Terminating Calculi for Propositional Dummett Logic with Subformula Property

In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on two semantical levels: the present and the next possible world. The second calculus employs the semantical levels of known or not known at the present state of knowledge, that are usual in tableau systems, and exploits a property of the construction of the completeness theorem to introduce a check which is an alternative to loop check mechanisms.     

行为时序逻辑与自反线性时序逻辑的关系

为了能够将哲学逻辑中的公理系统运用到行为时序逻辑的研究中。对行为时序逻辑公式的语义进行形式化定义．从语义和语法两方面研究行为时序逻辑公理系统和具有自反性质的线性时序逻辑公理系统之间的联系．提出并证明行为时序逻辑公式转换为自反线性时序逻辑公式的定理。按照集合论和模型论的思想,定义行为时序逻辑中项和行为时序逻辑原子公式的概念。定义Lesilie Lamport所提出的行为时序逻辑公式的语义。证明自反线性时序逻辑公理系统适用于行为时序逻辑公理系统．以此为基础证明行为时序逻辑的简单规则、基本规则和附加规则。     

Classical Modal Display Logic in the Calculus of Structures and Minimal Cut-free Deep Inference Calculi for S5

We begin by showing how to faithfully encode the Classical ModalDisplay Logic (CMDL) of Wansing into the Calculus of Structures(CoS) of Guglielmi. Since every CMDL calculus enjoys cut-elimination,we obtain a cut-elimination theorem for all corresponding CoScalculi. We then show how our result leads to a minimal cut-freeCoS calculus for modal logic S5. No other existing CoS calculifor S5 enjoy both these properties simultaneously.     

概率命题逻辑是经典命题演算形式系统的随机事件语义

经典命题演算形式系统(CPC)中的公式只是一些形式符号,这些形式符号的意义是由具体的解释给出的.概率逻辑是在标准概率空间上建立的一种逻辑体系,是CPC的随机事件语义,对联结词的解释就是集合运算,对形式公式的解释就是事件函数,对逻辑蕴涵和逻辑等价的解释就是事件(集合)包含和事件相等=.由于不存在处处适用的真值函数(算子),概率逻辑不能在CPC内实现概率演算,但可在CPC内实现事件演算,CPC完全适用于概率命题演算.     

直觉模糊逻辑的语义算子研究

首先引用Atanassov直觉模糊集的基本概念和运算。在阐明直觉模糊集的集中、扩张、归一化算子之后,新定义了强化算子。通过考察Atanassov直觉模糊集与Zadeh模糊集之间的关系,给出了直觉模糊语言、结构化直觉模糊语言和直觉模糊语义的数学描述,重点对基于直觉模糊集和直觉模糊关系的模糊语言的语义算子,如语气算子、模糊化算子、判定化算子及连接与否定算子等进行了研究,并举例阐明其应用,使直觉模糊逻辑的语义算子得到进一步的拓广。     

命题中介逻辑的可靠和完备Gentzen推导系统

中介逻辑是朱梧槚先生提出的一个3-值逻辑.给出了一个命题中介逻辑,其中引入中介连接词~、反对连接词◁以及蕴涵连接词→,并且定义否定连接词.给出了一个Gentzen-型的推导系统,使得该系统关于中介逻辑的3-值语义是可靠的和完备的.     

Theorem Prover for Intuitionistic Logic Based on the Inverse Method

The first-order intuitionistic logic is a formal theory from the family of constructive logics. In intuitionistic logic, it is possible to extract a particular example x = a and a proof of a formula P(a) from a proof of a formula ?xP(x). Owing to this feature, intuitionistic logic has many applications in mathematics and computer science. Many modern proof assistants include automated tactics for the first-order intuitionistic logic, which simplify the task of solving challenging problems, such as formal verification of software, hardware, and protocols. In this paper, a new theorem prover (called WhaleProver) for full first-order intuitionistic logic is presented. Testing on the ILTP benchmarking library has shown that WhaleProver performance is comparable with the state-of-the-art intuitionistic provers. Our prover has solved more than 800 problems from the ILTP version 1.1.2. Some of them are intractable for other provers. WhaleProver is based on the inverse method proposed by S.Yu. Maslov. We introduce an intuitionistic inverse method calculus which is, in turn, a special kind of sequent calculus. It is also described how to adopt for this calculus several existing proof search strategies proposed for different logical calculi by S.Yu. Maslov, V.P. Orevkov, A.A. Voronkov, and others. In addition, a new proof search strategy is proposed that allows one to avoid redundant inferences. The paper includes results of experiments with WhaleProver on the ILTP library. We believe that Whale- Prover can be used as a test bench for different inference procedures and strategies, as well as for educational purposes.     

相干命题逻辑系统R的一种演绎生成算法

本文提出了相干命题逻辑系统R的一种演绎生成算法--试探法。该算法采用后向推理法,依据推理规则将待证命题逐步分解成子命题并构造一棵证明树,对系统R中的定理证明取得了较好的效果。     

区分3种否定的模糊命题逻辑系统及其应用

在模糊知识表示与推理中,否定信息扮演了一个重要角色.从概念层面上区分了模糊知识中存在的3 种否定关系,即矛盾否定关系、对立否定关系和中介否定关系.为了建立能够完全描述这些不同否定关系的逻辑基础,提出一种区分矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM.讨论了FLCOM 特有的性质与意义,给出了FLCOM 的一种语义解释,并证明了可靠性定理.为了表明FLCOM 处理实际问题的适用性,进一步研究了FLCOM在一个模糊决策实例中的应用.具体地,基于FLCOM讨论了决策规则中的模糊命题及其不同否定的区分与形式表示,给出一种确定模糊命题及其不同否定的真值及其真值范围阈值的方法,并采用模糊产生式规则讨论了实例中的模糊推理与决策.从而表明,运用FLCOM 处理具有模糊性并且存在不同否定的实际问题是有效的.     

带有时钟变量的线性时序逻辑与实时系统验证

为了描述实时系统的性质和行为,10多年来,各种不同的时序逻辑,如Timed Computation Tree Logic,Metric Interval Temporal Logic和Real-Time Temporal Logic等相继提出来.这些时序逻辑适于表示实时系统的性质和规范,但不适于表示实时系统的实现模型.这样,在基于时序逻辑的实时系统的研究中,系统的性质和实现通常是用两种不同的语言来表示的.定义了一个带有时钟变量的线性时序逻辑(linear temporal logic with clocks,简称LTLC).它是由Manna和Pnueli提出的线性时序逻辑在实时情况下的一个推广.LTLC既能表示实时系统的性质,又能很方便地表示实时系统的实现.它能在统一的语义框架中表示出从高级的需求规范到低级的实现模型之间的不同抽象层次上的系统描述,并且能用逻辑蕴涵来表示不同抽象层次的系统描述之间的语义一致性.LTLC的这个特点将有助于实时系统的性质验证和实时系统的逐步求精.     

多变量控制系统的行化梯典范形与最小阶Kx-观测器的线性设计方法

本文提出了定基形矩阵的概念及多变量系统的行简化梯形典范形理论.该典范形与系统的可观测性矩阵或可控性矩阵之间可用子块集建立计算关系式.应用该理论可以把最小阶Kx-观测器设计中的一组非线性代数方程组化为一类可解的线性代数方程组(附录中介绍了这一分析过程).由此得到一种新的最小阶Kx-观测器线性设计法.该算法较Roman-Bullock设计法计算简单,计算误差小,且更便于用计算机设计.文中还用例题指出Sirisena设计法的缺点.     

基于线性时序逻辑的实时系统建模与求精

线性时序逻辑语言XYZ／E在统一的语义框架下．能表示从高层需求规范到低层实现模型之间的不同抽象层次的系统描述，也适于描述实时系统的模型和逐步求精过程．本文提出了一种基于构件的实时系统求精方法，并给出一个具体实例一电梯控制系统，采用XYZ／E语言描述了该系统的模型及其求精过程．     

Linear, Branching Time and Joint Closure Semantics for Temporal Logic

Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic notions are defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications.