Kripke Semantics for Modal Substructural Logics

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.     

关于BAN逻辑的语义模型的分析与改进

该文针对BAN逻辑及其语义模型的不足之处,提出了改进后的定义,它比BAN原作者们所提供的信念定义更加合理。     

The Basic Constructive Logic for Negation-Consistency

In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic B_Kc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending B_Kc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.     

The Basic Constructive Logic for Absolute Consistency

In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic B_Kc6, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending B_Kc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.     

Intuitionistic Logic as the Implement of Incremental Model Construction for Natural Language

The process of understanding natural language can be viewed as the process of model construction.This paper,employing Kripke frame for intuitionistic logic semantics as the implement of model construction for natural language,introduces a method of incremental model constuction.     

UML活动图的时序逻辑语义

UML活动图可以表示不同抽象级的控制流,很适合用于对系统的行为建模．但是缺乏精确的语义使得难以对它所表示的系统行为进行分析．XYZ／E是一可执行线性时序逻辑语言,既可描述系统的动态行为又可表示程序性质,用它对活动图形式化后,就可在统一的逻辑框架下分析活动图的性质．定义了一个有向图结构用以表示UML活动图,再给出其XYZ／E语义,并用一个例子说明活动图到XYZ／E的语义转换,为进一步的分析提供形式化基础．     

Paraconsistent Declarative Semantics for Extended Logic Programs

We introduce a fixpoint semantics for logic programs with two kinds of negation: an explicit negation and a negation-by-failure. The programs may also be prioritized, that is, their clauses may be arranged in a partial order that reflects preferences among the corresponding rules. This yields a robust framework for representing knowledge in logic programs with a considerable expressive power. The declarative semantics for such programs is particularly suitable for reasoning with uncertainty, in the sense that it pinpoints the incomplete and inconsistent parts of the data, and regards the remaining information as classically consistent. As such, this semantics allows to draw conclusions in a non-trivial way, even in cases that the logic programs under consideration are not consistent. Finally, we show that this formalism may be regarded as a simple and flexible process for belief revision.     

A Rewriting Logic Approach to Operational Semantics (Extended Abstract)

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuation-based semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Linguistic Applications of First Order Intuitionistic Linear Logic

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus. This revised version was published online in August 2006 with corrections to the Cover Date.     

Syntax and Semantics for a Fuzzy Temporal Constraint Logic

In this paper we establish the relationship between the syntax and semantics of a fuzzy temporal constraint logic (FTCL) proposed by Cárdenas et al. FTCL enables us to express interrelated events by means of fuzzy temporal constraints. Moreover, it provides a resolution principle for performing inferences which take these constraints into account. FTCL is compatible with the theoretical temporal reasoning model proposed by Marín et al. – the Fuzzy Temporal Constraint Networks (FTCN). The main contributions of this paper are, on the one hand, the proofs of the FTCL-deduction and the FTCL-refutation theorems, and, on the other, the proof of the soundness of the refutation by resolution in this formal system, together with an exhaustive study of its completeness.     

描述逻辑FL-循环术语集的语义及推理

循环术语集是描述逻辑长期以来的研究难点,它的最基本的问题即语义及推理问题没有得到合理的解决.文中分析了描述逻辑循环术语集的研究现状和存在的问题,在Baader的基础上进一步研究了描述逻辑FL~-循环术语集的语义及推理问题.给出了FL~-循环术语集的语法、语义和不动点模型的构造方法.针对FL~-循环术语集的需要,提出了一种新的有限自动机,使用有限自动机给出了不动点语义和描述语义下FL~-循环术语集的可满足性和包含推理算法,证明了推理算法的正确性,并给出了推理算法的复杂性定理.     

A Game Semantics for Grz

We present a game semantics for modal propositional logic Grz.Since intuitionistic logic may be embedded into Grz, the semanticsalso covers intuitionistic propositional logic. That semanticsis simpler than Lorenzen's ‘dialogue’ games, butlacks predicates.