同Vague谓词命题的概率逻辑

基于对Vague（或Fuzzy）概念的一种新的认知,使用随机集和概率论,引入了论域表达式及其适当测度的概念。进一步地,通过引入同Vague谓词命题及其他们真的概率（简称概率真度）的概念,提出了一种新的非经典命题逻辑,称为同Vague谓词命题的概率逻辑,并提供了其逻辑规律。其逻辑规律表明它与经典逻辑具有优良的和谐性。比较了同Vague谓词命题的概率逻辑与模糊逻辑的长处与不足。     

G-逻辑及其归结推理

该文提出了一种粒-逻辑，简记为G-逻辑，并构造了这种逻辑的近似推理系统，定义了G-公式、G-子句和G-文字，提出了这种逻辑的G-归结方法．G-归结的完备性定理也被证明了．这种逻辑公式的结构是有序二元对，第一元是断言；第二元是对应于这个断言的可定义集或不可定义域集的近似集．这种逻辑是定义在信息系统IS=(U，A)上，所以其公式中的个体变量被赋予U上的实体．公式中的命题或谓词被解释为属性集A上的属性，因此命题或谓词的意义集是U上的一个子集、属性及其意义集一起构成的二元对，被称做一个基本粒(granule)．而这种基本粒被当做这种逻辑中的一个G-原子，用G逻辑联结词组合这些G-原子便得到这种逻辑中的G-公式．公式的可满足性是其相应断言的意义集不空．当这种公式的定义域集不可定义时，则可将它移到其定义域集的Rough下和上近似集上去讨论．G-逻辑的提出为经典逻辑的应用开辟了新途径，也为处理非规范知识提供了较好的理论工具．G-逻辑的运算涉及整体到局部的分解和局部到整体的合并，以此提供了AI中问题求解的新思路．G-逻辑也是Rough逻辑的新扩充，其真值概念及其运算都不同于经典逻辑，也不同于其它非标准逻辑．这种逻辑中的演算既是逻辑的，又是集合论的．于是当处理真值及其运算时适合使用逻辑方法；而处理归结中的文字合一时可用集合论方法，这样可避免复杂的文字合一计算．最后，用实例说明了这种逻辑的G-归结方法的可行性和有效性，并给出了G-逻辑中机器定理证明的相关定理，讨论了G-归结反演的完备性和完全性．     

粒计算的α_决策逻辑语言

提出一种用于粒计算的α_决策逻辑语言．该语言是由Tarski意义下的模型和可满足性所描述的一种特殊的经典谓词逻辑．由属性值域的模糊子集代替经典的单值信息函数所得到的广义信息系统对应于模型，借助于模糊集理论的水平截集的概念，归纳地定义对泉在一定阈值水平下满足某公式．最后讨论如何利用α_决策逻辑语言描述不同的粒世界及分析形式概念和决策规则．     

基于直觉模糊逻辑的近似推理方法

针对直觉模糊逻辑及命题演算,提出了利用隶属度和犹豫度计算直觉模糊逻辑命题真值的合成方法．给出了直觉模糊逻辑命题的运算规则,重点研究了基于直觉模糊逻辑的近似推理方法．该方法包括直觉模糊取式推理,直觉模糊拒武推理及直觉模糊假官推理．井推导了相关的推理合成运算公式．以具体算例验证和表明了所提出的推导方法的正确性和有效性,以及对方法进行验证的详细步骤．     

命题时态逻辑定理证明新方法

本文通过对近１０年命题时态逻辑定理证明方法的研究，提出了一种新的证明方法，前人的工作基于对公式的现时部分和后时部分的分解，本文的工作是基于语义反驳树构造。这种新方法为计算机自动证明命题时态逻辑定理，提供了比较好的理论框架．最后还证明了该方法的可靠性和完全性．     

一阶模糊谓词逻辑公式的有限解释真度和可数解释真度的理论及其应用

通过引进公式变元集赋值的新概念给出了一阶模糊谓词逻辑（或一阶模糊语言）公式的有限解释真度及可数解释真度的定义,并讨论了它们的一系列性质及其在近似推理中的应用,从而为一阶谓词逻辑的近似推理理论提供了一种带度量的框架.     

推广规则后一阶逻辑公式的准真度

计量逻辑理论是逻辑概念程度化研究方向的一个重要分支。但目前计量谓词逻辑的相关研究中，都不曾涉及推广规则。一阶逻辑公式的准真度理论是计量谓词逻辑的一个重要的研究成果，讨论经过推广规则后，一阶逻辑公式准真度的变化情况，证明经过推广规则后，一阶逻辑公式在基于准真度的一阶逻辑公式集的分类中类别不变。     

一个带有相似性关系的模糊逻辑

模糊集与模糊逻辑是处理模糊性与不确定性信息的重要数学工具，相似性关系是模糊集的一个基本概念。为了在模糊逻辑中集成相似性关系并考虑其模糊推理，提出了一个带有相似性关系的模糊逻辑，给出了其语法及语义描述，在模糊谓词逻辑情形下，讨论并证明了基于归结与调解方法的模糊推理的有关属性，考虑到许多定理证明器和问题解决系统均是基于否证法，证明了归结与调解方法对模糊谓词演算的反驳完备性定理。     

利用谓词/变迁网证明的一阶谓词逻辑命题

研究了证明一般的一阶谓词逻辑命题的方法,根据网逻辑的思想,利用谓词/变迁网对一般形式的一阶谓词逻辑命题进行了图形表示,提出了2种一阶谓词逻辑命题的证明方法：图形证明法和矩阵证明法。举出一个实际的例子来说明证明思路。     

从经典逻辑知识构建ASP知识库的新方法

回答集程序设计(ASP)是一种主流的非单调知识表示工具。为了能够在利用ASP求解问题过程中使用现有的以经典逻辑表示的知识,给出了一种把以谓词逻辑公式表示的约束型知识和定义型知识转化为ASP程序或知识库的新方法,并以实例说明了其有效性。该方法满足转化后ASP程序的回答集与原公式集的模型具有一一对应关系。在实际应用中,该方法提供了一项从现存的以谓词逻辑为表示语言的知识库,构建以ASP为知识表示语言的非单调知识库的技术。     

Annotated Logic Applications for Imperfect Information

Imperfect information is a very general term that comprises different types of information, such as uncertain, vague, fuzzy, inconsistent, possibilistic, probabilistic, partially or totally incomplete information [2]. In the literature of knowledge representation we find a different formal model for each one of these distinct types. For example, annotated logic is a formal model to represent inconsistent information.Annotated logics are non-classical logics introduced in [20] as a logic programming theory. They were proved to be paraconsistent. Based on [5], we present in this work the annotated logic programming theory and some of its applications in Artificial Intelligence (AI). We present it as a formalism to reason with inconsistent information and investigate its possibility to represent other types of imperfect information, such as possibilistic and non-monotonic reasoning. Our main goal is to verify and confirm the importance of annotated logics as a tool for developing knowledge-based and automated reasoning systems in AI.     

Operational and complete approaches to belief revision

Two operational approaches to belief revision are presented in this paper.The rules of R-calculus are modified in order to deduce all the maximal consistent subsets.Another set of given in order to deduce all the minimal inconsistent subsets.Then a procedure,which can generate all the maximal consistent subsets,is presented.They are complete approaches,since all the maximal consistent subsets can be deduced or generated.In this paper,only the case of propositional logic is considered.     

A general framework for computing maximal contractions

This paper investigates the problem of computing all maximal contractions of a given formula set Γ with respect to a consistent set Δ of atomic formulas and negations of atomic formulas. We first give a constructive definition of minimal inconsistent subsets and propose an algorithmic framework for computing all minimal inconsistent subsets of any given formula set. Then we present an algorithm to compute all maximal contractions fromminimal inconsistent subsets. Based on the algorithmic framework and the algorithm, we propose a general framework for computing all maximal contractions. The computability of the minimal inconsistent subset and maximal contraction problems are discussed. Finally, we demonstrate the ability of this framework by applying it to the first-order language without variables and design an algorithmfor the computation of all maximal contractions.     

Knowledge-Driven versus Data-Driven Logics

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data-driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy rules as a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data-driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data-driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data-driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize.     

Possibilistic Petri nets

This paper presents the possibilistic Petri net model which combines possibility logic with Petri nets with objects. The main feature of this model is to allow one to reason about the aspects of uncertainty and change in dynamic discrete event systems. The paper presents relevant concepts of Petri nets with objects and possibility logic and how imprecision and vagueness are introduced in the marking of a Petri net with objects. The marking of a net is imprecise, or in a more general way, fuzzy, in order to represent an ill-known knowledge about a system state. A new marking updating according to the fuzzy marking such defined is also discussed. An example of shop door monitoring is presented that illustrates our approach.     

一种基于PROLOG的ES建造工具库的研究与实现

本文描述了一种基于ＰＲＯＬＯＧ的专家系统建造工具库ＰＴＥＳ的实验系统。ＰＴＥＳ是用ＰＲＯＬＯＧ编写的，该系统根据支持基于规则的知识表示及近似推理对ＰＲＯＬＯＧ的知识处理能力进行了扩充。ＰＴＥＳ的推理机制使用了可能性能逻辑及模糊集合理论作为其逻辑基础，并以一种形式化的方法提供了处理非确定事实及非确定规则的能力。     

具有多值决策过程的广义可能性计算树逻辑模型检测

模型检测是一种自动验证软硬件系统行为的有效技术。为了对包含非确定性信息、不一致信息的并发系统进行形式化验证,在可能性理论、多值逻辑的基础上,研究了具有多值决策过程的广义可能性多值计算树逻辑模型检测算法,及其在检验非确定性系统中的具体应用。首先构造了多值决策过程作为系统模型,用多值计算树逻辑描述系统属性。然后给出具有多值决策过程的广义可能性多值计算树逻辑的模型检测算法,该算法将模型检测的具体问题转换为多项式时间内的模糊矩阵运算。最后就包含非确定性选择的多值系统的模型检测问题,给出一个具体的应用实例。     

一种基于PROLOG的ES建造工具库的研究与实现

本文描述了一基于ＰＲＯＬＯＧ的专家系统建造工具库ＰＴＥＳ的实验系统。ＰＴＥＳ是用ＰＲＯＬＯＧ编写的，该系统根据支持基于规则的知识表示及近似推理对ＰＲＯＬＯＧ的知识处理能力进行了扩充。ＰＴＥＳ的推理机制使用了可能性逻辑及模糊集合理论作为其逻辑基础并以一种形式化的方法提供了处理非确定事实及非确定规则的能力。     

A programmable approach to maintenance of a finite knowledge base

In this paper,we present a programmable method of revising a finite clause set.We first present a procedure whose formal parameters are a consistent clause set Γand a clause A and whose output is a set of minimal subsets of Γwhich are inconsistent with A.The maximal consistent subsets can be generated from all minimal inconsistent subsets.We develop a prototype system based on the above procedure,and discuss the implementation of knowledge base maintenance.At last,we compare the approach presented in this paper with other related approaches,The main characteristic of the approach is that it can be implemented by a computer program.     

A modal proof theory for final polynomial coalgebras

An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets. The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor. The states of this final coalgebra are certain “maximal” sets of formulas that have natural syntactic closure properties.

The syntax of these logics extends that of previously developed modal languages for polynomial coalgebras by adding formulas that express the “termination” of certain functions induced by transition paths. A completeness theorem is proven for the logic of functors which have the Lindenbaum property that every consistent set of formulas has a maximal extension. This property is shown to hold if the deducibility relation is generated by countably many inference rules.

A counter-example to completeness is also given. This is a polynomial functor that is not Lindenbaum: it has an uncountable set of formulas that is deductively consistent but has no maximal extension and is unsatisfiable, even though all of its countable subsets are satisfiable.