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61.
Andreja Prijatelj 《Studia Logica》1996,57(2-3):437-456
In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.Presented by Jan Zygmunt 相似文献
62.
Wojciech Buszkowski 《Studia Logica》1996,57(2-3):303-323
We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono [11]. We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus [2] and the commutative product-free Lambek calculus [4].Presented by H. Ono 相似文献
63.
64.
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
65.
Michael Fisher 《Journal of Applied Logic》2011,9(4):223-238
Autonomous agents are not so difficult to construct. Constructing autonomous agents that will work as required is much harder. A clear way in which we can design and analyse autonomous systems so that we can be more confident that their behaviour is as required is to use formal methods. These can, in principle, allow us to exactly specify the behaviour of the agent, and verify that any implementation has the properties required. In addition to using a more formal approach, it is clear that problems of conceptualisation and analysis can be aided by the use of an appropriate abstraction.In this article we tackle one particular aspect of formal methods for agent-based systems, namely the formal representation and implementation of deliberation within agents. The key aspect here is simplicity. Agents are specified using a relatively simple temporal logic and are executed by directly interpreting such temporal formulae. Deliberation is captured by modifying the way in which execution handles its temporal goals. Thus, in this article we provide motivations, theoretical underpinnings, implementation details, correctness arguments, and comparisons with related work. 相似文献
66.
In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. 相似文献
67.
We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H
of the intuitionistic propositional logic to an implicational fragment TV
of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics. 相似文献
68.
69.
An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case. 相似文献
70.
In this paper we characterize, classify and axiomatize all axiomatic extensions of the IMT3 logic. This logic is the axiomatic extension of the involutive monoidal t-norm logic given by ¬φ3 ∨ φ. For our purpose we study the lattice of all subvarieties of the class IMT3, which is the variety of IMTL-algebras given by the equation ¬(x3) ∨ x ≈ ?, and it is the algebraic counterpart of IMT3 logic. Since every subvariety of IMT3 is generated by their totally ordered members, we study the structure of all IMT3-chains in order to determine the lattice of all subvarieties of IMT3. Given a family of IMT3-chains the number of elements of the largest odd finite subalgebra in the family and the number of elements of the largest even finite subalgebra in the family turns out to be a complete classifier of the variety generated. We obtain a canonical set of generators and a finite equational axiomatization for each subvariety and, for each corresponding logic, a finite set of characteristic matrices and a finite set of axioms. 相似文献