A Logical Framework for Knowledge Base Maintenance

The maintenance sequences of a knowledge base and their limits are introduced.Some concepts used in knowledge base maintenance,such as new laws,user‘s rejections,and reconstructions of a knowledge base are defined;the related theorems are proved.A procedure is defined using transition systems;it generates maintenance sequences for a given user‘s model and a knowledge base.It is proved that all sequences produced by the procedure are convergent,and their limit is the set of true sentences of the model.Some computational aspects of reconstructions are studied.An R-calculus is given to deduce a reconstruction when a knowledge base meets a user‘s rejection.The work is compared with AGM‘s theory of belief revision.     

An algebraic approach to revising propositional rule-based knowledge bases

One of the important topics in knowledge base revision is to introduce an efficient implementation algorithm. Algebraic approaches have good characteristics and implementation method; they may be a choice to solve the problem. An algebraic approach is presented to revise propositional rule-based knowledge bases in this paper. A way is firstly introduced to transform a propositional rule-based knowledge base into a Petri net. A knowledge base is represented by a Petri net, and facts are represented by the initial marking. Thus, the consistency check of a knowledge base is equivalent to the reachability problem of Petri nets. The reachability of Petri nets can be decided by whether the state equation has a solution; hence the consistency check can also be implemented by algebraic approach. Furthermore, algorithms are introduced to revise a propositional rule-based knowledge base, as well as extended logic programming. Compared with related works, the algorithms presented in the paper are efficient, and the time complexities of these algorithms are polynomial.     

A New Integrated System of Logic Programming and Relational Database

Based on the study of the current two methods-interpretation and compilation-for the integration of logic programming and relational database,a new precompilation-based interpretive approach is proposed.It inherits the advantages of both methods,but overcomes the drawbacks of theirs.A new integrated system based on this approach is presented,which has been implemented on Micro VAX Ⅱ and applied to practise as the kernel of the GKBMS knowledge base management system.Also discussed are the key implementation techniques,including the coupling of logic and relational database systems,the compound of logic and relational database languages,the partial evaluation and static optimization of user‘s programs,fact scheduling and version management in problem-solving.     

Decidable subsets of open logic and an algorithm for R-calculus

Open logic is an attractive logic theory that can describe the growth and evolution of knowledge.However, related studies show that open logic is undecidable in first-order logic and thus is hard to be programmed. This paper proposes that open logic should be implemented with constraints, and provides a set of syntax constraints under which open logic is decidable. Furthermore, it is shown that the constraints are necessary and sufficient for the decidable formulas of open logic. A Domino problem-based algorithm R-CP that implements the R-calculus of the constrained open logic is presented and its reachability is proved.     

A Reduction Algorithm Meeting Users Requirements

Generally a database encompasses various kinds of knowledge and is shared by many users.Different users may prefer different kinds of knowledge.So it is important for a data mining algorithm to output specific knowledge according to users‘ current requirements (preference).We call this kind of data mining requirement-oriented knowledge discovery (ROKD).When the rough set theory is used in data mining,the ROKD problem is how to find a reduct and corresponding rules interesting for the user.Since reducts and rules are generated in the same way,this paper only concerns with how to find a particular reduct.The user‘s requirement is described by an order of attributes,called attribute order,which implies the importance of attributes for the user.In the order,more important attributes are located before less important ones.then the problem becomes how to find a reduct including those attributes anterior in the attribute order.An approach to dealing with such a problem is proposed.And its completeness for reduct is proved.After that,three kinds of attribute order are developed to describe various user requirements.     

A Comparative Study of Default Reasoning and Epistemic Processes

A comparative study between the theories of default reasoning and open logic is given.Some concepts of open logic,such as new premises,rejections by facts,reconstructions ,epistemic processes,and its limit are introduced to describe th evolution of hypotheses.An improved version of the limit theorem is given and proved.A model-theoretic interpretation of the closed normal defaults is given using the above concepts and the corresponding completeness is proved.Any extension of a closed normal default theory is proved to be the linit of a δ-partial increasing epistemic process of that theory,and vice versa.It is proved that there exist two distinct extensions of a closed normal default theory iff there is an δ-non-monotonic epistemic process of that theory.The completeness of Reiter‘s proof is also given and proved,in terms of the epistemic processes.Finally,the work is compared with Gaerdenfors‘s theory of knowledge in flux.     

Default reasoning and belief revision: A syntax-independent approach

As an important variant of Reiter‘s default logic.Poole(1988) developed a nonmonotonic reasoning framework in the classical first-order language,Brewka and Nebel extended Poole‘s approach in order to enable a representation of priorities between defaults.In this paper a general framework for default reasoning is presented,which can be viewed as a generalization of the three approaches above.It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al.(1997).This esult provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case .As a by-product,an answer to the the question,raised by Mankinson and Gaerdenfors(1991),is also given about whether there is a counterpart contraciton in nonmonotonic logic.     

Formal Ontology: Foundation of Domain Knowledge Sharing and Reusing

Domain analysis is the activity of identifying and representing the relevant information in a domain,so that the information can be shared and reused in similar systems.But until now,no efficient approaches are available for capturing and representing the results of domain analysis and then for sharing and reusing the domain knowledge.This paper proposes an ontology-oriented approach for formalizing the domain models.The architecture for the multiple-layer structure of the domain knowledge base is also discussed.And finally,some genetic algorithm-based methods have been given for supporting the knowledge sharing and reusing.     

A sound and complete R-calculi with respect to contraction and minimal change

AGM postulates are for belief revision （revision by a single belief）, and DP postulates are for iterated revision （revision by a finite sequence of beliefs）. R-calculus is given for R-configurations △｜Г, where △ is a set of atomic formulas or the negations of atomic formulas, and Г is a finite set of formulas. We shall give two R-calculi C and M （sets of de- duction rules） such that for any finite consistent sets Г, △of formulas in the propositional logic, there is a consistent set ⊙ Г C of formulas such that △IГ → △, ⊙ is provable and⊙ is a contraction of F by A or a minimal change of F by A; and prove that C and M are sound and complete with respect to the contraction and the minimal change, respectively.     

扩充逻辑程序设计的R－演算──知识库维护的操作方法

本文首先介绍了知识库维护过程中诸如知识库序列、新规则、用户反驳以及重构等概念；然后给出了一个扩充逻辑程序设计的框架，在这一框架下，每个逻辑程序等价于一个知识库；进一步定义了一个转换系统，称为扩充逻辑程序设计的Ｒ－演算，对一个给定的知识库和用户反驳，此演算可以导出知识库的最佳修正；同时证明了该演算的可靠性和完备性；另外，对本文的工作与其他相关工作进行了比较；最后，给出了本文的结论．     

A Logical Framework for Knowledge Base Maintenance

1IntroductionAmongalltheoreticalworksonknowledgebasemaintenance,Doyle's"TruthMaintenanceSystem"[1]andAlchourr6n,GdrdenforsandMakinson's"LogicofThe-oryChange"[2]playthemostimportantrole.'Inthe"TruthMaintenanceSystem",everylawcontainedinaknowledgebase,orabaseforshort,isspecifiedby"in"and"out"status,whichindicatethededuciblerelationsbetweenthelawsofthebase.Whenalawofthebaseisrejectedbytheusers3arevisedversionofthebasecanbeobtainedbymechanicallychangingthe"in"and"out"statusofthelaws.Thismech…     

知识库维护过程中检查其协调性的有效方法

本文首先描述了知识库维护过程中的协调性问题，然后给出了扩充逻辑程序设计的框架，在此框架下，每个逻辑程序等价于一个知识库．为了检查知识库的协调性，本文为知识库中的推理规则构造了正支持集和负支持集，并给出了一些定义；基于这些概念和定义，提出了知识库维护过程中检查知识库协调性的一种有效方法，并证明了相关的定理；基于此方法，实现了一个算法ＣＨＩＭＥ，并给出了用ＣＨＩＭＥ分析一些知识库的实验结果．本文还提到一些相关的工作，最后给出结论.     

开放逻辑中基于一优先序的R-重构

在开放逻辑中,Ｒ－重构作为一知识库或信念集修正的结果并不唯一,有时甚至太多而难于明确计算和表示,为此,文中给出了基于一优先序的Ｒ－重构的概念,基于一优先序的Ｒ－重构往往要比Ｒ－重构少得多,不存在上述Ｒ－重构的问题,在用户给出的关于一知识库中知识的优先序时,基于该优先序的Ｒ－重构可以用来刻画对该知识库的合理维护。     

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.     

基于强相关逻辑的不精确应急时态知识表示

在强相关逻辑基础上扩展不精确时态关系,以满足不精确应急时态知识表示与推理的需要。给出了粗糙集及强相关逻辑的相关概念;通过定义不精确时态关系扩展了强相关逻辑,形成了粗糙时态强相关逻辑,给出了可靠性和完备性证明;通过实际例子说明粗糙时态强相关逻辑的知识表示和应用。结果表明扩展后的粗糙时态强相关逻辑可以实现不精确时态知识的表示与推理。     

基于粗糙描述逻辑的不精确时态知识表示研究

在粗糙描述逻辑基础上扩充不精确时态关系,以满足不精确时态知识表示与推理的需要。首先给出了粗糙集及粗糙描述逻辑的相关概念;接着通过定义粗糙时态描述逻辑不精确时态关系,扩展了粗糙描述逻辑中具体域,并给出了可靠性和完备性证明;最后通过实际例子说明粗糙时态描述逻辑的知识表示和应用,结果表明扩展后的粗糙时态描述逻辑可以实现不精确时态知识的表示与推理。     

基于知识Petri网和归结规则的推理方法

本文提出了一种基于知识Petri网和归结规则的推理方法.通过知识Petri网描述命题逻辑知识库,将归结规则映射到知识Petri网上,根据库所和变迁的连接关系,定义了知识Petri网中的归结结构.利用归结结构,给出了基于知识Petri网的归结推理算法和扩展知识库的推理算法,并利用Wumpus实例验证了推理算法.该推理方法是可靠且完备的,能够利用知识Petri网的网络结构降低计算复杂性.     

面向数据库中关系的描述逻辑

给出了两个面向数据库中关系的描述逻辑。在其中一个描述逻辑中,一个关系可以表示为一个知识库和这个知识库的模型,并且对于这个知识库的任意模型,都存在一个与该关系同构的子模型;在另一个描述逻辑中,一个关系可以表示为一个知识库和这个知识库的模型,以便这个知识库的任何模型都同构于这个关系。