集合代数是经典命题演算形式系统的语义解释

经典命题演算形式系统(CPC)中的公式只是一些形式符号,其意义是由具体的解释给出的.逻辑代数和集合代数都是布尔代数,都是CPC的解释.集合代数是CPC的集合语义,其中对联结词的解释就是集合运算;对形式公式的解释就是集合函数;对逻辑蕴涵.逻辑等价的解释就是集合包含和集合相等=.标准概率逻辑是在标准概率空间上建立的逻辑体系,命题表示随机事件,随机事件是集合,概率空间中的事件域是集合代数,概率逻辑就是CPC集合语义的实际应用.CPC完全适用于概率命题演算.     

概率逻辑系统是与集合代数同态的布尔代数

联结词的本质是命题的运算,只有对所有命题都适用的真值函数才能用于定义联结词.概率逻辑中由于命题的内涵相关性,任何[0,1]上的函数都不能完全适用于任意命题的运算,概率逻辑的联结词不能定义成真值函数.各种算子可以作为一种计算方法使用和研究,但不能代表一个逻辑系统研究系统的性质.概率逻辑系统是概率空间的逻辑表示,是与概率空间中的事件域(集合代数)同态的布尔代数.用事件域上的集合函数精确定义各种联结词,与经典二值逻辑相容,与事实相符,能够在经典逻辑框架内实现概率命题演算.     

基于n-值(L)ukasiewicz命题逻辑的概率计量化推理系统

通过把n-值Lukasiewicz命题逻辑中公式的概率真度函数抽象为模态词,把概率真度函数的基本恒等式抽象为关于模态词的公理,建立一个模态化的形式推理系统,构建其语构理论及语义理论,证明该系统关于概率真度函数的完备性定理,从而为概率计量逻辑奠定逻辑基础.     

基于n-值ukasiewicz命题逻辑的概率计量化推理系统

通过把n-值ukasiewicz命题逻辑中公式的概率真度函数抽象为模态词,把概率真度函数的基本恒等式抽象为关于模态词的公理,建立一个模态化的形式推理系统,构建其语构理论及语义理论,证明该系统关于概率真度函数的完备性定理,从而为概率计量逻辑奠定逻辑基础.     

Borel型概率计量逻辑

视全体赋值之集为通常乘积拓扑空间,利用该空间上的Borel概率测度在二值命题逻辑中引入了公式的概率真度概念.该方法既克服了计量逻辑学要求赋值集上的概率测度必须为均匀概率测度的无穷可数乘积的局限,又弥补了概率逻辑学只讲局部而缺乏整体性的不足;证明了计量逻辑学中公式的真度、随机真度以及概率逻辑学中公式的概率等概念都可作为本文提出的概率真度的特例而纳入到统一的框架中,从而实现了计量逻辑学与概率逻辑学的融合与统一;证明了逻辑闭理论与赋值空间中的拓扑闭集是一一对应的以及概率真度函数与赋值空间上的Borel概率测度是一样多的等若干结论;本文的第4节给出了公式的概率真度的公理化定义,证明了公式集上满足Kolmogorov公理的任一[0,1]值函数均可由赋值空间上的某Borel概率测度按本文的方法所表出,从而建立了二值命题逻辑框架下的概率计量逻辑的理论体系.     

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～.     

中介命题演算系统MP^M的公理完备集

本文基于中介逻辑命题演算系统MP^M构造了一个公理集合，证明了该公理集合的完备性。该公理集合中的公理均是由等式的形式给出，可以方便地对MP^M、MF^M系统上的等值公式进行推导和证明。本文还讨论了该公理集合在不完全信息数据库查询优化上的应用。     

移动进程的蛰伏性及空间逻辑

界程逻辑(Ambient Logic)定义了一个示范性的空间逻辑来描述移动界程演算中移动进程的空间性质.然而在某些移动计算系统中,界程逻辑对移动进程空间性质的描述粒度是不够的.分析移动进程的蛰伏性质,用蛰伏和活跃来描述移动进程的存在状态,由此给出一种界程逻辑的扩展,称为状态空间逻辑.该逻辑能够描述移动进程的蛰伏性,进而更细粒度地刻画进程空间性质,且其在移动界程演算上的满足性是可判定的.同时还给出了状态空间逻辑公式的形式解释和蛰伏空间公式的逻辑推导规则.     

ELNF演算的解释技术

ＥＬＮＦ演算是我们在ＬＮＦ演算的基础上扩充逻辑程序设计能力而得到的一种函数／逻辑演算系统，它构成了作者设计的函数／逻辑语言ＲＦＵＮＬＯＧ的基础．本文介绍ＥＬＮＦ演算的解释实现技术，包括数据结构、系统结构以及各个模块的设计思想．最后给出了在此解释系统下，几个典型程序的运行时间．     

基于信息系统的粒度计算机理研究

基于信息系统建立决策逻辑代数系统和论域的拓扑代数系统,并找到它们之间的关系定理.利用这两个代数系统建立粒度世界的三元模型.然后,基于该粒度世界模型通过对概念学习、规则获取的分析从理论上研究粒度计算的机理.同时,各种粒度计算方法在该模型中得到一致的解释,在一定程度上完成粒集合运算和粒描述演算(决策逻辑演算)的统一.     

Propositional trust logics

Propositional trust logics deal with propositions that are considered at a trust-distrust level from 51% to 100%. The rules of these logics and rules of 2-valued logic are proved to be of the same form.     

Propositional Attitudes and Causation

Predicting and explaining the behavior of others in terms of mental states is indispensable for everyday life. It will be equally important for artificial agents. We present an inference system for representing and reasoning about mental states, and use it to provide a formal analysis of the false-belief task. The system allows for the representation of information about events, causation, and perceptual, doxastic, and epistemic states (vision,belief, and knowledge), incorporating ideas from the event calculus and multi-agent epistemic logic. Unlike previous AI formalisms, our focus here is on mechanized proofs and proof programmability, not on metamathematical results. Reasoning is performed via relatively cognitively plausible inference rules, and a degree of automation is achieved by generalpurpose inference methods and by a syntactic embedding of the system in first-order logic.     

Propositional attitude framework requirements

Abstract

The purpose of this paper is to focus attention on various important aspects and problems of propositional attitude representation in the hope of engendering fruitful discussion on these topics, and in particular in the hope that such discussion might lead to a determination of useful criteria for evaluating the merits and drawbacks of individual systems. As such, the paper does not purport to offer ‘the solutions’ to the mentioned problems, nor are the problems discussed here intended to be an exhaustive catalogue of the problems that must be solved by successful systems. The problems are, however, advanced as a useful set of criteria for evaluating systems by considering which problems are tackled, and how they are tackled.     

The Propositional Formula Checker HeerHugo

HeerHugo is a propositional formula checker that determines whether a given formula is satisfiable or not. The underlying algorithm is based on a specific breadth-first search procedure, with several enhancements including unit resolution and 2-satisfiability tests. Its main ingredient is the branch/merge rule inspired by an algorithm proposed by Stållmarck, which is protected by a software patent. In this paper, the main elements of the algorithm are discussed, and its remarkable effectiveness is illustrated with some examples and computational results.     

Propositional logic of reflexive sentences

The author suggests a semantically closed language with Tarski’s truth predicate and variables based on formulas in which reflexive sentences (i.e., referring to themselves) are expressed explicitly (by the reflexivity quantor introduced by the author).     

Propositional representation for graphical knowledge

Multi-media interfaces with a graphics and a natural language component can be viewed as a Natural Language Graphics systems without a host program. We will investigate a theory of Natural Language Graphics that is based on the notion of “Graphical Deep Knowledge” defined in this research. Graphical Deep Knowledge is knowledge that can be used for display purposes as well as reasoning purposes and we describe the syntax and semantics of its constructs. This analysis covers forms, positions, attributes, parts, classes, reference frames, inheritability, etc. Part hierarchies are differentiated into three sub-types. The usefulness of inheritance along part hierarchies is demonstrated, and criticism of inheritance-based knowledge representation formalisms with a bias towards class hierarchies is derived from this finding. The presented theory has been implemented as a generator program that creates pictures from knowledge structures, and as an augmented transition network grammar that creates knowledge structures from limited natural language input. The function of the picture generation program Tina as a user interface for a circuit board maintenance system and as part of a CAD-like layout system is demonstrated.     

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.     

Propositional compositions of partial predicates

Compositions of partial predicates of the highest abstraction level that form the basis of infinitary propositional logics are defined and investigated. The compositions are completely described in terms of special algebras called Klee ne algebras, and a complete system of identities is constructed for such compositions. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 3–19, March–April, 2000.