缺省逻辑的Roos扩充

Reiter的缺省逻辑的一个缺陷是不能分情形进行推理,为了克服Reiter扩充的这一缺陷,Roos提出了缺省扩充的一种修正定义来解决这一问题。文中将讨论Roos扩充类似于Reiter扩充的一些性质,发现Reiter扩充的一些性质对Roos扩充不再成立,并指出它们的不同。     

不协调知识的缺省推理

提出了一个新的缺省推理理论,称为双缺省理论,使得缺省逻辑在四值语义下能够同时处理不协调的知识而不导致扩张的平凡性.为此,定义了命题公式的正变换和负变换,以便分离一个文字与其否定的语义联系.大多数关于缺省逻辑的定理都可以在双缺省逻辑下重建,证明了双缺省逻辑是缺省逻辑在不协调情形下的一般化.提供了一种方法使得超协调逻辑能够获得类似经典逻辑的推理能力.     

基于四值语义的缺省逻辑

基于公式变换,给出一组缺省理论的变换方法,将命题语言L中的缺省理论变换到对应的命题语言L^-＋中,保证了所得到的缺省理论的所有扩张均不平凡,并通过一种弱变换可同时保证缺省扩张的存在性．为缺省理论定义了各种四值模型,使得缺省逻辑具有非单调超协调推理能力,并证明了L^-＋中的缺省扩张与L中缺省理论的四值模型之间具有一一对应关系．四值模型描述了公式变换的语义,基于四值语义的缺省推理通过缺省理论的变换技术能在标准的缺省逻辑中实现．     

基于DFL的模糊缺省推理研究

统计缺省理论是经典缺省逻辑（Reiter缺省）的推广,借助错误参数ε,允许我们在标准的推理统计中模型化普遍的推理模式。本文针对研究对象以及它们之间的动态模糊性,提出了基于动态模糊逻辑（DFL）的模糊缺省推理,并通过算子语义的方法计算模糊缺省扩充。     

一种带缺省推理的描述逻辑

该文提出了一种新的带缺省推理的描述逻辑，它以描述逻辑为主要框架，对单调逻辑和非单调逻辑进行了整合，但又避免了一般缺省逻辑的困难．基于带缺省推理的描述逻辑，构建了一种同时具有Tbox，Abox和缺省规则的知识库系统，研究了带缺省推理的描述逻辑的可满足性、缺省可满足性、概念包含、缺省包含以及实例检测等推理问题，提出了一种用来检测可满足性和缺省可满足性的Tableau—D算法，并得到了缺省可满足性和缺省包含的转换定理．     

基于统计缺省逻辑的多Agent推理模型

统计缺省逻辑是经典缺省逻辑的推广,借助错误参数允许我们在标;隹的推理统计模型中模型化普遍的推理模式。多Agent系统所面临的推理环境是动态的、不确定的,在推理过程中可以通过设置错误参数,在允许错误的情况下进行推理。本文采用统计缺省逻辑描述了多Agent系统的推理过程,建立了基于统计缺省逻辑的多Agent推理模型。     

缺省理论中一种获取优先序的方法

引进了一种在缺省理论中提取优先序的方法.与已有方法相比,此方法不仅具有合理性且具有低难度.进而定义了缺省逻辑的优先稳定语义.这种方法在不增加复杂性的情况下,增强了谨慎稳定缺省推理的能力.     

正则无析取缺省理论

知识表示和推理一直是人工智能领域中的一个非常重要的研究课题。早在1958年，McCharthy就提倡用逻辑方法来研究知识表示和推理以达到人工智能的目的。Reiter的缺省逻辑就是最有效的工具之一，这是因为它能够很好地刻画和处理不完全信息下的推理。然而，缺省逻辑并不是完美无缺的。首先，有的缺省理论没有扩充。这样的缺省理论是没有意义的。其次，缺省推理具有高难度。在一般情况下，缺省推理处在复杂性分层的第二层上。即使对于disjunction-free缺省逻辑，它的复杂性也是NP-完全的。     

累积缺省逻辑的扩充

针对缺省理论的一大热点问题—缺省扩充,将Grigoris Antonion的语义算子理论算法及V.W.Marek和M.Frusz-cyuski的语构算法用于计算累积缺省逻辑(CDL)的扩充,系统地讨论了CDL及其新变种CADL与QDL的理论的扩充问题,从而使得具有累积性的缺省逻辑扩充的计算问题系统化,同时指出这两种方法可用于其他类型的缺省理论扩充的计算。     

基于逻辑推理的计算机试题评卷算法研究

到目前为止,填空等试题的计算机评分方法,基本上是利用评分关键字与考生的答案匹配进行评分,评分结果并不理想。由于考生的答案多种多样,存在着不一致(inconsistent)或不确定(uncertain)的问题。R.Reiter缺省逻辑(default logic)推理可以有效地解决在不一致或不确定的情况下进行逻辑推理的问题。在N.D.Belnap四值逻辑的基础上,可将经典缺省逻辑推理推广到四值逻辑的双格结构上。将四值缺省推理应用到填空等试题的评分方法中,可使填空等试题的评分结果更加准确和科学。     

Reasoning with Sets of Defaults in Default Logic

We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory , consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension.     

Restricted semantics for default reasoning

In nonmonotonic reasoning there are the problems of inconsistency and incoherence in general, and in default reasoning there may be only one trivial extension or no extension in special. We propose the restricted semantics of four-valued logic for default reasoning to resolve the problems of inconsistency and incoherence and in the meantime retain classical extensions in the presence of consistency and coherency. The restricted semantics can maintain both the expressiveness and reasoning ability of default logic. We provide a transformation approach to compute the restricted extensions by reducing them into classical ones.     

Default reasoning by deductive planning

This paper deals with the automation of reasoning from incomplete information by means of default logics. We provide proof procedures for default logics' major reasoning modes, namely, credulous and skeptical reasoning. We start by reformulating the task of credulous reasoning in default logics as deductive planning problems. This interpretation supplies us with several interesting and valuable insights into the proof theory of default logics. Foremost, it allows us to take advantage of the large number of available methods, algorithms, and implementations for solving deductive planning problems. As an example, we demonstrate how credulous reasoning in certain variants of default logic is implementable by means of a planning method based on equational logic programming. In addition, our interpretation allows us to transfer theoretical results, such as complexity results, from the field of planning to that of default logics. In this way, we have isolated two yet unknown classes of default theories for which deciding credulous entailment is polynomial.Our approach to skeptical reasoning relies on an arbitrary method for credulous reasoning. It does not strictly require rather the inspection of all extensions, nor does it strictly require the computation of entire extensions to decide whether a formula is skeptically entailed. Notably, our approach abstracts from an underlying credulous reasoner. In this way, it can be used to extend existing formalisms for credulous reasoning to skeptical reasoning.This author was a visiting professor at the University of Darmstadt while parts of this work were being carried out. This author also acknowledges support from the Commission of the European Communities under grant no. ERB4001GT922433.     

A New Research into Default Logic

In previous papers some important properties of extensions of general default theories were given. In order to dedicate further research to default logic, a characterization of extensions is presented again and some new algorithms for reasoning tasks in default logic are presented in this paper. A class of default theories, auto-compatible default theory, is also developed. We show that the characterization and notions of compatibility and auto-compatibility, suitably applied to logic programs, yield some sufficient conditions of existence of answer sets. All these essentially develop the theories of Reiter and his followers.     

DEFAULT LOGICS: A UNIFIED VIEW

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.     

Stable and extension class theory for logic programs and default logics

The stable model semantics (cf. Gelfond and Lifschitz [1]) for logic programs suffers from the problem that programs may not always have stable models. Likewise, default theories suffer from the problem that they do not always have extensions. In such cases, both these formalisms for non-monotonic reasoning have an inadequate semantics. In this paper, we propose a novel idea-that of extension classes for default logics, and of stable classes for logic programs. It is shown that the extension class and stable class semantics extend the extension and stable model semantics respectively. This allows us to reason about inconsistent default theories, and about logic programs with inconsistent completions. Our work extends the results of Marek and Truszczynski [2] relating logic programming and default logics.     

Representation theory for default logic

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, non-normal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formalizing Default Reasoning

Fuzzy set systems can be used to solve the problem with uncertain knowledge,and default logic can be used to solve the problem with incomplete knowledge,in some sense.In this paper,based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning an default ogic,and give the procedure of transforming monotonic reasoning into default reasoning.