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.     

命题逻辑公式模糊软集语义及其在决策分析中的应用

基于论域公式引入软命题逻辑公式概念,给出软命题逻辑公式的模糊软语义解释.将决策模糊信息系统转化为决策模糊软集,软决策规则表示为包含有蕴含联结词的软命题逻辑公式.引入软命题逻辑公式的基本真度、条件真度、绝对真度等指标,从充分性、必要性等方面评价软决策规则的有效性、合理性.提出基于决策软集的典型软决策规则提取算法和基于软决策分析的推荐算法,并通过实例和数值实验证明算法的有效性.     

动态模糊逻辑程序设计语言的指称语义

文献[8]借鉴Dijkstra的监督命令程序结构,给出了动态模糊逻辑程序设计语言的基本框架结构.在此基础上,进一步扩充和完善,并根据指称语义的原理和方法,用结构归纳法给出动态模糊逻辑程序设计语言的指称语义,主要包括:动态模糊程序设计语言的语义域、语义函数及其指称语义.最后给出了一个动态模糊程序设计语言的例子以观察程序的运行过程.     

Reasoning Processes in Propositional Logic

We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who classified the formula correctly before timeout (accuracy) and the mean response time among those participants (latency). We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies (p < .0001). For tautologies the correlation between latency and minimum proof length in T was .89 and for non-tautologies the correlation between latency and minimum proof length in NT was .87.     

Semantics of sub-probabilistic programs

The aim of this paper is to extend the probabilistic choice in probabilistic programs to sub-probabilistic choice, i.e., of the form (p)P ^⋈(q)Q where p + q ⩽ 1. It means that program P is executed with probability p and program Q is executed with probability q. Then, starting from an initial state, the execution of a sub-probabilistic program results in a sub-probability distribution. This paper presents two equivalent semantics for a sub-probabilistic while-programming language. One of these interprets programs as sub-probabilistic distributions on state spaces via denotational semantics. The other interprets programs as bounded expectation transformers via wp-semantics. This paper proposes an axiomatic systems for total logic, and proves its soundness and completeness in a classical pattern on the structure of programs.     

Semantics of probabilistic programs

This paper presents two complementary but equivalent semantics for a high level probabilistic programming language. One of these interprets programs as partial measurable functions on a measurable space. The other interprets programs as continuous linear operators on a Banach space of measures. It is shown how the ordered domains of Scott and others are embedded naturally into these spaces. We use the semantics to prove a general result about probabilistic programs, namely, that a program's behavior is completely determined by its action on fixed inputs.     

基于一类严格三角范数的命题逻辑

剩余模糊逻辑演算与连续三角范数是紧密相关的,三角范数是合取联结词的真值函数,三角范数的剩余是蕴涵联结词的真值函数. 在这些逻辑中,非运算都是由蕴涵和真值常量0定义的,即(→)P∶P→0-.在本文中,我们引入一种具有对合性质的强非运算联结词"～"和投影联结词"Δ",证明基于严格泛与运算模型T(x,y,h)(h∈(0.75,1))的命题演算逻辑PC(T)系统是基本严格模糊逻辑SBL;PC(T)～是基本严格模糊逻辑SBL的扩张SBL～.     

二值命题逻辑的无损求解

针对协同问题求解、协同设计等诸多领域中存在逻辑冲突的共性问题,从二值命题逻辑理论出发,研究面向冲突的无损求解(即初始解空间获取)问题.首先,提出简单合取式的扩充和Wh-析取范式等概念,在此基础上定义初始解空间,并通过提出的有效扩充概念得到初始解空间的简化表示——最简解空间,探讨了两类解空间的关系及各自的计算方法.其次,构造生成序列来辅助公式的析取化,从泛代数的角度定义了Wh-代数;提出了指数矩阵,并籍此给出了Wh-代数的等价表现形式,通过引入扩展指数矩阵构造出扩展Wh-代数.最后证明了扩展Wh-代数中的展开定理和逻辑简化定理,给出基于有效扩充的直接无损求解算法,并与提出的其他相关算法进行了对比,结果表明该算法较为理想.该研究对于协同问题求解等领域有着重要的推动作用.     

命题逻辑提升到一阶逻辑上的子句消去方法

在基于命题逻辑的可满足性问题（SAT）求解器和基于一阶逻辑的定理证明器上，子句集简化一直是必不可少的步骤，而其中子句消去方法在这些子句集简化方法中是非常重要的组成部分。将命题逻辑中的子句消去方法归结隐藏恒真消去方法（RHTE）和归结隐藏包含消去方法（RHSE）提升到一阶逻辑上，并且利用蕴含模归结原则（IMR）证明了这种提升方式在一阶逻辑上具有可靠性（Soundness），即依据这两种子句消去方法删除一阶逻辑公式集中的子句，并不会改变公式集的可满足性或者不可满足性。此外，将这两个方法与一阶逻辑子句消去方法锁子句消去方法（BCE）和归结包含消去方法（RSE）进行组合推广，发展得到一阶逻辑上新型子句消去方法（BC+RHS）E、（RS+RHT）E和（RHS+RHT）E，并且证明了这3种子句消去方法在一阶逻辑上的可靠性。最后，分析比较了这些子句消去方法的有效性，并且证明了这3种新型子句消去方法比组成它们的原始子句消去方法均具有更高的有效性。     

A Dynamic Logic for deductive verification of multi-threaded programs

We present MODL, a Dynamic Logic and a deductive verification calculus for a core Java-like language that includes multi-threading. The calculus is based on symbolic execution. Even though we currently do not handle non-atomic loops, employing the technique of symmetry reduction allows us to verify systems without limits on state space or thread number. We have instantiated our logic for (restricted) multi-threaded Java programs and implemented the verification calculus within the KeY system. We demonstrate our approach by verifying a central method of the StringBuffer class from the Java standard library in the presence of unbounded concurrency.     

Propositional dynamic logic with recursive programs

We extend the propositional dynamic logic PDL of Fischer and Ladner with a restricted kind of recursive programs using the formalism of visibly pushdown automata [R. Alur, P. Madhusudan, Visibly pushdown languages, in: Procceings of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), 2004, ACM, pp. 202–211]. We show that the satisfiability problem for this extension remains decidable, generalising known decidability results for extensions of PDL by non-regular programs. Our decision procedure establishes a 2-ExpTime upper complexity bound, and we prove a matching lower bound that applies already to rather weak extensions of PDL with non-regular programs. Thus, we also show that such extensions tend to be more complex than standard PDL.     

Propositional semantics for disjunctive logic programs

In this paper we study the properties of the class of head-cycle-free extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NP-completeness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion.     

Applying Propositional Logic to Workflow Verification

The increasing complexity of business processes in the era of e-business has heightened the need for workflow verification tools. However, workflow verification remains an open and challenging research area. As an indication, most of commercial workflow management systems do not yet provide workflow designers with formal workflow verification tools. We propose a logic-based verification method that is based on a well-known formalism, i.e., propositional logic. Our logic-based workflow verification approach has distinct advantages such as its rigorous yet simplistic logical formalism and its ability to handle generic activity-based process models. In this paper, we present the theoretical framework for applying propositional logic to workflow verification and demonstrate that logic-based workflow verification is capable of detecting process anomalies in workflow models.     

基于幂零泛与运算模型的命题模糊逻辑

本文讨论了泛与运算模型T(x,y．h)(h∈(o,0．75))的一些性质;证明了泛与运算模型T(x,y,h)(h∈(0,O.75))是一个幂零三角范数;而且泛与运算模型T(x,y．h)(h∈(0,0．75))与泛蕴涵运算模型,(x,y,h)(h∈(0,0.75))是一个伴随对;进一步证明了([0,1].∨,∧．*,→．0,1)作成一个MV-代数。给出了基于幂零泛与运算模型T(x,y,h)(h∈(0,0.75))的模糊命题演算系统PC(T),证明了此命题演算系统与Lukasiewicz逻辑命题演算系统是等价的。     

Timing Analysis of Combinational Circuits in Intuitionistic Propositional Logic

Classical logic has so far been the logic of choice in formal hardware verification. This paper proposes the application of intuitionistic logic to the timing analysis of digital circuits. The intuitionistic setting serves two purposes. The model-theoretic properties are exploited to handle the second-order nature of bounded delays in a purely propositional setting without need to introduce explicit time and temporal operators. The proof-theoretic properties are exploited to extract quantitative timing information and to reintroduce explicit time in a convenient and systematic way.We present a natural Kripke-style semantics for intuitionistic propositional logic, as a special case of a Kripke constraint model for Propositional Lax Logic (Information and Computation, Vol. 137, No. 1, 1–33, 1997), in which validity is validity up to stabilisation, and implication comes out as boundedly gives rise to. We show that this semantics is equivalently characterised by a notion of realisability with stabilisation bounds as realisers. Following this second point of view an intensional semantics for proofs is presented which allows us effectively to compute quantitative stabilisation bounds.We discuss the application of the theory to the timing analysis of combinational circuits. To test our ideas we have implemented an experimental prototype tool and run several examples.     

An Algebraic Approach to Propositional Fuzzy Logic

We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield , and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields.