多值逻辑的公理化

给出了一种新的多值逻辑系统，公理化所得到的ＧＭＬ３形式系统与二值逻辑有本质的区别，二值逻辑是它的一个退化．     

Characterizing sets of data structures by the connectivity relation

A formalism based on the directed graph connectivity relation is presented, in which a first-order predicate calculus notation is used with the purpose of defining sets of data structures and characterizing the structural operations on them. The formalism is designed so as to facilitate the proof that the intended operations on instances of a given set of data structures are correct, in the sense that they do not violate the structural form of the data.     

有穷时间投影时序逻辑的完备公理系统

为采用定理证明的方法对并发及交互式系统进行验证,研究了有穷论域下有穷时间一阶投影时序逻辑(projection temporal logic,简称PTL)的一个完备公理系统.在介绍PTL的语法、语义并给出公理系统后,提出了PTL公式的正则形(normal form,简称NF)和正则图(normal form graph,简称NFG).基于NF给出了NFG的构造算法,并利用NFG可描述公式模型的性质证明PTL公式的可满足性判定定理和公理系统的完备性.最后,结合实例展示了PTL及其公理系统在系统验证中的应用.结果表明,基于PTL的定理证明方法可方便用于并发系统的建模与验证.     

Trace 演算

文章定义了基于踪迹(trace)的逻辑语言L_Trace,它是一阶线性时序逻辑语言的扩充,同时也是“对象演算”研究工作的基础.Trace演算所述的“对象”用来刻画具有内部状态和外部行为的动态实体,语法上由对象标记表示.对象标记Ω=(S,F,A,E)包含4个部分:数据类型S、函数F、属性A和动作E.Σ=(S,F)构成通常代数规范意义下的标记,可将动作看成一广义数据类型,从而得到标记Σ的动作扩充ΣE.对象标记的语义解释结构由关于标记ΣE的代数、映射和动作与踪迹的关系定义.ΣE-代数给出关于数据参数的解释;映射给出属性在动作踪迹中所取的值;而动作与踪迹的关系则给出执行一有限踪迹以后该动作是否允许执行.在定义了Trace演算的语法和语义之后,文章给出了Trace演算的公理系统及其可靠性证明.     

An Equational Axiomatization of Dynamic Negation and Relational Composition

We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational axiomatization for these dynamic relation algebras. The completenessresult uses techniques from modal logic. We also lookat the variety generated by the class of dynamic relation algebras and note that there exist nonrepresentable algebras in this variety, ones which cannot be construedas spaces of relations. These results are also proved for an extension to a signature containing atomic tests and union.     

带Mismatch算子的高阶π演算

主要研究带mismatch的高阶进程演算的公理化问题。首先,建立存在mismatch时高阶进程的开弱高阶互模拟理论,证明了等价关系、同余性等重要性质;其次,沿用线性的方法,构建得到带 mismatch 的有限进程上的公理系统;最后,基于对开弱高阶互模拟的刻画,证明了该公理系统的完备性定理。该工作为带 mismatch 的高阶进程上互模拟判定的有效算法的设计与实现,进而为相关的应用建模工作提供了理论借鉴。