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81.
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
82.
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
83.
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
84.
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
85.
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
86.
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
87.
An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of the operations for belief change. Representation theorems are given for the local operators. 相似文献
88.
《Journal of Applied Logic》2014,12(4):558-569
In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes. 相似文献
89.
Mauro Ferrari 《Studia Logica》1997,59(3):303-330
In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual signs T and F. In this work we establish the soundness and completeness theorems for these calculi with respect to the Kripke semantics proposed by Fischer Servi. 相似文献
90.
Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission. 相似文献