Kripke bundle and C-set semantics are known as semantics which generalize standard Kripke semantics. In [4] and in [1, 2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics . Modal predicate logic Q-S4.1 is not Kripke bundle complete of the present paper). This is shown (...) by using difference of Kripke bundle semantics and C-set semantics. In this paper, by using the same idea we show that incompleteness results in Kripke bundle semantics which are extended versions of [2]. (shrink)

am going to discuss some issues inspired by a well-known paper ofKeith Donnellan, "Reference and Definite Descriptions,”2 but the interest—to me—of the contrast mentioned in my title goes beyond Donnellan's paper: I think it is of considerable constructive as well as critical importance to the philosophy oflanguage. These applications, however, and even everything I might want to say relative to Donnellan’s paper, cannot be discussed in full here because of problems of length. Moreover, although I have a considerable interest in (...) the substantive issues raised by Donnellan’s paper, and by related literature, my own conclusions will be methodological, not substantive. I can put the matter this way: Donnellan’s paper claims to give decisive objections both to Russell’s theory of definite descriptions (taken as a theory about English) and to Strawson’s. My concem is not primarily with the question; is Donnellan right, or is Russell (or Strawson)? Rather, it is with the question: do the considerations in Donneilarfs paper refute Russell’s theory (or Strawson’s)? For definiteness, I will concentrate on Donnellan versus Russell, leaving Strawson aside. And about this issue I will draw a definite conclusion, one which I think will illuminate a few methodological maxims about language. Namely, I will conclude that the considerations in Donnellan’s paper, by themselves, do not refute Russell’s theory. Any conclusions about Russell’s views per se, or Donnellan’s, must be tentative, IfI were to be asked for a tentative stab about Russell, I would say that although his theory does a far better job of handling ordinary discourse than many have thought, and although many popular arguments against it are inconclusive, probably it ultimately fails. The considerations I have in mind have to do with the existence of “improper” definite descriptions, such as “the table," where uniquely specifying conditions are not contained in the description itself.. (shrink)

Reference and Existence, Saul Kripke's John Locke Lectures for 1973, can be read as a sequel to his classic Naming and Necessity. It confronts important issues left open in that work -- among them, the semantics of proper names and natural kind terms as they occur in fiction and in myth; negative existential statements; the ontology of fiction and myth. In treating these questions, he makes a number of methodological observations that go beyond the framework of his earlier (...) book -- including the striking claim that fiction cannot provide a test for theories of reference and naming. In addition, these lectures provide a glimpse into the transition to the pragmatics of singular reference that dominated his influential paper, " Speaker's Reference and Semantic Reference " -- a paper that helped reorient linguistic and philosophical semantics. Some of the themes have been worked out in later writings by other philosophers -- many influenced by typescripts of the lectures in circulation -- but none have approached the careful, systematic treatment provided here. The virtuosity of Naming and Necessity -- the colloquial ease of the tone, the dazzling, on-the-spot formulations, the logical structure of the overall view gradually emerging over the course of the lectures -- is on display here as well. (shrink)

Această lucrare oferă o expunere a unor trăsături ale unei teorii semantice a logicilor modale. Pentru o anumită extensiune cuantificată a S5, această teorie a fost prezentată în ‘A Completeness Theorem in Modal Logic’ şi a fost rezumată în ‘Semantical Analysis of Modal Logic’ . Lucrarea de faţă se va concentra asupra unui aspect particular al teoriei – introducerea cuantificatorilor – şi se va restrînge în principal la o metodă particulară de a atinge acest scop. Accentul lucrării va fi pur (...) semantic şi în consecinţă se va omite folosirea tablourilor semantice, care este esenţială pentru o prezentare completă a teoriei . De asemenea, se va renunţa în mare parte la demonstraţii. (shrink)

This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses (...) semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations. (shrink)

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the (...) predicate case there are important many-valued logics like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)

There are two problematic assumptions in Kripke’s semantic argument against descriptivism. Assumption 1 is that the referential relation of a name to an object is only an objective or metaphysical relation between language and the world; it has nothing to do with the understanding of the name by our linguistic community. Assumption 2 is that descriptivism has to hold that, if name a has its meaning and the meaning is given by one description or a cluster of descriptions, the (...) description should supply a set of necessary and sufficient conditions for determining what a designates; and that it is possible for us to find out such a setof conditions. Emphasizing the sociality, intentionality, conventionality and historicity of language and meaning, this paper rejects Assumption 1, and argues that Assumption 2 is an unfair interpretation of descriptivism, and it is not necessary for descriptivists to hold Assumption 2. This paper finally concludes that Kripke’s semantic argument against descriptivism fails. (shrink)

We present here a Kripke-style semantics for propositional orthomodular logics that is based on the representation theorem for orthomodular lattices by D.J. Foulis , in which a sort of semigroups is employed. This semantics can characterize the logics above the orthomodular logic by some elementary conditions.

Classical logic, intuitionism, relevant logics and many other systems try to express implication as an entailment. The Jaskowski system Qf describes implication in connection with causality. Syntactic properties of Qf have been examined by Pieczkowski [4], [5]. The semantic characterization of Qf is the aim of this paper.

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set (...) models. As a corollary we can give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics. (shrink)

This paper deals with one kind of Kripke-style semantics, which we shall call algebraic Kripke-style semantics, for relevance logics. We first recall the logic R of relevant implication and some closely related systems, their corresponding algebraic structures, and algebraic completeness results. We provide simpler algebraic completeness proofs. We then introduce various types of algebraic Kripke-style semantics for these systems and connect them with algebraic semantics.

This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each system, we provide (...) a three-valued Kripke-style semantics with and without star operation . We prove soundness and completeness theorems in each case. Note that wB logics may be equivalent to logics with Baaz’s projection Δ. We finally introduce the G3 and the S53pB both with Δ and show that they are equivalent to G3wB and S53wB, respectively. (shrink)

In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form , where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (...) (i) for all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models. (shrink)

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of (...) individuals as abstract "n"-dimensional vectors', together with some transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type. (shrink)

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made (...) possible by restricting admissible interpretations. (shrink)

This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.

In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of truth values. Instead, we take a collection of algebras each of which is attached to a world as the set of truth values at the world, and obtain an extended semantics based on the traditional Kripke-type semantics, which we call here the algebraic (...) class='Hi'>Kripke semantics. We introduce algebraic Kripke sheaf semantics for super-intuitionistic and modal predicate logics, and discuss some basic properties. We can state the Gödel-McKinsey-Tarski translation theorem within this semantics. Further, we show new results on super-intuitionistic predicate logics. We prove that there exists a continuum of super-intuitionistic predicate logics each of which has both of the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic. (shrink)

In his influential Naming and Necessity lectures, Saul Kripke made new sense of modal statements: “Kant might have been a bachelor”, “Königsberg is necessarily identical with Kaliningrad”. Many took the notions he introduced-metaphysical necessity and rigid designation -- to herald new metaphysical issues and have important consequences. In fact, the Kripkean insight is at bottom semantic, rather than metaphysical: it is part of how proper names work that they purport to refer to individuals to whom modal properties can be (...) ascribed. We can see this by reflecting on analytic truths that ground modal claims like the two examples above. (shrink)

‘Natural kind essentialism’—here defined as the view that (i) the existence of natural kinds is a mind- and theory-independent matter, (ii) their essences are intrinsic, and (iii) they have a hierarchical structure—is commonly thought to be justified by appeal to Kripke–Putnam semantics, according to which propositions like ‘water is H20’ are necessary a posteriori. This chapter argues that the Kripke–Putnam semantics is in fact compatible with the denial of each of the three tenets of natural kind (...) essentialism. The basic argument is that, assuming the range of natural kinds goes beyond those kinds for which we have vernacular names, deference to scientific theories is required in fixing the reference of natural kind terms. That those theories describe mind- and theory-independent reality, and that they do not admit a non-hierarchical structure for the categories they deploy, are theses that are independent of anything derivable from Kripke–Putnam semantics itself. (shrink)

Kripke; possible-world semantics; pure and applied semantics; models of modal space; applicability.

Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) (...) if and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅; such frames with A=W or A=∅; such frames with A=W). Secondly, for all normal extensions of K45, KB4, KD45 and S5, in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981) (which concerned normal extensions of K5). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N. (shrink)

Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf 1 into 2 then the logic characterized by 1 is contained in the logic characterized by 2. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper (...) Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated. (shrink)

This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here substructural nuclear logics, and its subclass, called here substructural nuclear image-based logics, where N further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those logics. Finally, we introduce operational Kripke-style semantics for those logics and provide two (...) sorts of completeness results for them, one of which is based on algebraic completeness for all the logics and the other of which is based on set-theoretic one for the nuclear image-based logics. (shrink)

It is assumed that a Kripke–Joyal semantics \({\mathcal{A} = \left\langle \mathbb{C},{\rm Cov}, {\it F},\Vdash \right\rangle}\) has been defined for a first-order language \({\mathcal{L}}\) . To transform \({\mathbb{C}}\) into a Heyting algebra \({\overline{\mathbb{C}}}\) on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of \({\mathbb{C}}\) . A pretopology \({\overline{{\rm Cov}}}\) is defined on \({\overline{\mathbb{C}}}\) using the pretopology on \({\mathbb{C}}\) . A sheaf \({\overline{{\it F}}}\) is made up of (...) sections of F that obey functoriality. A forcing relation \({\overline{\Vdash}}\) is defined and it is shown that \({\overline{\mathcal{A}} = \left\langle \overline{\mathbb{C}},\overline{\rm{Cov}},\overline{{\it F}}, \overline{\Vdash} \right\rangle }\) is a Kripke–Joyal semantics that faithfully preserves the notion of forcing of \({\mathcal{A}}\) . That is to say, an object a of \({\mathbb{C}Ob}\) forces a sentence with respect to \({\mathcal{A}}\) if and only if the maximal a-crible forces it with respect to \({\overline{\mathcal{A}}}\) . This reduces a Kripke–Joyal semantics defined over an arbitrary site to a Kripke–Joyal semantics defined over a site which is based on a complete Heyting algebra. (shrink)

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.

Saul Kripke's influential ‘sceptical paradox’ of semantic rule-following alleges that speakers cannot have any justification for using a word one way rather than another. If it is correct, there can be no such thing as meaning anything by a word. I argue that the paradox fails to undermine meaning. Kripke never adequately motivates its excessively strict standard for the justified use of words. The paradox lacks the resources to show that its standard is truly mandatory or that speakers (...) do not frequently satisfy the well-motivated competitor I offer. So the paradox fails. (shrink)

Reviews of the papers mentioned in the title.

This article argues, first, that the fundamental structure of the skeptical argument in Kripke's book on Wittgenstein has been seriously misunderstood by recent commentators. Although it focuses particularly on recent commentary by John McDowell, it emphasizes that the basic misunderstandings are widely shared by other commentators. In particular, it argues that, properly construed, Kripke offers a fully coherent reading of PI #201 and related passages. This is commonly denied, and given as a reason for rejecting Kripke's reading (...) of Wittgenstein's text. Second, it is pretty universally accepted that Kripke's Wittgenstein is a `non-factualist' about ascriptions of meaning. The article argues that, when Kripke's discussion is rightly understood and the content of `non-factualism' is clarified, there is an important sense in which the skeptical solution is not committed to non-factualism. (shrink)