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1.
Lou Goble 《Studia Logica》2007,85(2):171-197
The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain
substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In
particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms
to the basic positive relevant logic B∘T, then LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural
logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself.
Presented by Rob Goldblatt 相似文献
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The logic BKc1 is the basic constructive logic in the ternaryrelational semantics (without a set of designated points) adequateto consistency understood as the absence of the negation ofany theorem. Negation is introduced in BKc1 with a negationconnective. The aim of this paper is to define the logic BKc1F.In this logic negation is introduced via a propositional falsityconstant. We prove that BKc1 and BKc1F are definitionally equivalent. 相似文献
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Bruno Teheux 《Studia Logica》2007,87(1):13-36
In this paper, we develop a duality for the varieties of a Łukasiewicz
n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived
and we propose some ideas for future research.
Presented by Daniele Mundici 相似文献
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H. B. Smith, Professor of Philosophy at the influential Pennsylvania School was (roughly) a contemporary of C. I. Lewis who was similarly interested in a proper account of implication. His research also led him into the study of modal logic but in a different direction than Lewis was led. His account of modal logic does not lend itself as readily as Lewis' to the received possible worlds semantics, so that the Smith approach was a casualty rather than a beneficiary of the renewed interest in modality. In this essay we present some of the main points of the Smith approach, in a new guise. 相似文献
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This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument. 相似文献
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We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper. 相似文献
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A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable. 相似文献
11.
《Journal of Applied Logic》2014,12(1):75-87
The expressions of a language distinguish between many different types of objects. These types can affect how the meanings of these expressions combine. This paper provides a formal picture of the process of meaning combination in a richly typed framework. 相似文献
12.
Ruy J. G. B. de Queiroz 《Studia Logica》2008,90(2):211-247
The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs,
it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea
that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means
the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest
an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device
of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic.
Presented by Heinrich Wansing 相似文献
13.
首先,我们构造认知系统EK1-EK3,给出它们的一些证明论结果。其次,我们引入邻域语义,给出EK1-EK3的特征公理和规则的框架条件,证明EK1-EK3相对这些框架条件分别是框架可靠的。最后,我们证明EK1-EK3相对这些框架条件分别是框架完全的。 相似文献
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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. 相似文献
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We study the matrices, reduced matrices and algebras associated to the systems SAT of structural annotated logics. In previous papers, these systems were proven algebraizable in the finitary case and the class of matrices analyzed here was proven to be a matrix semantics for them.We prove that the equivalent algebraic semantics associated with the systems SAT are proper quasivarieties, we describe the reduced matrices, the subdirectly irreducible algebras and we give a general decomposition theorem. As a consequence we obtain a decision procedure for these logics. 相似文献
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We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Markov chains and alternating temporal frames. We provide a generic canonical cut-free sequent system and a terminating proof-search strategy for the fragment without the difference modality but including the global modality. 相似文献
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Two extensions of the structurally free logic LC 总被引:1,自引:0,他引:1
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《Journal of Applied Logic》2014,12(1):50-66
Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [4] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [5] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.In this paper we study full linear logic from an algebraic point of view. The main additional hurdle is the exponential. We analyse this operation algebraically and use canonical extensions to obtain relational semantics. Thus, we extend the work in [4], [5] and use their approach to obtain relational semantics for full linear logic. Hereby we illustrate the strength of using canonical extension to retrieve relational semantics: it allows a modular and uniform treatment of additional operations and axioms.Traditionally, so-called phase semantics are used as models for (provability in) linear logic [8]. These have the drawback that, contrary to our approach, they do not allow a modular treatment of additional axioms. However, the two approaches are related, as we will explain. 相似文献
20.
Stefano Predelli 《Erkenntnis》2006,65(3):385-403
In this essay, I explain how certain suggestions put forth by Frege, Wittgenstein, and Schlick regarding the interpretation
of indexical expressions may be incorporated within a systematic semantic account. I argue that the ‘hybrid’ approach they
propose is preferable to more conventional systems, in particular when it comes to the interpretation of cases of cross-contextual
ellipsis. I also explain how the hybrid view entails certain important and independently motivated distinctions among contextually
dependent expressions, for instance between ‘here’ and ‘local’. 相似文献