the class of unit grid intersection graphs and other classes of bipartite graphs. H. Schwichtenberg University of Munich.
Logic for computable functionals and their approximations. Y. Moschovakis "... (a+bn)/n=x, hence God exists" — with Logic only! D. Richerby M.P.L.A. How to kill a Minotaur: An introduction to graph searching. Ch. Kapoutsis

27. Perspectives In Logic - List Of Books
Subsystems of second order arithmetic based on such axioms correspond to in book form of the classical decision problem of mathematical logic and its
http://www.aslonline.org/books-perspectives-list.html
 Books Lecture Notes in Logic Perspectives in Logic Other ASL Books ... Member Discounts Perspectives in Mathematical Logic This book series is now being published by the Association for Symbolic Logic on its own; the previous collaboration with Springer-Verlag came to an end on April 30, 2001. Thanks to the generosity of Springer-Verlag, ASL will distribute the available stock of certain books in the series to the logic community at a low price (as has been done with the existing stock of books in the Lecture Notes in Logic ). Some books in the series will continue to be made available by Springer-Verlag and others will be reprinted by ASL. At the moment (October 2001) the situation is in flux and plans for the future are being made. Inquiries may be made via the ASL business office : Association for Symbolic Logic Box 742, Vassar College 124 Raymond Avenue Poughkeepsie, New York 12604 USA Email: asl@vassar.edu

28. Branislav Boricic PhD
On some Subsystems of Dummett s LC , Zeitschrift fur mathematische Logik und Grunlagen On some interpretations of classical logic , Zeitschrift fur
http://www.ekof.bg.ac.yu/visitors/stuff/boricic.htm
 home page site map serbian Visitors info ... Publish Centre BORICIC Branislav, PhD, Full Professor e-mail: boricic@one.ekof.bg.ac.yu Born in Ivangrad (Berane), on 12 th May 1955 where he finished elementary and high school. Graduated from the Faculty of Science and Mathematics in 1977 on the Mathematics course. Got the MSc degree in 1980, and PhD degree in 1984. Previous positions: Present position: Full Professor at the Faculty of Economics, Belgrade since 1995. Teaching commitments: Algebra, linear algebra, analysis, mathematical logic, set theory, systems theory (undergraduate studies). Systems theory, functional analysis, methodology of scientific research, mathematical logic, basics of mathematics, theory of algorithms, automatic theorem proving and artificial intelligence (postgraduate studies) Research interests: Mathematical logic (proof theory, non-classical logics, preference logic). Professional improvement and advanced training: London (Imperial College, Chelsea College of Science and Technology in 1985), Iraklion (University of Crete, 1994-1996), Thessalonica (University of Macedonia in 1997), Patras (University of Patras in 1999). Other professional activities: Member of Association for Symbolic Logic, member of the American Mathematical Society, member of the Balkan Logical Society, member of the Serbian Mathematical Society, member of the Greek Mathematical Society, Interest Group on Propositional and Predicate Logic. A regular reviewer-associate of the journal "Zentralblatt fur Mathematik" and "Mathematical Reviews" with over 200 reviews. Outside associate of The Mathematical Institute of the Serbian Academy of Science and Arts, actively takes part in the work of the Department of Mathematics, the Department of mathematical logic, and the Department of the history and philosophy of mathematics. Took part in many scientific and professional meetings in Yugoslavia and abroad. Author or co-author of many professional, methodological papers and teaching aids for teachers, students and secondary school pupils, and of monographs. Translates from Russian and Greek.

29. Introduction
In the terminology of the Âinteracting cognitive SubsystemsÂ (ICS) model of . Of these, one is the classical logic prevalent in conscious thinking,
http://www.scispirit.com/wok/Introduction.html
 Ways of Knowing: Science and Mysticism Today Draft Introductory Chapter by Chris Clarke What does it mean, to know? (Norma Kassi) Not only do we know more about the universe, but our understanding is deeper, and the questions that we are asking are more profound. Still, our understanding of the origin and evolution of the universe has not yet caught up with what we know about it. (Wendy L. Freedman (Chris Bache) The sapiential perspective envisages the role of knowledge as the means of deliverance and freedom, of what the Hindu calls moksa. To know is to be delivered. (Seyyed Hossein Nasr) Yukon , is intensely practical and born of a lifetime of living close to nature. The knowledge of the cosmologist Wendy Freeman is derived from measurements from satellite observatories orbiting the earth, coupled with the full intellectual apparatus of modern theoretical physics; it is vast but seemingly remote from our lives. The vision of Chris Bache, seen in the trance of a psychedelic state of consciousness, claims to deliver similar cosmological information, but through direct awareness with no instrument other than the body-mind. And the knowledge dealt with by Sayed Hussein Nasr, knowledge of the ultimate nature of all existence, is attained through the long refinement of consciousness taught in traditional meditative spiritual paths. Astonishing Hypothesis which gives a pinnacle place to the sort of spiritual knowing being described by Nasr. Both these examples have come in for trenchant criticism, as well as enthusiastic praise, so that it now seems necessary to explore ways of knowing in which there is no boss-knowledge, no supreme ruler at the pinnacle.

 30. Anytime Approximations Of Classical Logic From Above Finger And One only has to restrict some axioms or derivation rules in order to obtain a subsystem of classical logic. Sound and incomplete methods are useful forhttp://logcom.oxfordjournals.org/cgi/content/full/17/1/53?ck=nck

31. Neil Tennant
We shall establish the decidability of classical monadic firstorder logic. We shall isolate intuitionistic logic as a subsystem of classical logic,
http://people.cohums.ohio-state.edu/tennant9/650.html
NEIL TENNANT
tennant.9@osu.edu
PHIL 650: Symbolic Logic
Lecture/seminar University Hall , Room 353
Times tba Aims of this course This course aims to provide a comprehensive coverage of the syntax and semantics of first-order languages, and the positive results concerning them. First-order languages contain the expressions "for some x ", "for every x " and " x is identical to y ", in addition to the connectives "not", "and", "or" and "if ... then ..." of propositional logic (which will have been studied in PHIL 250: Introduction to Symbolic Logic Topics We address various philosophical problems concerning reference, definite descriptions, predication, identity and existence; and cover the rudiments of informal set theory that are needed for a rigorous discussion of syntactic and semantic matters. We give a precise compositional grammar for the generation of well-formed expressions (both terms and formulae) of first-order languages. We give the famous Tarskian definition of

32. Springer Online Reference Works
In this sense constructive logic is broader than the logic of constructive mathematics. The most prominent difference from traditional (classical) logic
http://eom.springer.de/c/c025330.htm
 Encyclopaedia of Mathematics C Article referred from Article refers to Constructive logic A branch of mathematical logic studying arguments concerning constructive objects (cf. Constructive object ) and constructions. In this sense constructive logic is broader than the logic of constructive mathematics . The most prominent difference from traditional (classical) logic consists in the absence of the law of the excluded middle and the law of double negation (cf. Double negation, law of Heyting formal system ). Constructive arithmetic sometimes refers to Heyting arithmetic and sometimes to its extension obtained by adding Markov's principle (see Constructive selection principle ) and the scheme , expressing the equivalence of a formula and the assertion of its realizability (see Constructive semantics ). This extended system, which is sufficient for the proof of the fundamental results of constructive mathematical analysis, is not, in contrast to the Heyting one, a subsystem of classical arithmetic: The law of the excluded middle, , is refutable in it. Systems of

33. Hybrid Quantum-Classical Theory (was: Quantization Procedures) Text - Physics Fo
will only flow from the classical subsystem to the quantum subsystem is directly linked of empirical science involve manipulations in classical logic.
http://www.physicsforums.com/archive/index.php/t-57285.html
 Physics Help and Math Help - Physics Forums Physics General Physics sci.physics.research ... PDA View Full Version : Hybrid Quantum-Classical Theory (was: Quantization procedures) whopkins@csd.uwm.edu Basically, what I do in the 2 articles "Ab Initio Derivation of Quantum Mechanics" is show that the d/dt-compatibility and Jacobi-compatibility conditions that arise from putting together the equations of motion dq/dt = v, dv/dt = a(q,v); with the equal-time commutators [q(t),q(t)] (matrix form) = for all time t is the non-commutative analogue of the Helmholz conditions that in classical dynamics define the existence of a Lagrangian. This takes the 1991 JMP paper "No Lagrangian? No Quantization!" one step further, where the authors there had to resort to an explicit mention of a classical limit to get their results. Likewise, I'm restricting attention to c-number [q,v] commutators, because the more general case requires much deeper analysis using Lie algebras. A less restricted subset coming from relaxing the assumptions either to (a) q's have infinite number of degrees of freedom (then the critical use of a Schur's Lemma is blocked) or (b) [q,v]'s

34. Twenty-six Open Questions
Is there a single axiom for classical logic in A and N using the rules Is there, in particular, an NNfree axiom set for classical logic in C and N
http://web.ics.purdue.edu/~dulrich/Twenty-six-open-questions-page.htm
 Listed below are the twenty-six open questions, some old and some new, posed in A legacy recalled and a tradition continued Journal of Automated Reasoning , vol. 27, no. 2 (2001), pp. 97-122]. Explanations of terminological and notational matters connected with each question can be found in that paper (or, alternately, on the compact disk accompanying Larry Wos and Gail Peiper's Automated reasoning and the discovery of missing and elegant proofs , Rinton Press, Paramus, 2003, where it has been reprinted with silent corrections of a few typographical errors). For those questions where I've learned that answers have been found or that progress has at least been made, a current status report is given. Please e-mail me up-dated information about work on any of these questions as it becomes available: dulrich at purdue dot edu QUESTION A asked on page 105 of the "Legacy" paper, cf. page 113, and due originally to C. A. Meredith Is Meredith's 21-character single axiom CCCCCpqCNrNsrtCCtpCsp / p q r s r t t p s p )) for classical two-valued logic using the standard connectives ' C ' and ' N ' shortest possible?

 35. CAT.INIST Translate this page Intuitionist logic-Subsystem of, Extension of, or Rival to, classical logic? R SYLVAIN Philosophical studies 5311, 147-151, Kluwer, 1988.http://cat.inist.fr/?aModele=afficheN&cpsidt=11911023

36. Sytax Of Modal Logic
The minimal classical logic, which is axiomatized by (PC), (MP), and (CGR), is denoted E. In particular, one can show that E is a proper subsystem of M,
http://www.informatik.uni-leipzig.de/~duc/Thesis/node49.html
Next: Semantics for normal modal Up: Modal logic Previous: Modal logic Contents
Sytax of modal logic
The language of propositional modal logic is formed by extending that of the propositional calculus by an one-place modal operator . Formally:
The formula is read: it is necessarily true that . The possibility operator is introduced as an abbreviation: . If is a set of formulae then denotes the set . We stipulate that the modal operators bind more strongly than the Boolean connectives. Furthermore, we introduce the following abbreviations:
for all and All the modal systems we consider are formed by adding to a complete axiomatization of the propositional calculus some specific modal axiom schemata and rules of inference. We shall consider some modal logics determined by axioms and rules from the following lists:
(PC)
All propositional tautologies
(MP)
Modus ponens: from and to infer
(K) (T) (D) (N) (C) (G) (NEC)
From to infer (Necessitation)
(MON)
From to infer (Monotony)
(CGR)
From to infer (Congruence)
(RK
From to infer , for all
Instead of using (PC) for defining a logic to include all tautologies, it would suffice to include a set of schemata from which all tautologies can be derived by appropriate rules of inference, e.g., modus ponens. An example of such a set of schemata is:

37. Towards Mathematical Philosophy
In fact also many nonclassical logics, e.g., intuitionistic logic, .. Since classical propositional logic is Post-complete, any additional axiom in its
http://www.logika.umk.pl/TrendsIV/abstracts.htm
Studia Logica International Conference Towards Mathematical Philosophy Trends in Logic IV
ToruÃ±, Poland, September 1 - 4,
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Abstracts of the invited lectures: Ryszard WÃ³jcicki - "The Philosophical Foundations of Systems of Logical Inference" By an inference in a language L I mean a statement of the form Since A A n therefore , in symbols A A n B , where A A n , are sentences of L . Given a formalized language L, there are several strategies for separating from all inferences in that language those which are logically valid. The most typical strategy consists in setting conditions under which a compound sentence formed by means of a logical constant is true and than define a mode of inference to be logically valid if and only if it preserves truth. Aristotelian system of syllogistic and first order predicate logic are obvious examples of truth-preserving logics (systems of logical inference). In fact also many non-classical logics, e.g., intuitionistic logic, systems of modal logic, Â£ukasiewicz systems of many valued logic, were intended to be truth preserving. The following are two main questions I am going to discuss in my talk: (Q1) What do we actually mean by 'truth' when we pretend to reason in truth-preserving way?

38. Fuzzy Logic
classical logic relies on something being either true or false. Thus, something either completely belongs to a set or it is completely excluded from it.
http://www.danmeter.dk/products/neuromonitoring/dmtech/fuzzylogic/index.html
 Kildemosevej 13 Ã¢ÂÂ¢ DK-5000 Odense C Ã¢ÂÂ¢ Denmark Ã¢ÂÂ¢ Phone +45 63 11 29 30 Ã¢ÂÂ¢ Fax +45 63 11 29 31 Ã¢ÂÂ¢ E-mail info@danmeter.dk Home Company Information Products ... CSMNET Login Fuzzy Logic Back The brain and fuzzy logic Our brain gathers information constantly. The processing of this information is not governed by Ã¢ÂÂcrispÃ¢ÂÂ ON/OFF, black/white logic. Rather, it is based on Ã¢ÂÂfuzzy inputsÃ¢ÂÂ (truths, perceptions and inferences) which result in an averaged, summarized, normalized output. We then assign to this output a precise number or decision value which we verbalize, write down or act upon. The goal of fuzzy logic control systems is to perform this kind of process. What is fuzzy logic? Fuzzy logic is a problem-solving control system methodology that incorporates a simple, rule-based IF X AND Y THEN Z approach rather than attempting to model a system mathematically. The fuzzy logic model is empirically-based, relying on an operator's experience rather than their technical understanding of the system. In this sense, Ã¢ÂÂfuzzy logicÃ¢ÂÂ does not mean Ã¢ÂÂinaccurateÃ¢ÂÂ or Ã¢ÂÂinexactÃ¢ÂÂ logic. Fuzzy logic is not any less precise than any other form of logic: it is an organized method for handling complex concepts.

39. Department Of Philosophy
This is a course in symbolic logic up to and including predicate logic with . and intuitionistic logic as an important subsystem of classical logic.
http://philosophy.osu.edu/studentInfo/courses/CourseDescription.cfm
The Ohio State University www.osu.edu Help Campus Map ... Search Ohio State
101 Introduction to Philosophy
5 Credit Hours, Offered in: WI
Instructor: samuels.58
This course intoduces central topics in the philosophy of mind, philosophy of Religion and theory of knowledge. Course requirements: midterm and final exams, plus two writing assingnments.
130 Introduction to Ethics
5 Credit Hours, Offered in: WI
Instructor: darms.1
Are there any differences between moral judgments, on the one hand, and judgments of personal taste, etiquette, and aesthetics, on the other? Are moral judgments all relative, and, if so to what? Do moral requirements arise from the will of God, or from some other source? Should we decide what is the morally right thing to do by looking at the consequences of our actions, or are some actions simply right in and of themselves? After examining questions like these in the first part of the course, we will turn to a discussion of some specific and pressing moral questions that have divided American society. Possible topics include: terrorism, torture, and the ethics of war; abortion, euthanasia and parental selection of off spring; capital punishment; racial discrimination and affirmative action.

40. Intuitionistic Logic (Stanford Encyclopedia Of Philosophy/Fall 1999 Edition)
The GÃ¶delGentzen negative translation interpreted classical predicate logic in its intuitionistic subsystem. In 1965 Kripke provided a semantics with
http://www.science.uva.nl/~seop/archives/fall1999/entries/logic-intuitionistic/
This is a file in the archives of the Stanford Encyclopedia of Philosophy
Stanford Encyclopedia of Philosophy
A B C D ... Z
Intuitionistic Logic
Intuitionistic logic encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his intuitionistic mathematics, beginning in [1907]. Because these principles also underly Russian recursive analysis and the constructive analysis of E. Bishop and his followers, intuitionistic logic may be considered the logical basis of constructive mathematics Philosophically, intuitionism differs from logicism by treating logic as a part of mathematics rather than as the foundation of mathematics; from finitism by allowing (constructive) reasoning about infinite collections; and from platonism by viewing mathematical objects as mental constructs with no independent ideal existence. Hilbert's formalist program, to justify classical mathematics by reducing it to a formal system whose consistency should be established by finitistic (hence constructive) means, was the most powerful contemporary rival to Brouwer's developing intuitionism. In his 1912 essay Intuitionism and Formalism Brouwer correctly predicted that any attempt to prove the consistency of complete induction on the natural numbers would lead to a vicious circle.

41. 1995 - Technical Reports - Computing - Imperial College London
To support this, we have used classical logic to represent partial subsystem analysis leaves out information from the subsystem environment (context),
http://www.doc.ic.ac.uk/research/technicalreports/1995/
Skip over navigation Quick Navigation Imperial home page A-Z of Departments Courses Research Alumni Faculty of Engineering Faculty of Life Sciences Faculty of Medicine Faculty of Physical Sciences Business School Spectrum (restricted to College users) People finder Help Note: Your browser does not support javascript or you have javascript turned off. Although this will not affect your accessibility to the content of this site, some of the advanced navigation features may not be available to you. Home Research Technical Reports Note: Some of the graphical elements of this site are only visible to browsers that support accepted web standards . The content of this site is, however, accessible to any browser or Internet device.
1995 - Technical Reports
Number Report Title FINITE ALGORITHMS FOR DECODING RECURRENT ITERATED FUNCTION
A. Edalat, 21pp TRANSACTIONS AND UPDATES IN DEDUCTIVE DATABASES
D. Montesi, E. Bertino , M. Martelli, 56pp A BOUNDING CIRCLE FOR THE ATTRACTOR OF AN IFS
A. Edalat, 2pp

42. AUTHOR INDEX
The systems presented are versions of singlesuccedent sequent systems for classical logic. The cut-elimination results for the single-succedent systems can
http://www.filozof.uni.lodz.pl/bulletin/v343.html
BULLETIN OF THE SECTION OF LOGIC TABLE OF CONTENTS 1. Hirohiko KUSHIDA, Applicability of Motohashi's Method to Modal Logics [Abstract] [DVI] 2. Dolph ULRICH, D-complete Axioms for the Classical Equivalential Calculus [Abstract] [DVI] 3. Adam KOLANY, Rado Selection Lemma and Other Combinatorial Statements Uniformly Proved [Abstract] [DVI] 4. Andrzej INDRZEJCZAK, Sequent Calculi for Monotonic Modal Logics [Abstract] [DVI] 5. Norihiro KAMIDE, Cut-free Single-succedent Systems Revisited [Abstract] [DVI] 6. Gemma ROBLES, Francisco SALTO and Jose M. MENDEZ, A Constructive Negation Defined with a Negation Connective for Logics Including Bp+ [Abstract] [DVI]
ABSTRACTS
1. Hirohiko KUSHIDA, Applicability of Motohashi's Method to Modal Logics Motohashi showed that the intuitionistic predicate logics (with the constant domains and with increasing domains) can be faithfully embedded in the classical predicate logic by a proof-theoretic method. The embedding treated could be considered a combination of the modal embedding of intuitionistic logic in the modal logic S4 and the ``standard translation'' of S4 to classical predicate logic. By extending Motohashi's method, In the present paper, we show that Motohashi's method can be applied to a wide range of modal predicate logics. We prove correspondence theorems based on the standard translation between classical predicate logic and the quantified versions of S4 and S5 and some subsystems of them, in a uniform way.
2. Dolph ULRICH

43. 3. KGC 1993: Brno, Czech Republic
Problems in logic Programming, Database Theory and classical logic. Giovanni Faglia Double Exponential Inseparability Of Robinson Subsystem Q+ From
http://www.informatik.uni-trier.de/~ley/db/conf/kgc/kgc93.html
KGC 1993: Brno, Czech Republic
Georg Gottlob Alexander Leitsch Daniele Mundici Lecture Notes in Computer Science 713 Springer 1993, ISBN 3-540-57184-1 BibTeX DBLP
Contributed Papers

 44. Machine Learning (Theory) Â» What Can Type Theory Teach Us About Machine Learnin classical logic rather than constructive logic. This however is systems but making ÂinterfacesÂ between subsystems. These interfaceshttp://hunch.net/?p=54

45. NORM
None the less, the claims to universality of classical logic must be rejected. . CL as a subsystem, the classical and the dialectical logic are united .
http://nb.vse.cz/kfil/elogos/logpoint/94-1/ZELN.htm
JINDÃÂICH ZELENÂ
In the last two decades, the idea of a "paraconsistent logic" has been advanced and elaborated in several modifications . Numerous paraconsistent logical calculi have been constructed which allow the formula " A A " to be true (derivable) under some special conditions and thus tolerate (A A) without becoming trivial. Some of the adherents of this new trend in contemporary logic investigate explicitly also its philosophical presuppositions and implications. Among other problems, the question of the relationship between the idea of paraconsistency and the traditional and/or contemporary forms of dialectical thinking is being examined. This is the question we want to focus on here. It seems to us that in the philosophy of paraconsistency a differentiation can be observed to-day. One of the tendencies, represented by da Costa, Arruda, Quesada, Pena a. o., while assessing highly important philosophical implications of the logic of paraconsistency, insists upon the view that paraconsistency is closely linked with the theory of logical calculi. The philosophizing logicians of this tendency give, as a rule, only modest hypothetical accounts of the relationship between paraconsistency and dialectic. The other tendency, represented by G. Priest a. o., dares to defend vehemently more radical and ambitious assumptions about the philosophical and scientific implications of paraconsistent logic, concerning not only the relation to dialectic, but also the conception of rationality in general.

46. CASC-17 Entrants' System Descriptions
Gandalf version c stands for the Gandalf for classical logic. . FINDER Sla94 (a finite model generator) as a subsystem of OTTER in order to determine
http://www.cs.miami.edu/~tptp/CASC/17/SystemDescriptions.html
Bliksem 1.10
H. de Nivelle
nivelle@mpi-sb.mpg.de
Architecture
Bliksem is a resolution and paramodulation based theorem prover. It implements many different orders, including many orders that define decision procedures. The automatic selection of strategies is poor. A special feature of Bliksem is that it is able to output totally specified proofs. After processing, these proofs can be checked by Coq.
Implementation
Bliksem is written in portable C. High priority has been given to portability. Bliksem has been compiled succcessfully using cc, gcc, and djpcc. The data structures have been carefully chosen after benchmark tests on the basic operations. Bliksem can be obtained from: http://www.mpi-sb.mpg.de/~bliksem
Expected Competition Performance
The system does not differ from last year's entry. So it is reasonable to expect the same competition performance as last year.

 47. This Is The Programme Of The Biannual Conference Of Iqsa That Was MONDAY ORDER STRUCTURES 9.00 9.40 D. Foulis The Quantum-logic . Faux - Boolean Algebras and classical logic in the Modal Interpretation POSTER SESSIONhttp://www.vub.ac.be/CLEA/IQSA/textberlin.txt

48. The QED Manifesto - Some Background
We regard this `bootstrapping problem -how to get, rigorously, from checking theorems in a weak logic to theorems in a powerful classical logic,
http://rbjones.com/rbjpub/logic/qedres03.htm
Some Background, Being a Critique of Current Related Efforts
In some sense project QED is already underway, via a very diverse collection of projects. Unfortunately, progress seems greatly slowed by duplication of effort and by incompatibilities. If the many people already involved in work related to QED had begun cooperation twenty-five years ago in pursuing the construction of a single system (or federation of subsystems) incorporating the work of hundreds of scientists, a substantial part of the system, including at least all of undergraduate and much of first year graduate mathematics and computer science, could already have been incorporated into the QED system by now. We offer as evidence the nontrivial fragments of that body of theorems that has been successfully completed by existing proof-checking systems. Too much code to be trusted Too strong a logic Too limited a logic Too unintelligible a logic Too unnatural a syntax Parochialism Too little extensibility Too little heuristic search support Too little care for rigour Complete absence of inter-operability Too little attention paid to ease of use 1. Too much code to be trusted. There have been a number of automated reasoning systems that have checked many theorems of interest, but the amount of code in some of these impressive systems that must be correct if we are to have confidence in the proofs produced by these systems is vastly greater than the few pages of text that we wish to have as the foundation of QED.

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