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	Intuitionistic Logic (Stanford Encyclopedia of Philosophy)
		Intuitionistic logic encompasses the principles of logical reasoning which were used by L. Brouwer in developing his intuitionistic mathematics, beginning in [1907].
		Intuitionistic arithmetic can consistently be extended by axioms (such as Church's Thesis) which contradict classical arithmetic, enabling the formal study of recursive mathematics.
		While identity can of course be added to intuitionistic logic, for applications (e.g., to arithmetic) the equality symbol is generally treated as a distinguished predicate constant satisfying nonlogical axioms (e.g., the primitive recursive definitions of addition and multiplication) in addition to reflexivity, symmetry and transitivity.
	plato.stanford.edu /entries/logic-intuitionistic (6581 words)

	NationMaster - Encyclopedia: Intuitionistic logic (Site not responding. Last check: )
		Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism.
		The syntax of formulæ of intuitionistic logic is similar to propositional logic or first-order logic.
		A corresponding theorem is true for intuitionistic logic, but instead of assigning each formula a value from a Boolean algebra, one uses values from a Heyting algebra, of which Boolean algebras are a special case.
	www.nationmaster.com /encyclopedia/Intuitionistic_logic (2565 words)

	Encyclopedia :: encyclopedia : Intuitionistic logic (Site not responding. Last check: )
		Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism.
		The syntax of formulæ of intuitionistic logic is similar to propositional logic or first-order logic.
		A corresponding theorem is true for intuitionistic logic, but instead of assigning each formula a value from a Boolean algebra, one uses values from a Heyting algebra, of which Boolean algebras are a special case.
	www.hallencyclopedia.com /topic/Intuitionistic_logic.html (1252 words)

	Intuitionistic logic
		The thought behind this is that the validity of a mental construct is dependent upon its coherence with its context (the mind).
		In classical logic, ¬P asserts that P is false; in intuitionistic logic, ¬P asserts that P is refutable (i.e., that there is a proof that there is no proof of P).
		With these assignments, intuitionistically valid formulas are precisely those that are assigned the value of the entire plane.
	www.brainyencyclopedia.com /encyclopedia/i/in/intuitionistic_logic.html (1400 words)

	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 programme of intuitionism.
		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.
		With these assignments, intuitionistically valid formulas are precisely those that are assigned the value of the entire plane.
	en.wikipedia.org /wiki/Intuitionistic_logic (1119 words)

	[No title]
		Having spent the greater part of my career doing intuitionistic mathematics, while continuing to do classical mathematics, I have come to feel that most comparisons of these two approaches to mathematics miss the essential point: intuitionism, in its simplest form, is a generalization of classical mathematics that accomodates both classical and computational models.
		Intuitionistic analysis, unlike recursive analysis, is not the study of constructive functions of constructive real numbers.
		But any theorem in intuitionistic analysis is a theorem in realist analysis, interpreted in terms of realist functions of realist real numbers; and an intuitionistic proof is an acceptable proof to a realist mathematician, although he may not understand why some of the moves are made.
	www.math.fau.edu /Richman/Docs/philmath.html (1926 words)

	Good Math, Bad Math : Intuitionistic Logic (partial rerun)
		Intuitionistic logic is a variation of predicate logic which is built on the idea that there should be a stronger notion of "truth" in logic: that the strict categorization of all statements in classical logic as either true or false is too strong.
		One way to think of intuitionistic logic is to think of it as if there were actually three values that can be assigned to a predicate: it can be in one of two definite states (proved true or proved false) or it can be in an indefinite state (unproven).
		I was having trouble reconciling this with the conventional wisdom that in intuitionistic mathematics "A or B" is true only if you have a proof of either A or B. The solution to the paradox is that while synthetic differential geometry uses intuitionistic logic, it's not philosophically intuitionistic.
	scienceblogs.com /goodmath/2007/03/intuitionistic_logic_partial_r_1.php (1843 words)

	Intuitionistic Logic (Stanford Encyclopedia of Philosophy/Spring 2004 Edition)
		Bishop and his followers, intuitionistic logic may be considered the logical basis of constructive mathematics.
		Anticipating applications (for example to intuitionistic arithmetic) we use s,t as metavariables for terms; in the case of pure predicate logic, terms are simply individual variables.
		Thus to show that (¬∀x¬P(x) → ∃xP(x)) is intuitionistically unprovable, it is enough to consider a Kripke structure with K = {k, k′}, k < k′, D(k) = D(k′) = {0}, T(P,k) empty but T(P,k′) = {0}.
	www.seop.leeds.ac.uk /archives/spr2004/entries/logic-intuitionistic (6049 words)

	Intuitionistic Logic
		Intuitionists conclude that the meaning of a statement resides not in its truth conditions but in the means of proof or verification.
		Hence intuitionistic logic can be used for program synthesis.
		However, proof search in intuitionistic logic is more difficult than in first-order classsical logic; there are no normal forms like conjunctive normal form or prenex form and Skolemization cannot, in general, be applied to intuitionistic formulas.
	cs.wwc.edu /~aabyan/Logic/Intuitionistic.html (502 words)

	Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator. Part I (Site not responding. Last check: )
		Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator.
		In this paper, we develop intuitionistic propositional calculus IPC in the extended language with single modal operator.
		In the forthcoming Part II of this paper, we shall prove, among others, a number of intuitionistically valid formulas with negation.
	mizar.org /JFM/Vol15/intpro_1.html (209 words)

	Article: Conputational content, intuitionistic proofs (Site not responding. Last check: )
		The aim of this paper is to show that the constructive character of intuitionistic logic manifests itself not only on the level of computability but, in case of the propositional fragment, also on the level of polynomial time computability.
		Recent progress in proof complexity of propositional logic, which concerns various proof systems, suggest that the study of the complexity of intuitionistic propositional proofs may be a fruitful area.
		Such theorems enable one to extract a boolean circuit from a proof; the size of the circuit is polynomial in the size of the proof.
	math.ucsd.edu /~sbuss/ResearchWeb/intuitionisticDP2/index.html (349 words)

	CS 611: Intuitionistic logic and the Halting Problem (Site not responding. Last check: )
		[Intuitionistic logic, intuitionistic logic at FOLDOC] Our discussions of a "Turing machine either halts or it doesn't, but I don't know which one" has lead to some disagreements of the form "yeah, but if you don't know which one then you don't know that it either halts or it doesn't.
		In intuitionistic logic, you don't get A \/ ~A as an axiom (like you do in classical logic, which is the logic we all learned).
		In intuitionistic logic, you get A \/ ~A if you can justify, or prove, A or you can justify, or prove, ~A. Until you have a proof of either A or ~A you only know that A \/ ~A is "undetermined." The language in the above link parallels this discussion very closely.
	lal.cs.byu.edu /cs611/archive/000213.html (219 words)

	Intuitionistic Logic -- from Wolfram MathWorld
		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.
		Intuitionistic predicate logic has the existence property: If is a formula without free variables, and it is provable in intuitionistic predicate logic, then there is term
	mathworld.wolfram.com /IntuitionisticLogic.html (320 words)

	Some benchmark formulae for intuitionistic propositional logic
		There, however, the organisation was (a) a wider range of benchmarks; (b) a special interest in experimenting with the speedups, if any, gained with a parallel algorithm and (c) little consideration of the range of values n for which the n^th formula could be quickly decided.
		The same work comments that "Experience suggests that decision procedures for intuitionistic propositional logic are very much more sensitive to the exact formulation of a problem than classical algorithms, and it is probably difficult to justify the choice of any particular set of benchmarks".
		which is intuitionistically provable, but is (intended as) quite a tough exercise for students to prove by natural deduction.
	www-theory.dcs.st-and.ac.uk /~rd/logic/marks.html (2462 words)

	I P M - Homepage
		Intuitionistic logic is obtained by dropping the principle of excluded middle $A\vee\neg A$ from classical logic.
		Kripke semantics for intuitionistic logic was invented by Saul Kripke in 1965.
		Any intuitionistic theory is sound and complete with respect to its Kripke models.
	www.ipm.ac.ir /IPM/activities/ViewProgramInfo.jsp?PTID=206 (507 words)

	Intuitionistic type theory - Wikipedia, the free encyclopedia
		Intuitionistic type theory, or constructive type theory, or Martin-Löf type theory or just Type Theory is a logical system and a set theory based on the principles of mathematical constructivism.
		Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs.
		This extension is not universally accepted by Intuitionists since it allows impredicative, i.e.
	en.wikipedia.org /wiki/Intuitionistic_type_theory (1324 words)

	4. On Classical and Intuitionistic Theories
		Namely, the simple fact that, for any natural number n, there exists a finite set S (in fact, infinitely many sets) such that the simplest equation providing a Diophantine representation of S is more complex than n, can easily be proved in most classical theories of arithmetic, e.g.
		Note, on the other hand, that the limiting constant of a formalized arithmetical theory is the same whether it uses intuitionistic or classical logic.
		Strictly speaking, one has to grant that the complexity of a Diophantine equation is a metamathematical property; still, I would argue that it is a fairly harmless and elementary one, compared to, say, the notions of provability and consistency, which are more often used for such unprovability results.
	www.hf.uio.no /ifikk/filosofi/njpl/vol2no2/diophantine/node4.html (546 words)

	ILTP Library - Benchmarking Theorem Provers for 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.
		If these problems are of interest for testing and benchmarking classical theorem provers as well, we would suggest to submit them to the TPTP library in order to make them available to people involved in developing ATP systems for classical logic as well.
	www.cs.uni-potsdam.de /ti/iltp (387 words)

	LICS'O5 - IMLA'05 (Site not responding. Last check: )
		Practical issues center around the question which modal connectives with associated laws or proof rules capture computational phenomena accurately and at the right level of abstraction.
		The workshop continues a series of previous LICS-affiliated workshops, entitled "Intuitionistic Modal Logic and Applications (IMLA)" which were held as part of FLoC'99, Trento, Italy and of FLoC2002, Copenhagen, Denmark.
		Yde Venema, University of Amsterdam - Intuitionistic Modal Logic: observations from algebra and duality
	www.cs.cmu.edu /~fp/imla05 (391 words)

	AMCA: Interpolation Theorems for Intuitionistic Predicate Logic by Grigori Mints
		Craig interpolation theorem (which holds for intuitionistic logic) implies that the derivability of \Gamma, \Gamma' ===> \Delta' implies existence of a Craig interpolant I in the common language of \Gamma and \Gamma' ===> \Delta' such that both \Gamma ===> I and I, \Gamma' ===> \Delta' are derivable.
		For intuitionistic logic the partition ;C ===> C; is a counterexample.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/c/s/24.htm (640 words)

	Intuitionistic Fuzzy PostgreSQL: Project Home Page
		Welcome to the Intuitionistic Fuzzy PostgreSQL Project Home Page
		The Intuitionistic Fuzzy PostgreSQLproject is a PostgreSQL Community project that is a part of the pgFoundry.
		The pgFoundry page for the project is at http://pgfoundry.org/projects/ifpg, where you can find downloads, documentation, bug reports, mailing lists, and a whole lot more.
	ifpg.projects.postgresql.org (60 words)

	Citations: Logic Programming in Intuitionistic Linear Logic: Theory - Hodas (ResearchIndex)
		The output context # 2 of G 1, which is not used by G 1, is given as input context of G 2 to....
		While the speci cation of Ob in L given in the previous section could directly be implemented in Forum, an implementation of the Forum system is still subject of study (cf.
		implements an extension of the rst order syntax of an intuitionistic fragment of Forum (called Lolli) that provides the sort of higher order features distinctive of L: speci cally it allows variables of type o to occur nested within terms and in formula position, and it provides a uni cation.
	citeseer.ist.psu.edu /context/1486/0 (1528 words)

	2nd CFP: Intuitionistic Modal Logic and Applications
		The intuitionistic and the modal frameworks are usually investigated separately.
		However, a growing body of published work, stimulated by theoretical considerations and fed by various applications in Computer Science, shows that both paradigms may fruitfully be merged.
		Intuitionistic modal logic (IML) and modal type theory (MTT) can exploit both the proof-theoretic strengths of intuitionistic logic and the model-theoretic features of modal logics.
	www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg00096.html (441 words)

	D:\j\grteach\resource\newtemp.htm
		Students who did not take M04N last year will find this half-course to be self-contained, as it begins with a brief review of intuitionistic logic using excerpts from last year's notes.
		Constructive mathematical reasoning is based on intuitionistic logic, which can be described loosely as classical logic with the Aristotelian law [A or not A] weakened to the principle that a contradiction implies every sentence.
		b) Intuitionistic propositional and predicate logic as sublogics of the corresponding classical logics.
	www.math.ucla.edu /~joan/m05n (581 words)

	Intuitionistic Logic (Stanford Encyclopedia of Philosophy/Winter 1999 Edition)
		Intuitionistic systems have inspired a variety of interpretations, including Beth's tableaus, Rasiowa and Sikorski's topological models, and Kleene's recursive realizabilities.
		k' and k forces A then k' forces A. Kripke's Soundness and Completeness Theorems establish that a sentence of L is provable in intuitionistic predicate logic if and only if it is forced by every node of every Kripke structure.
		xP(x)) is intuitionistically unprovable, it is enough to consider a Kripke structure with K = {k, k'}, k
	www.science.uva.nl /~seop/archives/win1999/entries/logic-intuitionistic (1533 words)

	Porgi (Site not responding. Last check: )
		Porgi is a Proof-Or-Refutation Generator for Intuitionistic propositional logic.
		Given a sequent, Porgi either finds a minimally sized, normal natural deduction of the sequent, or it finds a "small", tree-based Kripke countermodel of the sequent.
		Kripke: a countermodel checker for intuitionistic propositional logic
	www.cis.ksu.edu /~allen/porgi.html (161 words)

	Intuitionistic Zermelo-Fraenkel Set Theory in Coq (Site not responding. Last check: )
		This development contains the set-as-pointed-graph interpretation of Intuitionistic Zermelo Fraenkel set theory in system F_omega.2++ (F_omega + one extra universe + intuitionistic choice operator), which is described in chapter 9 of the author's PhD thesis (for IZ) and in the author's CSL'03 paper (for the extension IZ -> IZF).
		Intuitionistic Zermelo-Fraenkel set theory in Coq ================================================ These Coq-files contain the set-as-pointed graph interpretation of Intuitionistic Zermelo Fraenkel set theory in type theory, which is described in chapter 9 of the author's PhD thesis (for IZ) and in the author's CSL'03 paper (for the extension IZ -> IZF).
		The corresponding proofs rely on some extra-axioms that define the Intuitionistic version of Hilbert's choice operator, such as described in the author's LICS'03 submitted paper.
	pauillac.inria.fr /coq/contribs/IZF-in-coq.html (207 words)

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