共查询到20条相似文献,搜索用时 15 毫秒
1.
Frank Wolter 《Mathematical Logic Quarterly》1996,42(1):145-171
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Norihiro Kamide 《Mathematical Logic Quarterly》2005,51(4):331-341
A spatial modal logic (SML) is introduced as an extension of the modal logic S4 with the addition of certain spatial operators. A sound and complete Kripke semantics with a natural space (or location) interpretation is obtained for SML. The finite model property with respect to the semantics for SML and the cut‐elimination theorem for a modified subsystem of SML are also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Olivier Gasquet 《Mathematical Logic Quarterly》1998,44(1):45-49
The problem of completeness for predicate modal logics is still under investigation, although some results have been obtained in the last few years (cf. [2, 3, 4, 7]). As far as we know, the case of multimodal logics has not been addressed at all. In this paper, we study the combination of modal logics in terms of combining their semantics. We demonstrate by a simple example that in this sense predicate modal logics are not so easily manipulated as propositional ones: mixing two Kripke-complete predicate modal logics (one with the Barcan formula, and the other without) results in a Kripke-incomplete system. 相似文献
4.
Yutaka Miyazaki 《Mathematical Logic Quarterly》2001,47(3):341-362
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 ([2]), in which a sort of semigroups is employed. This semantics can characterize the logics above the orthomodular logic by some elementary conditions. 相似文献
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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 ([6]). Modal predicate logic Q-S4.1 is not Kripke bundle complete ([3] - it is also yielded as a corollary to Theorem 6.1(a) 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]. 相似文献
7.
Guido Bertolotti Pierangelo Miglioli Daniela Silvestrini 《Mathematical Logic Quarterly》1996,42(1):501-536
We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90. 相似文献
8.
Petr Cintula 《Archive for Mathematical Logic》2006,45(6):673-704
This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance.The work was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AVOZ10300504. 相似文献
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We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K. 相似文献
11.
A. D. Yashin 《Algebra and Logic》2003,42(3):207-216
We give an exhaustive classification of Novikov complete extensions of the intuitionistic propositional logic in a language with extra logical constants. 相似文献
12.
Yoshihito Tanaka 《Mathematical Logic Quarterly》2001,47(3):327-339
In this article, a cut‐free system TLMω1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames.The system TLMω1 is a kind of Gentzen style sequent calculus, but a sequent of TLMω1 is defined as a finite tree of sequents in a standard sense. We prove the cut‐elimination theorem for TLMω1 via its Kripke completeness. 相似文献
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Mladen Vuković 《Mathematical Logic Quarterly》2008,54(4):368-373
Interpretability logic is an extension of provability logic. Veltman models and generalized Veltman models are two semantics for interpretability logic. We consider a connection between Veltman semantics and generalized Veltman semantics. We prove that for a complete image‐finite generalized Veltman modelW there is a Veltman model W ′ that is bisimular to W. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Each information system (or data table) leads to a hierarchy of binary relations on the object set in a natural way; these relational systems can serve as frames for the semantics of modal logics. While relations of indiscernibility and their logics have been frequently studied, the situation in the case of relations which distinguish objects is much less clear. In this paper, we present complete logical systems for relations of complementarity derived from information systems. 相似文献
16.
The paper presents a semantics for quantified modal logic which has a weaker axiomatization than the usual Kripke semantics. In particular, the Barcan Formula (BF) and its converse are not valid with the proposed semantics. Subclasses of models which validate BF and other interesting formulas are presented. A completeness theorem is proved, and the relation between this result and completeness with respect to Kripke models is investigated. 相似文献
17.
本文首先讨论嵌套论域语义的相应代数语义并由Hughes和Cresswell在[5]中建立的关于具有嵌套论域的正规量词模态系统的关系语义完全性定理推出其相应的代数语义完全性定理:然后对于具有任意可变论域语义的正规系统,我们用Henkin方法给出其关于狭义Kripke语义的关系语义完全性定理,由此通过将关系语义转化为代数语义从而亦推得其代数语义完全性定理。 相似文献
18.
MIPC is a well-known intuitionistic modal logic of Prior (1957) and Bull (1966). It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal. 相似文献
19.
Hiroshi Aoyama 《Mathematical Logic Quarterly》1998,44(2):167-175
In this paper we will study a formal system of intuitionistic modal predicate logic. The main result is its semantic completeness theorem with respect to algebraic structures. At the end of the paper we will also present a brief consideration of its syntactic relationships with some similar systems. 相似文献
20.
V. V. Rybakov 《Algebra and Logic》2002,41(5):323-336
The article studies Barwise's information frames and settles the problem of Barwise dealing in finding axiomatizations for the modal logics generated by information frames. We find axiomatic systems for: (i) the modal logic of all complete information frames; (ii) the logic of all sound and complete information frames; (iii) the logic of all hereditary and complete information frames; (iv) the logic of all complete, sound, and hereditary information frames; (v) the logic of all consistent and complete information frames. The notion of weak modal logics is also proposed, and it is shown that the weak modal logics generated by all information frames and by all hereditary information frames are K and K4, respectively. Toward a general theory, we prove that any Kripke complete modal logic is a modal logic of a certain class of information frames, and that every modal logic generated by any given class of complete, rarefied, and fully classified information frames is Kripke complete. 相似文献