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91.
In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in
LAST. 相似文献
92.
In this paper we improve the results of [2] by proving the product f.m.p. for the product of minimal n-modal and minimal n-temporal logic. For this case we modify the finite depth method introduced in [1]. The main result is applied to identify new fragments of classical first-order logic and of the equational theory of relation algebras, that are decidable and have the finite model property. 相似文献
93.
Completeness of Certain Bimodal Logics for Subset Spaces 总被引:1,自引:0,他引:1
Subset Spaces were introduced by L. Moss and R. Parikh in [8]. These spaces model the reasoning about knowledge of changing states.In [2] a kind of subset space called intersection space was considered and the question about the existence of a set of axioms that is complete for the logic of intersection spaces was addressed. In [9] the first author introduced the class of directed spaces and proved that any set of axioms for directed frames also characterizes intersection spaces.We give here a complete axiomatization for directed spaces. We also show that it is not possible to reduce this set of axioms to a finite set. 相似文献
94.
Dorota Leszczyńska-Jasion 《Journal of Philosophical Logic》2009,38(2):151-177
The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic
proofs for modal logics, which is grounded in the logic of questions IEL. 相似文献
95.
Josep Maria Font 《Studia Logica》2009,91(3):383-406
This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract
algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the
conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage
of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying
these in the particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices
are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the
need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the
idea of truth degree and to some mathematical difficulties. 相似文献
96.
In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification
and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued
Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without
distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix,
incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy
logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which
correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi
of ordinary, two-valued sequents.
Presented by Yaroslav Shramko and Heinrich Wansing 相似文献
97.
William Edward Morris 《Philosophia》2009,37(3):441-454
Although Hume has no developed semantic theory, in the heyday of analytic philosophy he was criticized for his “meaning empiricism,”
which supposedly committed him to a private world of ideas, led him to champion a genetic account of meaning instead of an
analytic one, and confused “impressions” with “perceptions of an objective realm.” But another look at Hume’s “meaning empiricism”
reveals that his criterion for cognitive content, the cornerstone both of his resolutely anti-metaphysical stance and his
naturalistic “science of human nature,” provides the basis for a successful response to his critics. Central to his program
for reforming philosophy, Hume’s use of the criterion has two distinct aspects: a critical or negative aspect, which assesses
the content of the central notions of metaphysical theories to demonstrate their unintelligibility; and a constructive or
positive aspect, which accurately determines the cognitive content of terms and ideas. 相似文献
98.
Experts in all fields are able to see what is invisible to others. Experts are also able to see what is visible to all—and this is explored by Bilalić and Gobet. We question the method of normalizing all subjects in an experimental condition, and asking experts to behave as if they were novices. We claim that method leads Bilalić and Gobet to a nonsequitur . 相似文献
99.
Knowledge on Treelike Spaces 总被引:1,自引:0,他引:1
This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system. 相似文献
100.
In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. 相似文献