Geometry.net Online Store

1. Intuitionistic Logic - Wikipedia, The Free Encyclopedia Intuitionistic logic, or constructivist logic, is the symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer s http://en.wikipedia.org/wiki/Intuitionistic_logic

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Intuitionistic logic From Wikipedia, the free encyclopedia Jump to: navigation search Intuitionistic logic , or constructivist logic , is the symbolic logic system originally developed by Arend Heyting to provide a formal basis for Brouwer 's programme of intuitionism . The system preserves justification , rather than truth , across transformations yielding derived propositions. From a practical point of view, there is also a strong motivation for using intuitionistic logic, since it has the existence property , making it also suitable for other forms of mathematical constructivism Contents Syntax Axiomatization Interdefinability of operators Sequent calculus ... edit Syntax The syntax of formul¦ of intuitionistic logic is similar to propositional logic or first-order logic . The difference is that many tautologies of these classical logics can no longer be proven within intuitionistic logic. Examples include not only the law of excluded middle P P , but also Peirce's Law P Q P P , and even double negation elimination . In classical logic, both

2. Intuitionistic Logic (Stanford Encyclopedia Of Philosophy) Intuitionistic logic encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his Intuitionistic mathematics, http://plato.stanford.edu/entries/logic-intuitionistic/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Intuitionistic Logic First published Wed Sep 1, 1999; substantive revision Tue Feb 6, 2007 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.

3. Intuitionistic Logic A very concise introduction to the subject. Includes overview of the syntax, Kripke models, analytic tableau, natural deduction. http://cs.wwc.edu/KU/Logic/Intuitionistic.html

4. Intuitionistic Logic -- From Wolfram MathWorld A very brief overview of the subject by Alex Sakharov from MathWorld. http://mathworld.wolfram.com/IntuitionisticLogic.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... Sakharov Intuitionistic Logic The proof theories of propositional calculus and first-order logic are often referred to as classical logic Intuitionistic propositional logic can be described as classical propositional calculus in which the axiom schema is replaced by Similarly, intuitionistic predicate logic is intuitionistic propositional logic combined with classical first-order predicate calculus. Intuitionistic logic is a part of classical logic, that is, all formulas provable in intuitionistic logic are also provable in classical logic. Although, even some basic theorems of classical logic do not hold in intuitionistic logic. Of course, the law of the excluded middle does not hold in intuitionistic propositional logic. Here are some examples of propositional formulas that are not provable in intuitionistic propositional logic: Here are some examples of first-order formulas that are not provable in intuitionistic predicate logic: Truth tables for propositional connectives define the interpretation of classical propositional calculus over the domain of two elements: true and false . This interpretation is a model of classical propositional calculus, that is

5. Good Math Has Moved To Syntactically, Intuitionistic logic looks the same as first order predicate logic. In Intuitionistic logic, a statement is only true if there is a proof http://goodmath.blogspot.com/2006/05/logic-fun-intuitionistic-logic.html

ScienceBlogs : Logic Fun: Intuitionistic Logic @import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=23588438"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "23588438"; Good Math has moved to ScienceBlogs Wednesday, May 24, 2006 Logic Fun: Intuitionistic Logic It's time for a bit of a side-track from the series of articles about lambda calculus. Models of lambda calculus are based on something called intuitionistic logic , so I'm going to write a bit about that. It's also quite interesting in its own right. Syntactically, intuitionistic logic looks the same as first order predicate logic . But the meanings of statements in it are often quite different. The basic idea behind intuitionistic logic is that some of the statements that you can make in propositional logic are too strong. In intuitionistic logic, a statement is only true if there is a proof that it is true; a statement that something is false means that that statement cannot be proved - so the negative statement "not P" can be read as an affirmative statement: "There is a proof that there is no proof for P".

6. Some Benchmark Formulae For Intuitionistic Propositional Logic Our purpose here is to apply the same method to develop a benchmark suite for Intuitionistic propositional logic, providing data that will allow a rough http://www.dcs.st-and.ac.uk/~rd/logic/marks.html

Some benchmark formulae for intuitionistic propositional logic Roy Dyckhoff, University of St Andrews, 30 June 1997 Abstract We propose a small collection of problem classes, mainly gathered from other sources, for benchmarking theorem provers for intuitionistic propositional logic. Our approach is based on that of Heuerding et al [HS] , in proposing not just certain particular formulae but classes of formulae that will scale up for faster machines and better techniques. Nonprovable formulae are used as well as provable ones, to ensure that provers tuned to spot positive answers have some work to do. Introduction [HS] has proposed a suite of benchmarks for several propositional modal logics, using a method which is intended to allow the comparison of provers even when faster machines and better techniques make old benchmarks obsolete. Our purpose here is to apply the same method to develop a benchmark suite for intuitionistic propositional logic, providing data that will allow a rough comparison of several techniques. One intended use of the benchmarks is for a comparison of submissions of results by others, in association with the Tableaux'98 meeting. For details of this, see

7. LogBlog: Skolemization In Intuitionistic Logic | Richard Zach | Philosophy | Uni On the Skolemization of existential quantifiers in Intuitionistic logic. Annals of Pure and Applied logic 142 (2006) 269295. http://www.ucalgary.ca/~rzach/logblog/2007/07/skolemization-in-intuitionistic-lo

@import "http://www.ucalgary.ca/templates/styles/uofc-drupal.css"; @import "http://www.ucalgary.ca/templates2/styles/uofc-level-c.css"; @import "http://wcm2.ucalgary.ca/rzach/files/rzach/custom_colors/uofc_c_v7.css"; @import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=7108230"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "7108230"; 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 LogBlog Logic . Philosophy . Other Fun Stuff Site Navigation Primary links Home Research Teaching CV ... LogBlog Search LogBlog Most Recent Posts Previous Posts Moscow-Vienna Workshop The Review of Symbolic Logic Oh Noes! Caturday ... Church’s Thesis and Functional Programming Links My Homepage Calgary Philosophy Department UC Berkeley Logic Group Association for Symbolic Logic Blogroll Subscribe to Posts [ Atom LogBlog Tuesday, July 03, 2007

8. Wadler: Linear Logic Two different operational interpretations of Intuitionistic linear logic have been Girard described two translations of Intuitionistic logic into linear http://homepages.inf.ed.ac.uk/wadler/topics/linear-logic.html

Linear Logic Philip Wadler Down with the bureaucracy of syntax! Pattern matching for classical linear logic Philip Wadler. Manuscript, April 2004. This paper introduces a new way of attaching proof terms to proof trees for classical linear logic, which bears a close resemblance to the way that pattern matching is used in programming languages. It equates the same proofs that are equated by proof nets, in the formulation of proof nets introduced by Dominic Hughes and Rob van Glabbeek; and goes beyond that formulation in handling exponentials and units. It provides a symmetric treatment of all the connectives, and may provide programmers with improved insight into connectives such as "par" and "why not" that are difficult to treat in programming languages based on an intuitionistic formulation of linear logic. Available in: pdf Operational Interpretations of Linear Logic David N. Turner and Philip Wadler. Special issue on linear logic, Theoretical Computer Science , to appear. Two different operational interpretations of intuitionistic linear logic have been proposed in the literature. The simplest interpretation recomputes non-linear values every time they are required. It has good memory-management properties, but is often dismissed as being too inefficient. Alternatively, one can memoize the results of evaluating non-linear values. This avoids any recomputation, but has weaker memory-management properties. Using a novel combination of type-theoretic and operational techniques we give a concise formal comparison of the two interpretations. Moreover, we show that there is a subset of linear logic where the two operational interpretations coincide. In this subset, which is sufficiently expressive to encode call-by-value lambda-calculus, we can have the best of both worlds: a simple and efficient implementation, and good memory-management properties.

9. Foundations Of Mathematics :: Intuitionistic Logic --  Britannica Online Encycl Britannica online encyclopedia article on foundations of mathematics, Intuitionistic logic The Dutch mathematician LEJ Brouwer (18811966) in the early 20th http://www.britannica.com/eb/article-35457/foundations-of-mathematics

var britAdCategory = "other"; Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic This Article's Table of Contents Expand all Collapse all Introduction Ancient Greece to the Enlightenment ... Number systems The reexamination of infinity Calculus reopens foundational questions Non-Euclidean geometries Elliptic and hyperbolic geometries Riemannian geometry ... Cantor The quest for rigour Formal foundations Set theoretic beginnings Foundational logic Impredicative constructions Nonconstructive arguments changeTocNode('toc35452','img35452'); Intuitionistic logic Other logics Formalism Recursive definitions ... Computers and proof Category theory Abstraction in mathematics Isomorphic structures Topos theory Intuitionistic type theories ... Print this Table of Contents Linked Articles fundamental Intuitionistic type theories Topos theory Shopping Revised, updated, and still unrivaled. 2008 Britannica Ultimate DVD/CD-ROM The world's premier software reference source. Great Books of the Western World The greatest written works in one magnificent collection.

10. An Afternoon On Intuitionistic Logic I will present a concrete enumeration of the nonderivable, admissible rules of Intuitionistic propositional logic (IPC), along with semantic criterions. http://staff.science.uva.nl/~gfontain/ipc/

An afternoon on intuitionistic logic 18 April 2007, Amsterdam Speakers Gaelle Fontaine (ILLC) Automorphisms of free Heyting algebras Joost J. Joosten (ILLC) Restricting the creative subject Lex Hendriks (ILLC) Junwei Yu and intuitionistic negation Bi-intuitionistic logic is not finitely axiomatizable with only modus ponens Nikolas Vaporis (University of Utrecht) The admissible rules of intuitionistic propositional logic Yde Venema (ILLC) The Heyting implication of free distributive lattices Fan Yang (ILLC) Operations on Intuitionistic Descriptive Frames and Duality Theorems Program The workshop will start at 13.00 on Wednesday April 18 and will finish at 17.00. Gaelle Fontaine Automorphisms of free Heyting algebras Nikolas Vaporis The admissible rules of intuitionistic propositional logic Yde Venema The Heyting implication of free distributive lattices Fan Yang Operations on Intuitionistic Descriptive Frames and Duality Theorems Lex Hendriks Junwei Yu and intuitionistic negation Bi-intuitionistic logic is not finitely axiomatizable with only modus ponens Joost J. Joosten

11. COMPUTABILITY LOGIC Homepage One of the main so far rather abstract intuitions associated with Intuitionistic logic is that it must be a logic of problems (Kolmogorov 1932); http://www.cis.upenn.edu/~giorgi/cl.html

Giorgi Japaridze's Computability Logic Homepage This material is based upon work supported by the National Science Foundation under Grant No. 0208816. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. What is computability logic? Lecture notes on computability logic Potential applications of computability logic Papers on computability logic ... LaTeX macros for the operators of computability logic What is computability logic? Computability is certainly one of the most interesting and fundamental concepts in mathematics and computer science, and it would be more than natural to ask what logic it induces. Let us face it: this question has not only never been answered, but never even been asked within a reasonably coherent and comprehensive formal framework. This is where Computability Logic comes in. It is a formal theory of computability in the same sense as classical logic is a formal theory of truth. In a broader and more proper sense, computability logic is not just a particular theory but an ambitious and challenging program for redeveloping logic following the scheme "from truth to computability". It was introduced in 2003 and, at present, still remains in its infancy stage, with open problems prevailing over answered questions. It is largely a virgin soil offering plenty of research opportunities, with good chances of interesting findings, for those with interests in logic and its applications in computer science.

12. [0708.2252] Focusing And Polarization In Intuitionistic Logic We present a new, focused proof system for Intuitionistic logic, called LJF, and show how other proof systems can be mapped into the new system by inserting http://arxiv.org/abs/0708.2252

arXiv.org cs Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PostScript PDF Other formats Citations CiteBase p revious n ... ext Computer Science > Logic in Computer Science Title: Focusing and Polarization in Intuitionistic Logic Authors: Chuck Liang Dale Miller (INRIA Futurs) (Submitted on 16 Aug 2007) Abstract: A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof search and the proof normalization approaches to computation. Various proof systems in literature exhibit characteristics of focusing to one degree or another. We present a new, focused proof system for intuitionistic logic, called LJF, and show how other proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing. We also use LJF to design a focused proof system for classical logic. Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard's LC and LU proof systems. Subjects: Logic in Computer Science (cs.LO)

13. Median Logic Intuitionistic logic has disjunction and existence properties and thus constructive proofs Whereas supersets of median logic are less Intuitionistic, http://sakharov.net/median.html

Home Email Alexander Sakharov Irina ... Tim Projects Resources Sport Photos Median Logic Math Foundations Badminton Clubs Trip Photos ... Assertion Propagation Median Logic The question 'Which of the two logics - classical and intuitionistic - is better?' has been around for about a century. Each has certain advantages over the other in certain dimensions. Both intuitionistic and classical logic have issues, too. Classical logic has decent models but existence proofs are not constructive in it. Intuitionistic logic has disjunction and existence properties and thus constructive proofs but the propositional fragment of intuitionistic logic while being finite does not have a finite model. It seems that classical logic has a 'better' propositional part whereas intuitionistic logic is 'better' suited for purely predicate statements. Is it possible to combine the best of both worlds? Research in this domain was initiated by Godel and Tarski almost as soon as intuitionistic logic emerged. Since derivable intuitionistic formulas constitute a subset of derivable classical formulas, the focus of this research is on investigating properties of the logics lying between the two. Such logics are called intermediate or superintuitionistic. Intermediate logics are usually defined by adding one or more axiom schemas weaker than LEM to intuitionistic logic. I introduced a bizarre intermediate logic that coincides with classical logic in its propositional part and coincides with intuitionistic logic in its purely predicate part. This logic is closed under modus ponens and closed under propositional substitution. This logic is a minimal intermediate logic that coincides with classical logic in its propositional part and coincides with intuitionistic logic on the set of formulas not containing propositional symbols. The minimality of median logic is critical because it implies that no other extension covering classical propositional logic can be made more ‘intuitionistic’ than median logic. Whereas supersets of median logic are less intuitionistic, its subsets are not fully classical in the propositional part.

14. Explicit Provability: The Intended Semantics For Intuitionistic And Modal Logic Abstract The intended meaning of Intuitionistic logic is given by the BrouwerHeyting-Kolmogorov (BHK) semantics which informally defines Intuitionistic http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA

15. A Hybrid Intuitionistic Logic: Semantics And Decidability - ECS EPrints Reposito Chadha, R., Macedonio, D. and Sassone, V. (2006) A Hybrid Intuitionistic logic Semantics and Decidability. Journal of logic and Computation, 16 (1). pp. http://eprints.ecs.soton.ac.uk/11850/

@import url(http://eprints.ecs.soton.ac.uk/style/auto.css); @import url(http://eprints.ecs.soton.ac.uk/style/print.css); @import url(http://eprints.ecs.soton.ac.uk/style/nojs.css); Site Search Home UG Study MSc Admissions PG Opportunities ... Intranet Breadcrumb trail: University of Southampton ECS Research Publications ... Browse by year Intranet Tools Add publications Modify RAE Information RSS 1.0 Feed RSS 2.0 Feed ... Atom Feed A Hybrid Intuitionistic Logic: Semantics and Decidability Chadha, R., Macedonio, D. and Sassone, V. (2006) A Hybrid Intuitionistic Logic: Semantics and Decidability. Journal of Logic and Computation, 16 (1). pp. 27-59. Download Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader Abstract the logic is decidable. Creators: R. Chadha D. Macedonio V. Sassone Item Type: Article Keywords: Additional Information: To appear Research Group: Dependable Systems and Software Engineering Research Group Deposited On: 27 Jan 2006 by Sassone, Vladimiro ID Code: Last Modified: 16 Nov 2007 04:19 Tools Look up in Google Scholar Metadata BibTeX OpenURL ContextObject OpenURL Dissertation OpenURL Journal Dublin Core DIDL EndNote HTML Citation Demo for Kirk METS MODS EPrints Application Profile (experimental) Reference Manager Refer Simple Metadata ASCII Citation EP3 XML Download Statistics Members of ECS may view the download statistics dashboard for this record.

16. ScienceDirect - Journal Of Applied Logic : A General Method For Proving Decidabi Intuitionistic modal logic is simply a modal logic with Intuitionistic, in Intuitionistic logic. The following clauses are encountered in the literature http://linkinghub.elsevier.com/retrieve/pii/S1570868305000431

Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Journal of Applied Logic Volume 4, Issue 3 , September 2006, Pages 219-230 Methods for Modalities 3 (M4M-3) Abstract Full Text + Links PDF (151 K) Related Articles in ScienceDirect Constructive modal logics I Annals of Pure and Applied Logic Constructive modal logics I Annals of Pure and Applied Logic Volume 50, Issue 3 14 December 1990 Pages 271-301 Duminda Wijesekera Abstract Abstract Abstract + References PDF (2151 K) Topological duality for intuitionistic modal algebras ... Journal of Pure and Applied Algebra Topological duality for intuitionistic modal algebras Journal of Pure and Applied Algebra Volume 148, Issue 2 28 April 2000 Pages 171-189 Barnaby P. Hilken Abstract This paper describes a generalisation of the adjunction and duality between topological spaces and frames, inspired by the Kripke semantics of modal logic. A relational space is defined as a topological space with a binary relation on the points, and a

17. ILTP Library - Benchmarking Theorem Provers For Intuitionistic Logic The Intuitionistic logic Theorem Proving (ILTP) library provides a platform for testing and benchmarking automated theorem proving (ATP) systems for http://www.cs.uni-potsdam.de/ti/iltp/

The ILTP Library Benchmarking Theorem Provers for Intuitionistic Logic Welcome Benchmark Problems Provers and Results Contact Welcome to the ILTP Library The Intuitionistic Logic Theorem Proving (ILTP) library provides a platform for testing and benchmarking automated theorem proving (ATP) systems for first-order and propositional intuitionistic logic. It includes two problem collections for first-order and propositional intuitionistic ATP systems and tools for converting the problems into the input syntax of some existing intuitionistic ATP systems. It also includes information about currently available ATP systems for intuitionistic logic and their performance results on the problems in the ILTP library. Please contact us for further information or if you want to submit new benchmark problems or performance results. Features of the ILTP Library: About 2800 propositional and first-order benchmark problems in a standardized syntax. Information about the intuitionistic status of all benchmark problems, i.e. Theorem, Non-Theorem, Unknown or Open.

18. DI & CoS - Classical And Intuitionistic Logic This paper presents systems for firstorder Intuitionistic logic and several of its extensions in which all the propositional rules are local, http://alessio.guglielmi.name/res/cos/CL/index.html

This page is no longer updated, please refer to this page Alessio Guglielmi's Research Deep Inference and the Calculus of Structures / Classical and Intuitionistic Logic Deep Inference and the Calculus of Structures Classical and Intuitionistic Logic So far, for classical logic in the calculus of structures we achieved: the cut rule trivially reduces to atomic form; one can show cut elimination for the propositional fragment by the simplest argument to date; the propositional fragment is fully local, including contraction; first order classical logic can be entirely made finitary; cut elimination and decomposition theorems are proved. We can present intuitionistic logics in the calculus of structures with a fully local, cut-free system. The logic of bunched implications BI can be presented in the calculus of structures. Japaridze's cirquent calculus benefits from a deep-inference presentation, in particular in the case of propositional logic. The basic proof complexity properties of propositional logic are known. Atomic Cut Elimination for Classical Logic System SKS is a set of rules for classical propositional logic presented in the calculus of structures. Like sequent systems and unlike natural deduction systems, it has an explicit cut rule, which is admissible. In contrast to sequent systems, the cut rule can easily be restricted to atoms. This allows for a very simple cut elimination procedure based on plugging in parts of a proof, like normalisation in natural deduction and unlike cut elimination in the sequent calculus. It should thus be a good common starting point for investigations into both proof search as computation and proof normalisation as computation.

19. Intuitionistic Logic Intuitionistic logic. logic, mathematics Brouwer s foundational theory of mathematics which says that you should not count a proof of (There exists x such http://burks.brighton.ac.uk/burks/foldoc/80/59.htm

The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: intuitionism Next: intuitionistic probability intuitionistic logic logic mathematics In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic). History

20. American Plan For Intuitionistic Logic 2 Generalized Kripke the analysis of consequence in Intuitionistic logic. On the basis of falsity we generalize Kripkesemantics for Intuitionistic logic and http://logic.ru/en/node/342

21. IngentaConnect The Pleasures Of Anticipation: Enriching Intuitionistic Logic B. We are especially interested in the case in which the logic is Intuitionistic (propositional) logic and are much concerned with an extension of that http://www.ingentaconnect.com/content/klu/logi/2001/00000030/00000005/00358074

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"); The Pleasures of Anticipation: Enriching Intuitionistic Logic Author: Humberstone L. Source: Journal of Philosophical Logic , Volume 30, Number 5, October 2001 , pp. 395-438(44) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: ) of the formula A Keywords: New intuitionistic connectives dual intuitionistic negation rules conservative extension Language: English Document Type: Regular paper Affiliations: Department of Philosophy, Monash University, Clayton Campus, Wellington Road, Clayton VIC. 3800, Australia

22. On Proof Realization Of Intuitionistic Logic - Storming Media In 1933 Godel Introduced an axiomatic system, currently known as S4, for a logic of an absolute provability. The problem of finding a fair probability model http://www.stormingmedia.us/50/5034/A503443.html

Are you from the UK? Click here for our UK site. Home About Us Contact Us ... Theoretical Mathematics On Proof Realization of Intuitionistic Logic Authors: S. N. Artemov CALIFORNIA UNIV BERKELEY Abstract: In 1933 Godel Introduced an axiomatic system, currently known as S4, for a logic of an absolute provability. The problem of finding a fair probability model for S4 was left open. In the current paper we demonstrate how the Intuitionistic propositional logic Int can be directly realized by proof polynomials. It is shown that Int is complete with respect to this proof realizability. Limitations: APPROVED FOR PUBLIC RELEASE Description: Technical rept. Pages: Report Date: OCT 1997 Contract Number: Report Number: Keywords relating to this report: BOOLEAN ALGEBRA CALCULUS MATHEMATICAL LOGIC MATHEMATICAL MODELS ... THEOREMS Adobe PDF - $18.95 Printed Format - $21.95 Please check the box for the format you wish to order. Shipping Terms About Electronic Delivery Email This Abstract Home About Us Contact Us View Cart ... Restrictions on PDF Usage

23. SICS Publications Database - Logic Programming And The Intuitionistic Sequent Ca The report contains some basic logical results and observations relevant to the use of Intuitionistic logic as a programming language. http://eprints.sics.se/2546/

@import url(http://eprints.sics.se/eprints.css); @import url(http://eprints.sics.se/eprints.css); @import url(http://eprints.sics.se/print.css); Home About Browse Search ... Help Logic programming and the intuitionistic sequent calculus Franz©n, Torkel Logic programming and the intuitionistic sequent calculus. SICS Research Report Swedish Institute of Computer Science ISSN Full text not available from this repository. Abstract The report contains some basic logical results and observations relevant to the use of intuitionistic logic as a programming language. In particular, a Kripke completeness proof is given for a formalization of intuitionistic logic incorporating quasi-free identity, and it is argued that full intuitionistic logic is too complicated to be useful, in spite of its superficial "constructive" aspects. Type: SICS Report (SICS Research Report) Additional Information: Original report number R88002. ID Code: Deposited By: Vicki Carleson BibTeX: Deposited On: 05 November 2007 Repository Admin Staff Only: edit this item Contact Information

24. Reverse Mathematics And Completeness Theorems For Intuitionistic Logic In this paper, we investigate the logical strength of completeness theorems for Intuitionistic logic along the program of reverse mathematics. http://projecteuclid.org/handle/euclid.ndjfl/1063372197

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Reverse Mathematics and Completeness Theorems for Intuitionistic Logic Takeshi Yamazaki Source: Notre Dame J. Formal Logic Volume 42, Number 3 (2001), 143-148. Abstract In this paper, we investigate the logical strength of completeness theorems for intuitionistic logic along the program of reverse mathematics. Among others we show that is equivalent over to the strong completeness theorem for intuitionistic logic: any countable theory of intuitionistic predicate logic can be characterized by a single Kripke model. Primary Subjects: Keywords: reverse mathematics; second-order arithmetic; completeness theorems; intuitionistic logic Full-text: Access granted (open access) Screen Optimized PDF File (131 KB) PDF File (117 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1063372197 Digital Object Identifier: doi:10.1305/ndjfl/1063372197 Mathematical Reviews number (MathSciNet): Zentralblatt Math identifier: back to Table of Contents References [1] Gabbay, D. M.

25. JSTOR Intuitionistic Logic. Dialogues as a foundation for Intuitionistic logic. Ibid., pp. 341372. Intuitionism was born in Brouwer s dissertation of 1907 (1551); but, http://links.jstor.org/sici?sici=0022-4812(199206)57:2<754:IL>2.0.CO;2-Q

26. Intuitionistic Logic @ Computer-Dictionary-Online.org Intuitionistic logic @ Computer Dictionary Online. Computer terminology definitions including hardware, software, equipment, devices, jargon abbreviations http://www.computer-dictionary-online.org/?q=intuitionistic logic

27. Clausal Intuitionistic Logic I. Fixed-point Semantics Clausal Intuitionistic logic I. Fixedpoint semantics. Source, Journal of logic Programming archive Volume 5 , Issue 1 (March 1988) table of contents http://portal.acm.org/citation.cfm?id=49426.49427

28. [FOM] Some Informative Questions About Intuitionistic Logic And Mathematics 2) Can one define in Intuitionistic logic counterparts of the classical connectives so that the resulting translation preserves the consequence relation http://cs.nyu.edu/pipermail/fom/2005-November/009298.html

[FOM] Some informative questions about intuitionistic logic and mathematics Richard Heck rgheck at brown.edu Thu Nov 3 22:10:18 EST 2005 Previous message: [FOM] Some informative questions about intuitionistic logic and mathematics Next message: [FOM] Some informative questions about intuitionistic logic and mathematics Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] 1) Is there a definable (in the same way implication is definable in classical logic in terms of disjunction and negation) unary connective @ of intuitionistic logic such that for every A, B we have that (DNE) A and A intuitionistically follow from each other, A, at A I think the answer to this question is "No". It's easy to prove that it is if we're allowed /reductio/, since we can show that (%) and reductio for @entail that ~A and @A are interderivable: [1] (1) ~A Premise [2] (2) A Premise [1,2] (3) Falsum /ex falso quodlibet/ for ~ [1] (3) @A (1)[2]reductio for @ and /mutatis mutandis/ back the other way, in which case we need EFQ for @ and reductio for ~. But then, of course, we have DNE for ~, by DNE for @. It's hard to get moving without reductio, since then we have no introduction rule for "@". But the proof that @A entails ~A survives, of course, and it's worth noting that we don't need (DNE) either way for the proof of equivalence. What this shows is that the standard intuitionistic introduction and elimination rules for ~ fix its meaning up to interderivability. > 2) Can one define in intuitionistic logic counterparts of the

29. Atlas: Interpolation Theorems For Intuitionistic Predicate Logic By Grigori Mint Craig interpolation theorem (which holds for Intuitionistic logic) implies that the derivability of \Gamma, \Gamma = \Delta implies existence of a http://atlas-conferences.com/c/a/c/s/24.htm

Atlas home Conferences Abstracts about Atlas First St.Petersburg Days of Logic and Computability May 26-29, 1999 Steklov Institute of Mathematics St. Petersburg, Russia Organizers Evgeny Dantsin, Gennadii Davydov, Dima Grigoriev, Eduard Karavaev, Nickolai Kossovskii, Vladimir Lifschitz, Maurice Margenstern, Yuri Matiyasevich (chairman), Grigori Mints, Vladimir Orevkov, Anatol Slissenko, Maxim Vsemirnov View Abstracts Conference Homepage Interpolation Theorems for Intuitionistic Predicate Logic by Grigori Mints Dept. of Philosophy, Stanford University Interpolation Theorems for Intuitionistic Predicate Logic G. Mints Dept. of Philosophy, Stanford Univ., Stanford, CA 94305, USA Propositional Interpolation Craig interpolant Nevertheless some interpolation properties for disjunction are true also in the intuitionistic case. We present here a multiple-succedent version of interpolation true for intuitionistic propositional (but not for predicate) logic. Similar result was established earlier by L. Maksimova [4]. More complicated version holds for the predicate case. L E Definition . Let v , ... , v

30. Introduction To Linear Logic For pedagogical purposes we shall also have a look at Classical logic as well as Intuitionistic logic. Linear logic was introduced by J.Y. Girard in 1987 http://www.brics.dk/LS/96/6/BRICS-LS-96-6/BRICS-LS-96-6.html

Introduction to Linear Logic Torben Braüner December 1996 Abstract: Contents Classical and Intuitionistic Logic Classical Logic Intuitionistic Logic The -Calculus The Curry-Howard Isomorphism Linear Logic Classical Linear Logic Intuitionistic Linear Logic A Digression - Russell's Paradox and Linear Logic The Linear -Calculus The Curry-Howard Isomorphism The Girard Translation Concrete Models A Logics A.1 Classical Logic A.2 Intuitionistic Logic A.3 Classical Linear Logic A.4 Intuitionistic Linear Logic B Cut-Elimination for Classical Linear Logic B.1 B.2 Putting the Proof Together Available as PostScript PDF DVI BRICS WWW home page

31. Joan Moschovakis Intuitionistic logic, revised 2003, in Stanford OnLine Encyclopedia of Philosophy. Analyzing realizability by Troelstra s methods, Annals of Pure and http://www.math.ucla.edu/~joan/

Joan Rand Moschovakis Guest of the UCLA Mathematics Department Education Ph.D., Mathematics, University of Wisconsin, 1965 M.S., Mathematics, University of Wisconsin, 1961 BA, Mathematics, UC Berkeley, Summa Cum Laude, 1959 Honors Woodrow Wilson and NSF Graduate Fellowships Research Interests Foundations of Intuitionistic Analysis, Intuitionistic Interpretations of Classical Mathematics, Classical Interpretations of Intuitionistic Mathematics Admissible Rules of Intuitionistic Logic History and Philosophy of Intuitionistic Logic Selected Publications and Preprints The Logic of Brouwer and Heyting , to appear in the Handbook of the History of Logic, ed. Woods and Gabbay, Oxford. logicofBandH.pdf logicofBandH.ps (with Garyfallia Vafeiadou, in Greek): Ôá åíïñáôéêÜ ìáèçìáôéêÜ êáé ç ëïãéêÞ ôïõò (in Greek), to appear. gvfjrmgr.pdf gvfjrmgr.ps (with Garyfallia Vafeiadou, English translation): Intuitionistic mathematics and logic gvfjrmeng.pdf gvfjrmeng.ps Proceedings of 5th Panhellenic Logic Symposium (2005). pls5.ps The effect of Markov's Principle on the intuitionistic continuum, Proceedings of Oberwolfach Proof Theory week (April 2005).

32. Book A Short Introduction To Intuitionistic Logic, General Titles On Mathematics book general titles on mathematics Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of http://www.lavoisier.fr/notice/gbJYOK62XMKXCO2O.html

Search on All Book CD-Rom eBook Software The french leading professional bookseller Description Approximate price A short introduction to intuitionistic logic Author(s) : MINTS Publication date : 11-2000 Language : ENGLISH 138p. Paperback Status : In Print (Delivery time : 10 days) Description Summary Introduction. I: Intuitionistic Propositional Logic. 1. Preliminaries. 2. Natural Deduction for Propositional Logic. 3. Negative Translation: Glivenko's Theorem. 4. Program Interpretation of Intuitionistic Logic. 5. Computations with Deductions. 6. Coherence Theorem. 7. Kripke Models. 8. Gentzen-type Propositional System LJpm. 9. Topological Completeness. 10. Proof-Search. 11. System LJpm. 12. Interpolation Theorem. II: Intuitionistic Predicate Logic. 13. Natural Deduction System NJ. 14. Kripke Models for Predicate Logic. 15. Systems LJm, LJ. 16. Proof-Search in Predicate Logic. References. Index. Subject areas covered: Mathematics and physics General titles on mathematics New search Your basket Information New titles BiblioAlerts E-books Customer services Open an account Ordering non-listed items Order tracking Help Lavoisier.fr

33. Springer Online Reference Works A set of methods for proving statements which are valid from the point of view of intuitionism. In a narrow sense, Intuitionistic logic means the http://eom.springer.de/I/i052150.htm

Encyclopaedia of Mathematics I Article referred from Article refers to Intuitionistic logic A set of methods for proving statements which are valid from the point of view of intuitionism . In a narrow sense, intuitionistic logic means the intuitionistic predicate calculus which was formulated by A. Heyting in . This calculus, which is usually formulated in the language of predicate calculus , contains all axiom schemes and derivation rules of intuitionistic propositional calculus (but for the language of predicate calculus), and, in addition, the following quantifier axioms and derivation rules. The axioms: and the two derivation rules Here is a variable, is a term of the language and the formula does not contain as a parameter. The completeness of intuitionistic predicate calculus depends on the semantic principles that underlie the intuitionistic theory under consideration. Thus, Markov's constructive selection principle in the form is not derivable in intuitionistic predicate calculus, but is considered true in certain approaches to constructivism. Another example of this nature is the so-called uniformization principle which is true in some intuitionistic interpretations and is at the same time incompatible with the constructive selection principle within the framework of the arithmetic theory supplemented by the Church thesis . The examples given show that there is no complete intuitionistic predicate calculus that could serve as a logical basis for all the intuitionistic theories in use. Depending on the semantic conventions, essentially different variants of intuitionistic logic are possible. The development of the intuitionistic theory of derivation (cf.

34. Talks.cam : Intuitionistic Logic Intuitionistic logic. Add to your list(s) Download to your calendar using vCal. Alexander Gurney (University of Cambridge); Thursday 13 December 2007, http://talks.cam.ac.uk/talk/index/9340

Skip over navigation Access key help University of Cambridge Talks.cam ... Intuitionistic logic Behaviour.register(leftbar_rules) Browse A-Z Log in Cambridge users (raven) Other users No account? Information on Finding a talk Adding a talk Syndicating talks Who we are ... Everything else Intuitionistic logic Add to your list(s) Download to your calendar using vCal Alexander Gurney (University of Cambridge) Thursday 13 December 2007, 11:30 GS15, Computer Laboratory If you have a question about this talk, please contact Alexander Gurney Abstract not available This talk is part of the Logic and Semantics for Dummies series. Tell a friend about this talk: Behaviour.register(tickle_rules); This talk is included in these lists: CURE Featured lists GS15, Computer Laboratory Logic and Semantics for Dummies Note that ex-directory lists are not shown. Other lists Rausing Lecture Evolution and Development Seminar Series Talks at the Institute for Manufacturing Other talks Why Greek vowels aren't boring Enterprise Tuesday 2007/08 - Building a Dream Team Evaluating the performance of laser-Doppler predictions Not Mammoth Steaks Again?! ... Accessibility policy

35. Practical Foundations Of Mathematics In particular, Intuitionistic logic does not save us from any inconsistency (the ability to prove ^) which might arise classically. http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/s18.html

Practical Foundations of Mathematics Paul Taylor Classical and Intuitionistic Logic Mathematical reasoning as commonly practised makes use of two other logical principles, excluded middle and the axiom of choice, which we shall not use in our main development. Classical predicate calculus consists of the rules we have given together with excluded middle. Excluded middle ``Every proposition is either true or false.'' D EFINITION Excluded middle may be expressed as either of omitted prooftree environment omitted prooftree environment which are equivalent in the sense that a a a b b b decidable or complemented (as on the right). In saying that we shall not use excluded middle, beware that we are not affirming its negation f f f f , which is falsity. If we are able to prove neither f f then we remain silent about them Of course there are instances of case analysis even in intuitionism, in particular the properties of finite sets. A recurrent example will be parsing of terms in free algebras, for example a list either is empty or has a head (first element) and tail (Section ) and ( E ) are incorporated to give indirect rules omitted proofbox environment pt omitted proofbox environment known as reductio ad absurdum and tertium non datur (Latin: the third is not given) respectively. Some Real Mathematicians use the former habitually, starting

36. Some Informative Questions About Intuitionistic Logic And Mathematics 2) Can one define in Intuitionistic logic counterparts of the classical connectives so that the resulting translation preserves the consequence relation of http://osdir.com/ml/science.mathematics.fom/2005-11/msg00009.html

var addthis_pub = 'comforteagle'; science.mathematics.fom Top All Lists Date Thread Some informative questions about intuitionistic logic and mathematics Subject Some informative questions about intuitionistic logic and mathematics List-id More with this subject... Current Thread Previous by Date: colour or colours A.R.D.Mathias Next by Date: Re: Mathematical explanation mjmurphy Previous by Thread: Kleene's Philosophy addamo-5tc4TXWwyLM Next by Thread: Re: Some informative questions about intuitionistic logic and mathematics Richard Heck Indexes: Date Thread Top All Lists Recently Viewed: qnx.openqnx.dev... network.tin.bug... hardware.sony.l... text.xml.cocoon... ... advertise var dc_UnitID = 14; var dc_PublisherID = 4576; var dc_AdLinkColor = 'blue'; var dc_adprod='ADL';

37. Classical And Intuitionistic Logic With Kanren ; ; This File Classical and Intuitionistic logic with Kanren ; ; This file illustrates the use of the typechecking relation (file ; ./typeinference.scm) for proving http://okmij.org/ftp/Scheme/logic.scm

38. Papers Dirk Van Dalen 1963. Extension Problems In Intuitionistic Intuitionistic logic, In Handbook of Philosophical logic, III eds. How connected is the Intuitionistic continuum? J Symb logic, 62 11741150. http://www.phil.uu.nl/~dvdalen/papers.htm

Papers Dirk van Dalen Extension problems in intuitionistic plane projective geometry. Dissertation. Amsterdam. Extension problems in intuitionistic plane projective geometry, I and II. Ind Math A note on spread cardinals. Comp Math Fans generated by nondeterministic automata. Zeitschr. f. Mathematische Logik und Grundlagen der Mathematik Reducibility in Intuitionistic Topology. J Symb Logic A note on Some Systems of Lindenmayer. Math.Systems Theory Projections of Lawless Sequences. In (Eds. J. Myhill, A. Kino, R.E. Vesley) Intuitionism and Proof Theorie (Proc. Summer Conference Buffalo 1968), pages 163186, Amsterdam. North-Holland. Independence problems in subsystems of intuitionistic arithmetic. Ind Math Lectures on Intuitionism. In (Eds. A. Mathias, H. Rogers) Proc.Cambridge Summer Conference on Logic . SLNM 337, pages 194, Berlin. Springer Verlag. Logique et theories formelles. Nico, 15: 22. A model for HAS. A topological interpretation of second-order intuitionistic arithmetic with species variables. Fund. Math.

39. ESSLLI 2005 - Introductory Course: Intuitionistic Logic Intuitionistic logic has a historical significance but there is much more than that. There are many applications and insights to be obtained nowadays and http://www.macs.hw.ac.uk/esslli05/giveabs.php?38

40. A Short Introduction To Intuitionistic Logic - Mathematical Logic And Founda...J A Short Introduction to Intuitionistic logic Mathematics. Intuitionistic logic is presented here as part of familiar classical logic which allows http://www.springer.com/west/home/math?SGWID=4-10042-22-33303481-0

41. Avoiding Duplications In Tableau Systems For Intuitionistic Logic And Kuroda Log Both at the propositional and the predicate level, in tableau systems of Intuitionistic logic as well as in the corresponding sequent and natural calculi, http://jigpal.oxfordjournals.org/cgi/content/abstract/5/1/145

@import "/resource/css/hw.css"; @import "/resource/css/igpl.css"; Skip Navigation Oxford Journals Contact Us My Basket ... Volume 5, Number 1 Pp. 145-167 Logic Journal of IGPL 1997 5(1):145-167; doi:10.1093/jigpal/5.1.145 Oxford University Press This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive ... Request Permissions Google Scholar Articles by Miglioli, P Articles by Ornaghi, M Search for Related Content Avoiding duplications in tableau systems for intuitionistic logic and Kuroda logic P Miglioli U Moscato and M Ornaghi Both at the propositional and the predicate level, in tableau systems of intuitionistic logic as well as in the corresponding sequent and natural calculi, the problem arises of reducing as much as possible the duplication of formulas, i.e., the reuse of formulas already used in a proof, in order to single out efficient proof search techniques. This problem has been analyzed

42. Plato.stanford.edu Intuitionistic Logic - StartAid Below is a small excerpt of StartAid members bookmark description, for more information on Intuitionistic logic please visit the original webisite http://www.startaid.com/comment/2452408/Intuitionistic-Logic.html

var WEB_ROOT="http://www.startaid.com/" Intuitionistic Logic SignIn Username: Password: Remember Me Click here to create your own StartAid account! Below is a small excerpt of StartAid members bookmark description, for more information on Intuitionistic Logic please visit the original webisite : http://plato.stanford.edu/entries/logic-intuitionistic ingwhich were used by L. E. J. Brouwer in developing his intuitionisticmathematics, beginning in [1907]. Because these principles also underlyRussian recursive analysis and the constructive analysis of E. Bishopand his followers, intuitionistic logic may be considered the logicalbasis of constructiv For additional, member comments, reviews and information on plato.stanford.edu please we provide them below. Please log in to post a comment 0 Member Comments: Non Members reviews and comments. No reviews have been provided. Be the first to write a review Feel free to post your own review and comment StartAidHome DiscussionBoard AboutUs TermsOfUse ... ContactUs © 2005-2006 StartAid - AllRightsReserved showallcomment('2452408','http://plato.stanford.edu/entries/logic-intuitionistic')

43. CS792: Computational Logic Intuitionistic logic introduces lambdacalculus (the theory on which Lisp, Scheme, and other functional languges are based) as a mechanism for representing http://cs-people.bu.edu/mairson/Courses/cs792/factsheet.html

Computer Science 792 Computational Logic Spring Term, 2000 Course instructor: Harry Mairson ( mairson@cs.bu.edu ), MCS 283, phone 353-8926. Office hours 11am-12pm Tuesday and Friday, and by arrangement. I especially encourage you to communicate with me via electronic mail, for fastest and most reliable responses to your questions. I try to read e-mail every 5 minutes, 24 hours a day. Time and place: Tuesday and Thursday, 9.30-11am, MCS B46. What is this course about? This course is a (non-comprehensive) introduction to topics in logic that are relevant to computer science. Unlike typical logic courses, it stresses computational metaphors: algorithmics and constructive mathematics, computational complexity, and decidability. The basic topics of the course are Propositional logic (6 lectures) First-order logic (5 lectures) Intuitionistic logic (7 lectures) Higher-order logic and realizability (4 lectures) Linear logic (7 lectures) linear logic , a so-called resource-conscious logic; we will discuss the relationship between cut-elimination (proof simplification) in linear logic, and evaluation of programs written in lambda-calculus. Required work: Work for the course will include several problem sets, and some class presentations. Even though I love grading problem sets, I'm going to try to have it done by you on a round-robin basis. Please

44. 2003 Tbilisi Logic Conference Abstracts A prolongation of the Gödel Modal Translation of Intuitionistic logic up to Provability logic an algebraic and topological considerations http://sierra.nmsu.edu/morandi/TbilisiConference/Abstracts.html

45. Intuitionistic Logic - Indopedia, The Indological Knowledgebase Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. http://www.indopedia.org/Intuitionistic_logic.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Logic Logic in computer science Mathematical logic ... Wikipedia Article Intuitionistic logic ज्ञानकोश: - The Indological Knowledgebase Intuitionistic logic , or constructivist logic , is the logic used in mathematical intuitionism and other forms of mathematical constructivism Roughly speaking, "intuitionism" holds that logic and mathematics are "constructive" mental activities. That is, they are not analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs (really, a kind of game). In a stricter sense, intuitionistic logic can be investigated as a very concrete and formal kind of mathematical logic . While it may be argued whether such a formal calculus really captures the philosophical aspects of intuitionism, it has properties which are also quite useful from a practical point of view. Both notions of the term will be considered below.

46. CiteULike: Tag Intuitionistic-logic [8 Articles] posted to regularlogic regular-categories reduction Intuitionistic-logic heyting-categories classical-logic boolean-categories by Scis0000002 on 2007-08-04 http://www.citeulike.org/tag/intuitionistic-logic

Register Log in FAQ CiteULike News Discussion Journals Browse current issues Groups Search groups Tag intuitionistic-logic [8 articles] Recent papers classified by the tag intuitionistic-logic. A Topos Foundation for Theories of Physics: I. Formal Languages for Physics ArXiv Quantum Physics e-prints (March 2007) by A Doering , CJ Isham posted to type-theory topos-theory topos-morphisms toposes ... cartesian-closed-categories by on 2007-07-07 14:51:07 as along with 3 people gpi madhadron A Modular Reduction of Regular Logic to Classical Logic (2001), pp. 221-226. by Ramon Bejar , Reiner Hahnle , Felip Manya posted to regular-logic regular-categories reduction intuitionistic-logic ... boolean-categories by on 2007-08-04 09:43:25 as Disjunctive Quantum Logic in Dynamic Perspective (22 Apr 2002) by Bob Coecke posted to chu-space heyting-algebra intuitionistic-logic lattice ... quantum-logic by on 2006-09-05 15:31:47 as Computability Logic: a formal theory of interaction (10 Dec 2004) by Giorgi Japaridze posted to abstract-state-machines adaptability aixi all-logical-theories ... relativity by on 2006-09-19 16:36:44 as A complete axiomatization of higher-order intuitionistic logic by M Coniglio , C Sernadas posted to axiomatization computability-logic intuitionism intuitionistic-logic by on 2007-03-17 14:08:06 as along with 1 person Constructivity Complete Lattices Represent Complete Heyting Algebras (Or: Quantum Logic With An Intuitionistic Implication) by Bob Coecke posted to unified-concept-theory topos-theory stone-duality quantum-logic ... atomisticity by on 2007-05-09 22:41:14 as

47. Intuitionistic Logic On GlobalSpec GlobalSpec offers a variety of Intuitionistic logic for engineers and through SpecSearch the Intuitionistic logic can be searched for the exact http://semiconductors.globalspec.com/Industrial-Directory/intuitionistic_logic

Free Registration Download Engineering Toolbar GlobalSpec Home Find: Advanced Search >> The Engineering Web Part Number Search Engineering News Application Notes Material Properties Patents Standards changeSearchInfo('products', true, null); Welcome to GlobalSpec! We found this content for: intuitionistic logic Click on a category to narrow your results. Product Alerts Keep current on the latest products, new suppliers, and technical articles of interest to you. ( See Topics All Part Number Search Engineering News ... Standards Product Categories for intuitionistic logic Logic Analyzers (56 companies) Logic analyzers are used to characterize and debug hardware, design and test firmware and software, and perform synthesis integration. Learn more about Logic Analyzers Programmable ... Devices (PLD (135 companies) Programmable logic devices (PLD) are designed with configurable logic and flip-flops linked together with programmable interconnect. PLDs provide specific functions, including device-to-device interfacing, data communication, signal processing, data display, timing and control operations, and almost every other function a system must perform. Programmable logic devices (PLD) are designed with configurable logic and flip-flops linked together with programmable interconnect. PLDs provide specific functions, including device-to-device interfacing, data communication, signal processing.

48. Negation - W3C RIF-WG Wiki Intuitionistic logic is a part of classical logic, that is, all formulas provable Indeed, Intuitionistic negation in constructive logic is definable by http://www.w3.org/2005/rules/wg/wiki/negation

W3C RIF-WG Wiki Search: Login negation FrontPage RecentChanges ... negation Immutable Page Info Attachments More Actions: Raw Text Print View Render as Docbook Delete Cache Check Spelling Like Pages Local Site Map Rename Page Delete Page My Pages Subscribe User Remove Spam Package Pages Negation In the ongoing discussion about monotonic vs. non-monotonic negation (better known as negation as failure), it is often overlooked that not only non-monotonicity is an issue but actually there are several definitions of both monotonic and non-monotonic forms of negation in the literature) with subtle but important differences. On this page we aim to shed light on the "landscape" of different forms of negation and clarification of terminology. This overview is by no means to be understood to be exhaustive, but shall cover and clarify the most prominent forms of negation in the context of logics and rule languages, especially those mentioned in discussions within the RIF working group. For the sake of simplicity we will restrict ourselves to the propositional case although all mentioned logics have first-order extensions. Monotonic Negation First of all, we treat the most important forms of negation in non-monotonic logics. Monotonicity meas that whenever some sentence φ is provable from a theory T, φ will still be provable from any superset of T.

49. EWSCS 2004/EATTK 2004: Sergei Artemov, Abstract According to Brouwer, the truth in Intuitionistic logic means The ideas of BHK led to a discovery of computational semantics of Intuitionistic logic, http://cs.ioc.ee/yik/schools/win2004/artemov.php

CIDEC Estonian Winter Schools in Computer Science Eesti arvutiteaduse talvekoolid EWSCS 2004 ... EATTK 2004 th Estonian Winter School in Computer Science (EWSCS) IX Eesti Arvutiteaduse Talvekool (EATTK) Palmse, Estonia February 29 - March 5, 2004 Sergei Artemov Graduate Center City University of New York USA Proof Polynomials Prerequisites Basic knowledge of undergraduate logic. Abstract According to Brouwer, the truth in intuitionistic logic means provability. On this basis Heyting and Kolmogorov introduced an informal Brouwer-Heyting-Kolmogorov (BHK) semantics for intuitionistic logic. The ideas of BHK led to a discovery of computational semantics of intuitionistic logic, in particular, realizability semantics and Curry-Howard isomorphism of natural derivations and typed lambda-terms. However, despite many efforts the original semantics of intuitionistic logic as logic of proofs did not meet, until recently, an exact mathematical formulation. Gödel in 1933 suggested a mechanism based on modal logic S4 connecting classical provability (represented as S4-modality) to intuitionistic logic. This did not solve the BHK problem, since S4 itself was left without an exact provability model. In 1938 Gödel suggested using the original BHK format of proof carrying formulas to build a provability model of S4. This Gödel's program was accomplished in 1995 when proof polynomials and the Logic of Proofs (LP) were discovered, shown to enjoy a natural provability semantics, and to be able of realizing all S4-modalities by proof polynomials. The Logic of Proofs became both an explicit counterpart of modal logic and a reflexive combinatory logic (reflexive lambda-calculus) thus providing a uniform mathematical model of knowledge and computability.

50. Intuitionistic Logic - Explanation-Guide.info - For Information, Definition, Mea Intuitionistic logic as a paradigm for logical reasoning,Intuitionistic logic as a formal logical calculus,Heyting algebra semantics,Kripke semantics. http://explanation-guide.info/meaning/Intuitionistic-logic.html

Monday 24th December UTC Intuitionistic logic: Meaning (information, definition, explanation, facts) Intuitionistic logic , or constructivist logic , is the logic used in mathematical intuitionism and other forms of mathematical constructivism Roughly speaking, 'intuitionism' holds that logic and mathematics are 'constructive' mental activities. That is, they are not analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs (really, a kind of game). In a stricter sense, intuitionistic logic can be investigated as a very concrete and formal kind of mathematical logic . While it may be argued whether such a formal calculus really captures the philosophical aspects of intuitionism, it has properties which are also quite useful from a practical point of view. Both notions of the term will be considered below. Intuitionistic logic as a paradigm for logical reasoning In intuitionistic logic, epistemologically unclear steps in proofs are forbidden. In classical logic, a formula (say

51. Intuitionistic Logic - Definitions From Dictionary.com Definitions of Intuitionistic logic at Dictionary.com. http://dictionary.reference.com/browse/intuitionistic logic

var pid = 311241; var nid = 311283; var mid = 679788; var word = 'intuitionistic%20logic'; SafeAddOnload(init_near); Premium Content Register Log In Help ... The Web Advertisement 1 result for: intuitionistic logic Browse Nearby Entries intuitional intuitionalism intuitionalist ... intuitionist logic intuitionistic logic intuitionless intuitions intuitive intuitive feeling ... Share This intuitionistic logic logic, mathematics Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle ); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of

52. Intuitionistic Logic Definition Of Intuitionistic Logic In The Free Online Encyc Encyclopedia article about Intuitionistic logic. Information about Intuitionistic logic in the Columbia Encyclopedia, Computer Desktop Encyclopedia, http://encyclopedia2.thefreedictionary.com/Intuitionistic logic

Domain='thefreedictionary.com' word='intuitionistic logic' Printer Friendly 728,490,814 visitors served. TheFreeDictionary Google Word / Article Starts with Ends with Text subscription: Dictionary/ thesaurus Medical dictionary Legal dictionary Financial dictionary Acronyms Idioms Encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia intuitionistic logic Also found in: Wikipedia 0.04 sec. (logic, mathematics) intuitionistic logic - Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of

53. Intuitionistic Logic - Definition Of Intuitionistic Logic By Webster's Online Di Intuitionistic logic explanation. Definition of Intuitionistic logic is provided by 1913 Webster s Dictionary, WordNet Lexical Database, Dictionary of http://www.webster-dictionary.org/definition/intuitionistic logic

Word: Browse Intrusionist Intrusive Intrusive rocks Intrusive Testing ... intuitionist logic intuitionistic logic intuitionistic probability Intuitive intuitive feeling Intuitively ... Intussuscepted intuitionistic logic Advertisement (logic, mathematics) intuitionistic logic Brouwer s foundational theory ... Online Dictionary Home

54. Intuitionistic Logic - Computing Reference - ELook.org Information and links on Intuitionistic logic. intuitionism, classical logic constructive intuitionism Intuitionistic logic Intuitionistic probability http://www.elook.org/computing/intuitionistic-logic.htm

eLook Home eLook Computing Reference Search Computing Reference By Letter: Non-alphabet A B C ... Email this page to a friend Intuitionistic logic Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B. In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic). History (http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html). Terms Containing intuitionistic logic Intrinsics Intrusion Countermeasure Electronics Intrusive Testing Intuition ... Contact

55. Papers By Christoph Kreitz Automated Deduction Deciding Intuitionistic Propositional logic via Translation into Classical logic A Constructively Adequate Refutation System for Intuitionistic logic http://www.cs.cornell.edu/Info/People/kreitz/research-deduction.html

Automated Deduction: Proof Systems and Inference Techniques My research in the area of automated deduction aims at the development automatic proof search procedures for classical and non-classical logics. Together with former students from the Technical University of Darmstadt I work on proof search methods based on matrix-characterizations of logical validity, a very compact representation of the search space. We have developed a uniform proof search procedure for classical logic, intuitionistic logic, various modal logics, fragments of linear logic, and induction. We have also developed a uniform algorithm for transforming the machine-found matrix proofs into sequent proofs, which enables us guide the development of proofs in interactive assistants such as Nuprl. Most of my publications in the area of Automated Deduction are available online in postscript or PDF format. An abstract with a complete reference and corresponding bibtex entry is also provided. Automated deduction tools can be downloaded from this page A list of related web pages is given to simplify cross references.

56. Intuitionistic Logic - Definition Of Intuitionistic Logic By The Online Dictiona Definition of Intuitionistic logic in the Online Dictionary. Multiple meanings, detailed information and synonyms for Intuitionistic logic. http://onlinedictionary.datasegment.com/word/intuitionistic logic

Online Dictionary I : intuitionistic logic intuitionistic logic 1 definition found intuitionistic logic Free On-line Dictionary of Computing (26 May 2007) : excluded middle ); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A). This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic). History (http://britanica.com/bcom/eb/article/3/0,5716,118173+14+109826,00.html) . (2001-03-18)

57. Intuitionistic Logic - Spock Search Kurt Gödel, Arend Heyting, Haskell Curry, Neil Tennant, Dick de Jongh, Andrey Kolmogorov and other people matching \ http://www.spock.com/q/intuitionistic-logic

Processing (could take a few minutes)... You should enable javascript to use Spock Name or Email: Tags: Example: senator republican married Location: Example: San Francisco, CA Age: any to any male female any Must have picture! Click here to see where people you know are on the web Login Sign up Grid ... Kurt G¶del male, deceased Logician incompleteness theorems G¶del numbering incompleteness ... Add tag Kurt G¶del (April 28, 1906 Br¼nn, Austria-Hungary (now Brno, Czech Republic) - January 14, 1978 Princeton, New Jersey) was an Austrian American ma... See: Tags (46) Pictures (1) Related People (1) News Web: plus.maths.org biographyshelf Wikipedia abc.net.au ... Arend Heyting male, deceased L.E.J. Brouwer dutch Logician mathematician ... Add tag Arend Heyting (May 9, 1898 - July 9, 1980) was a Dutch mathematician and logician. He was a student of L.E.J. Brouwer, and did much to put... See: Tags (9) Pictures (2) Related People (0) News Web: Wikipedia Haskell Curry male, deceased

58. Computer Science: Publication: Proof Search Issues In Some Non-Classical Logics Chapter 5 is a short investigation of embedding Intuitionistic logic in A new embedding of Intuitionistic logic in Intuitionistic Linear logic is given. http://www.cs.kent.ac.uk/pubs/1998/946/

Skip to main section Search Site Map Contact ... University of Kent Computing at Kent Home Research People Undergrad ... Skip to content Research Research home Events Groups Projects ... Seminars Related Links Becoming a postgraduate Conferences People University Links Research at Kent Proof Search Issues in Some Non-Classical Logics J. M. Howe PhD thesis, University of St Andrews, December 1998 Available as University of St Andrews Research Report CS/99/1. Abstract This thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investigation into issues in proof search in both these senses for some non-classical logics. Gentzen systems are well suited for use in proof search in both senses. The rules of Gentzen sequent calculi are such that implementations can be directed by the top level syntax of sequents, unlike other logical calculi such as natural deduction. All the calculi for proof search in this thesis are Gentzen sequent calculi. Chapter 5 is a short investigation of embedding intuitionistic logic in Intuitionistic Linear Logic. A new embedding of intuitionistic logic in Intuitionistic Linear Logic is given. For the hereditary Harrop fragment of intuitionistic logic, this embedding induces the calculus MJ for intuitionistic logic.