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Topic: Kripke semantics

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	Kripke semantics - Wikipedia, the free encyclopedia
		Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems, created in late 1950's and early 1960's by Saul Kripke.
		The discovery of Kripke semantics was a major breakthrough in the development of non-classical logics, as the model theory of such logics was virtually nonexistent before Kripke.
		Kripke semantics for the intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different definition of satisfaction.
	en.wikipedia.org /wiki/Kripke_model (2700 words)

	HAHN
		As for the fact that the disambiguation is itself pragmatic, an argument is needed that it is, therefore, irrelevant to semantics and not on a par with, say, the distinction between using "this" as a pronoun of laziness and using it as an anaphoric pronoun.
		Saul Kripke's article "Speaker's Reference and Semantic Reference" [1977] is often cited approvingly and included in anthologies both for it's deflationary account of Keith Donnellan's seminal but enigmatic distinction between referential and attributive uses of definite descriptions [1966], and for the distinction promised by the article's title in which the critical account is grounded.
		I believe that Kripke's interpretation of Donnellan's distinction is mistaken, the arguments given in the paper inadequate, and the distinction between speaker's and semantic reference too crude and thus both uninteresting in itself and irrelevant to the referential/attributive distinction.
	nb.vse.cz /kfil/elogos/logpoint/94-3/NHAHN.htm (5260 words)

	DIRECT, RIGID DESIGNATION AND A POSTERIORI
		Kripke notes that the distinction between the two cases is not due to a semantic ambiguity of the definite description, but is a pragmatic distinction dependent on the speech acts.
		Kripke believes the former procedure is a case of a priori knowledge and the latter a case of a posteriori knowledge.
		Kripke’s [1971] and [1972] reiterate Plantinga’s [1970] thesis that the metaphysical distinction between necessity and possibility is not equivalent to the epistemological distinction between a priori and a posteriori.
	www.qsmithwmu.com /direct,_rigid_designation_and_a_posteriori.htm (15989 words)

	Semantics (Site not responding. Last check: 2007-10-14)
		The concept of semantics or meaning is illustrated in Figure 1 where an element of a language is mapped to an object in some structure and it is this mapping or association that provides the meaning.
		In logic, there are three equivalent approaches to semantics, boolean semantics using valuation functions which map formulas to true or false, Tarskian semantics which interprets formulas in terms of correspondence with objects in a structure, and Herbrand semantics which let formulas stand for themselves.
		A fourth approach, Kripke semantics, is used to provide semantics for modal logics and is often called possible world semantics.
	moonbase.wwc.edu /~aabyan/Logic/semantics.html (2618 words)

	Bienvenue dans Adobe GoLive 6
		Relational semantics has gained the place of one of the mainstay semantics for exploring mathematical properties of various formal languages.
		It was shown that modal logics the semantics of which can be represented in the so-called guarded fragment of first-order are all decidable.
		The aim of this tutorial is to introduce the basics of relational semantics and give participants a taste of the plethora of its uses in modern logic.
	www.uni-log.org /kripke.html (475 words)

	Laws, Facts, and Contexts
		Veltman (1996) characterized dynamic semantics by the slogan "You know the meaning of a sentence if you know the change it brings about in the information state of anyone who accepts the news conveyed by it." Dynamic semantics is complementary to Hintikka's game-theoretical semantics and Peirce's endoporeutic.
		In terms of Dunn's semantics, an obligation is a proposition used as a law that determines a certain kind of behavior.
		Kripke, Saul A. (1963) "Semantical analysis of modal logic I," Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9, 67-96.
	www.jfsowa.com /pubs/laws.htm (13712 words)

	Re: SUO: Model theory for modal logics (via CobWeb/3.1 planetlab5.csail.mit.edu) (Site not responding. Last check: 2007-10-14)
		It is an improvement at least in the sense that it generalizes Kripke's semantics and does a bit of work towards spelling out a richer notion of laws.
		And a Kripke model is just essentially the case where L is the set of logical truths and is fixed across all worlds.
		Bottom line: (i) Formally, Dunn's semantics is a robust and intuitively well-grounded generalization of Kripke semantics.
	suo.ieee.org.cob-web.org:8888 /email/msg10546.html (425 words)

	Review of New Theory of Reference
		Smith, Soames contended, had done Kripke "a grave injustice", written as if Kripke had "appropriated the major views expressed in Naming and Necessity from Marcus while denying her proper credit, and suggests that it is a scandal that the rest of the profession was thereby duped" (p.
		Comparing Kanger's and Kripke's semantics for modal logic, Lindström finds that Kanger's semantics is adequate for the notion of logical necessity and that Kripke's adequately captures a form of metaphysical necessity, but that neither semantics is capable of adequately handing the notion captured by the other.
		Another important part of the overall picture is, of course, the development of possible worlds logic, which in the hands of Hintikka, Kripke and others eventually proved to be a particularly effective device for exposing logical form and viewing the inner workings of analytic philosophy's brave new logic.
	perso.wanadoo.fr /rancho.pancho/Marcus.htm (1359 words)

	BI
		In addition, we propose a new resource semantics by considering a partially defined monoid, which generalizes the semantics of BI pointer logic and is complete for BI.
		This semantics may be motivated from a basic model of the notion of resource.
		As consequences of the relationships between semantics of BI and resource tableaux, we prove two strong new results for propositional BI: its decidability and the finite model property with respect to topological semantics.
	www.cs.bath.ac.uk /~pym/BI.html (1338 words)

	Thinking About Thought: Consciousness, Life and Meaning
		Kripke defined modality through the notion of possible worlds: a property is necessary if it is true in all worlds, a property is possible if it is true in at least one world.
		The advantage of Kripke's semantics is that it can interpret sentences that are not extensional (that do not satisfy Leibniz's law), such as those that employ opaque contexts (to know, to believe, to think) and those that employ modal operators.
		Kripke rejects the view that either proper or common nouns are associated with properties that serve to select their referents.
	www.thymos.com /tat/meaning.html (6637 words)

	[CL] Re: Some comments on future directions
		Enrico, That's true: EF> But you DON'T have specialistic semantics builtin in CL. You need a context mechanism, in which the modalities are axiomatized at the metalevel.
		My proposal is (a), but to dump Kripke semantics.
		Kripke had a brilliant idea in 1963, from which we all learned a lot.
	grimpeur.tamu.edu /pipermail/cl/2004-May/000074.html (453 words)

	[CL] Re: Some comments on future directions
		I was recommending Dunn's semantics, which uses two levels of FOL: pure FOL at the object level, and pure FOL at the metalevel for axiomatizing the object level.
		I believe that Dunn's semantics provides what you are asking for with a much simpler and more general structure.
		With Dunn's semantics, you have one system of logic, and you add whatever axioms you need for only those verbs that occur in your application.
	grimpeur.tamu.edu /pipermail/cl/2004-May/000079.html (968 words)

	Kripke semantics (Site not responding. Last check: 2007-10-14)
		Kripke semantics are also called possible world semantics.
		Kripke semantics are used in modal logics (See Chapter
		Linear time temporal logic is an example of a logic that uses multiple world semantics.
	cs.wwc.edu /~aabyan/CII/BOOK/book/node92.html (283 words)

	Disjunctive Logic Programs with Negation (Site not responding. Last check: 2007-10-14)
		This is mainly because the additional expressive power of disjunctive logic programs significantly simplifies the problem of modeling disjunctive statements of various nonmonotonic formalisms in the framework of logic programming, and consequently facilitates the use of logic programming as an inference engine for nonmonotonic reasoning.
		However, logic programming semantics have rarely been characterized in terms of Kripke structures, which is quite unusual.
		The main reason, we believe, is that the Kripke structure, as with any other model theoretical tools, is an ideal tool for capturing monotonic semantics of logic of knowledge and belief but it has inherent difficulty in characterizing negative introspection, which forms the basis for default reasoning.
	www.cs.ualberta.ca /~yuan/lp.html (189 words)

	Semantics for normal modal logic: Kripke models
		Normal modal logics can be given a nice semantics by means of Kripke models, also known as possible worlds semantics.
		Probably the most important reason for the popularity of possible-worlds semantics is that common modal axioms correspond exactly to certain algebraic properties of Kripke models in the following sense: an axiom is valid in a model
		In the following theorem, a Kripke model is said to be reflexive iff its accessibility relation is reflexive, and so on.
	www.informatik.uni-leipzig.de /~duc/Thesis/node50.html (162 words)

	Laws, Facts, and Contexts
		Leibniz's intuition that necessity corresponds to truth in all possible worlds enabled Kripke to define a rigorous model theory for several axiomatizations of modal logic.
		Unfortunately, Kripke's model structures lead to a combinatorial explosion when they are extended to all the varieties of modality and intentionality that people routinely use in ordinary language.
		As an alternative, any semantics based on possible worlds can be replaced by a simpler and more easily generalizable approach based on Dunn's semantics of laws and facts and a theory of contexts based on the ideas of Peirce and McCarthy.
	www.jfsowa.com /talks/laws.htm (1211 words)

	Saul Kripke - Wikipedia, the free encyclopedia
		During his sophomore year at Harvard, Kripke taught a graduate level logic course at nearby MIT.
		The real significance of "Kripkenstein" was to give a clear statement for the idea that there is no fact in virtue of which a word has its meaning; this "meaning skepticism" generated a large secondary literature.
		In late January 2006, Kripke attended a conference celebrating his 65th birthday and work at the Graduate Center of the City University of New York, and delivered a 70-minute talk on "The First Person", discussing the meaning and reference of the pronoun "I".
	en.wikipedia.org /wiki/Saul_Kripke (1592 words)

	Workshop Semantics and Meanings - Program (Site not responding. Last check: 2007-10-14)
		In modern language, it is required to ensure the meaning of theoretical a priori terms and the truth conditions of theoretical a priori judgments, philosophic as well as scientific, in the domain of interpretation constituted by objects of possible representational experience.
		Is shows, in a schematic manner, how are raised and answered questions about the possibility of synthetic judgments a priori of doctrines of morals, esthetics, of law, of virtue and of history, especial attention being given to the multiplicity of domains of interpretation and the subsequent modification of the concept of objective validity.
		Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations are governed by the usual tarskian axioms.
	www.cle.unicamp.br /seme_2005/abstracts.html (3061 words)

	Completeness Theorems. Model Theory. Mathematical Logic. Part 4.
		Kripke models for modal logic, a discovery he made in his teen-age years, became part of the standard vocabulary of mathematical logicians after his first article appeared in 1963, when he was just 23 years old.
		Kripke established that a formula is provable in the constructive propositional logic, if and only if it is true at all nodes in all Kripke scenarios.
		Since F is true at all nodes in all Kripke scenarios, it cannot have counterexamples; hence, the sequent (0, {F}) (i.e.
	www.ltn.lv /~podnieks/mlog/ml4a.htm (5502 words)

	Neighborhood Semantics for the Exponentials (Site not responding. Last check: 2007-10-14)
		The Kripke model paper of Mike Dunn and myself is in the other directory, /pub/gtall/relation.
		Gerry \centerline{\bf Abstract} {\narrower This paper presents a neighborhood semantics for the ``exponentials'' of Girard's Linear Logic.
		In Allwein and Dunn, {\it Kripke Models for Linear Logic}, the lattice representation work of Alasdair Urquhart, {\it A topological representation theory for lattices}, is used to yield a Kripke style semantics for propositional Linear Logic without the exponentials.
	www.cis.upenn.edu /~bcpierce/types/archives/1992/msg00177.html (339 words)

	4 Calculi, Kripke semantics and conclusions
		And then, in the seventies, de Jongh in Amsterdam and Boolos and Kripke in the USA considered seriously the conjecture that the Löb axiom is the only missing axiom, i.e.
		In the rest of this section I deal with a sequent calculus for GL and with a Kripke semantics of GL.
		An example of a Kripke model is in Fig.
	www.hf.uio.no /ifikk/filosofi/njpl/vol4no2/provlog/node4.html (2721 words)

	Completeness Theorems. Model Theory. Mathematical Logic. Part 4. (via CobWeb/3.1 planetlab5.csail.mit.edu) (Site not responding. Last check: 2007-10-14)
		Kripke models and the results that depend upon them are cited today not only in philosophy and logic, but also in linguistics and computer science..." (The Gazette.
		Kripke established that a formula is provable in the constructive propositional logic, iff it is true at all nodes in all Kripke scenarios.
		Together with Lemma 4.4.3 this Corollary implies the above Theorem 4.4.2 - Kripke's theorem on the completeness of the constructive propositional logic: a formula F is true at all nodes in all Kripke scenarios, iff F is provable in the constructive propositional logic.
	linas.org.cob-web.org:8888 /mirrors/www.ltn.lv/2005.01.29/~podnieks/mlog/ml4a.htm (5448 words)

	Ars Mathematica » Blog Archive » Saul Kripke
		I had no idea until the past few days that Saul Kripke is an important and widely influential philosopher.
		I knew him from his work in modal logic, but I imagined that he was a logician who worked on a technical subject on the margins of philosophy.
		Perhaps because he published while still in high-school, Kripke’s name got attached to the idea of possible-worlds semantics for modal logic.
	www.arsmathematica.net /archives/2006/05/13/saul-kripke (397 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Abstract: Everyone knows the Curry-Howard isomorphism relating lambda-calculus and intuitionistic propositional logic (IPL), and Kripke semantics for IPL are equally familiar.
		That suggests trying to give Kripke semantics for the lambda-calculus.
		In fact, the equational theory of beta-eta equivalence is deductively complete with respect to this simple semantics.
	www.wesleyan.edu /cgi-bin/cdf_manager/template_renderer.cgi?item=20610 (118 words)

	A Kripke-style Semantics for the Intuitionistic Logic of Pragmatics ILP -- Bellin and Ranalter 13 (5): 755 -- Journal ...
		A Kripke-style Semantics for the Intuitionistic Logic of Pragmatics ILP -- Bellin and Ranalter 13 (5): 755 -- Journal of Logic and Computation
		A Kripke-style Semantics for the Intuitionistic Logic of Pragmatics ILP
		Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues.
	dx.doi.org /10.1093/logcom/13.5.755 (225 words)

	On Kripke-style Semantics for the Provability Logic of Godel's Proof Predicate with Quantifiers on Proofs -- Yavorskiy ...
		On Kripke-style Semantics for the Provability Logic of Godel's Proof Predicate with Quantifiers on Proofs -- Yavorskiy 15 (4): 539 -- Journal of Logic and Computation
		On Kripke-style Semantics for the Provability Logic of Gödel's Proof Predicate with Quantifiers on Proofs
		Kripke-style semantics is suggested for the provability logic
	dx.doi.org /10.1093/logcom/exi037 (161 words)

	Re: Reference: Kripke Semantics (via CobWeb/3.1 planetlab5.csail.mit.edu) (Site not responding. Last check: 2007-10-14)
		> Kripke was (1) an independent discoverer, (2) early on the > scene, (3) the first to make the ideas widely comprehensible, > and (4) the first to make the importance clear.
		It is not > always easy, however, to find a specific point on which he > was absolutely the first.
		> It probably did not hurt that already in 1960 Quine was touting Kripke as the "first person to make modal logic intelligible" Michael
	bureau.philo.at.cob-web.org:8888 /phlo/199707/msg00118.html (111 words)

	Mathematical Logic 2005
		Discussion of the proof of the Soundness Theorem; before you read this proof, be sure that you understand the soundness proof for propositional logic!
		Intuitionistic semantics, the Brouwer-Heyting-Kolmogorov interpretation of the logical constants (section 5.1).
		Equality in ND and most of section 3.1 (the completeness theorem for predicate logic)
	www.cs.chalmers.se /Cs/Grundutb/Kurser/matlog (316 words)

	modalhistory.html (Site not responding. Last check: 2007-10-14)
		This is a survey of the origins of mathematical semantics for modal logics, and its development over the last century or so.
		It focuses on the algebraic semantics using Boolean algebras with operators and the relational semantics using structures often called Kripke models.
		McKinsey's algebraic construction for the finite model property.
	www.mcs.vuw.ac.nz /~rob/papers/modalhistory.html (133 words)

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