开放的缺省理论

本文基于开放逻辑理论，给出了缺省理论Ｔ＝＜Ｄ，Ｗ＞扩充Ｅ的新假设，事实反驳、ｅ－重构、ｅ－认识进程及其极限等概念的意义，讨论了Ｗ变化时新扩充的变化规律，并证明了相关的定理，本文还建立了缺省理论的一个动态描述过程，证明了其极限是某一特定问题的经验公式集，最后与相关工作进行了比较。     

在一类缺省理论中关于证明理论的完备性问题

缺省推理是各种非单调推理系统中最在影响的系统之一。Ｒ。Ｒｅｉｔｅｒ对规范缺省理论作了一系列的研究。他还提出了证明理论，并证明了这一证明理论对于规范缺省理论来说是完备的。Ｗ。Ｅｔｈｅｒｉｎｇｔｏｎ则提出了应用范围更为广泛的有序半规范缺省理论。本文先证明了这类缺省理论具有半单调性等各种性质，然后证明了Ｒ。Ｒｅｉｔｅｒ的证明理论对于有序半规范缺省理论也是完备的。     

缺省逻辑的e扩充和me扩充

缺省逻辑的扩充概念有二个弊端：１、无法描述缺省规则田固有的逻辑关系；２．无法描述结论与验证式之间的逻辑依赖关系。Ｗ．Ｌｕｋａｓｚｅｗｉｃａ提出的ｍ扩充概念解决了问题２但没有解决问题１；本文首先提出了ｅ扩充的概念，它解决了问题但没有解决问题２。最后我们提出了ｍｅ扩充的概念，解决了缺省逻辑遇到的两个问题，避免了相当一类的反常性，一个重要的结论是，每一封闭的缺省理论都有ｍｅ扩充。     

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。     

若干限制形式的缺少推理的复杂性

该研究判定一字是否出现在缺省理论〈Ｄ,Ｗ〉的某一扩张中的复杂性,其中,Ｄ是一种Ｈｏｒｎ缺省规则,而Ｗ是ｄｅｆｉｎｉｔｅ公式或Ｂｉ－Ｈｏｒｎ公式。     

子句型缺省理论的推理算法

1 引言缺省理论自1980年Reiter提出之后,已成为非单调推理的热点。在缺省逻辑中,扩张的概念至为重要。Reiter对特殊的缺省理论——正规缺省理论做了许多研究,并得出了一些漂亮的结果。Etherington给出了生成任意有穷有序半正规缺省理论的扩张的程序。张明义提出缺省的一种子类——自相容缺省理     

扩张与强相容缺省集

本文对一般形式的缺省理论进行了讨论，通过引入强相容缺省集概念，获得了缺省理论扩张存在的充分必要条件等重要结果，结果表明，缺省理论的扩张问题可以依据缺省集本身与初始公理作出判断，而不需要依赖于事先给定的闭公式集，最后，我们给出一实例，以示强相容集的构造方法。     

缺省推理与认识进程

本文概述了一个可以刻画知识的增长、更新以及假说的进化的开放逻辑理论;给出了有关新假设、事实反驳、假说的重构、认识进程及其极限等概念,讨论了它们的性质并证明了与之有关的定理。本文对开放逻辑和Reiter缺省推理理论做了比较研究,并用开放逻辑的概念给出了缺省的一个模型论解释,给出了扩充的构造,并证明了Reiter缺省证明概念的完全性。     

扩充与缺省规则的简化和分类

文章从缺省理论扩充的定义出发,在求扩充前根据缺省规则的特征,把对计算扩充没有影响的规则不予考虑,同时把具有不相容判断的规则分开考虑,也即就是在求扩充前对缺省规则进行适当的简化和分类,通过分析讨论给出了若干简化和分类的原则,从而使计算得以简化。     

子句型自相容缺省理论的扩张

自相容缺省理论是一种颇具优良性质的特殊缺省理论,从子句着手是一般逻辑揄常用的方法,文中Ｒｅｉｔｅｒ缺省理论和张明义的自相容缺省的理论的研究基础上,进一步研究了子句型闭自相容缺省理论,文中首先给出了自相容缺省理论的扩张个数的单调性定理,然后将Ｒｅｔｅｒ关于正规缺省理论的证明论推广到自相容缺省理论,得出了自相容缺省理论的缺省证明、自顶向下缺省证明和信念个性的相关定理。     

Ordered seminormal default theories and their extensions

Abstract

The concept of extension plays an important role in default logic. The notion of an ordered seminormal default theory has been introduced (Etherington 1987) to characterize a class of seminormal default theories which have extensions. However, the original definition has a drawback because of its dependence on specific representations of the default theory. We introduce the ‘canonical representation’ of a default theory and redefine the orderedness of a default theory based on its canonical representation. We show that under the new definition, the orderedness of a default theory Δ = (W,D) is intrinsic to the theory itself, independent of the specific representations of W and D. We present a modification of the algorithm in Etherington (1987) for computing extensions of a default theory. More importantly, we prove the conjecture (Etherington 1987) that a modified version of the algorithm in Etherington (1987) converges for general ordered, finite seminormal default theories, while the original algorithm was proven (Etherington 1987) to converge for ordered, finite network default theories which form a proper subset of the theories considered in this paper.     

缺省推理中的三个定理

本文证明了缺省推理中的三个定理.定理1表明了缺省推理的非单调性这一特点.定理2的实际意义在于,在一个封闭规范缺省理论(D,W)中,只要W能推出D中某些缺省的结论,则可以把这样的缺省规则从理论中删除,所得到的较小的缺省理论其延伸仍与原来缺省理论一样.尤其是若W能推出D中所有的缺省规则结论,则(D,W)的延伸就是W,这就是本文推论的结论.     

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.     

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.     

Tableau-based characterization and theorem proving for default logic

In this paper, we present a new method for computing extensions and for deriving formulae from a default theory. It is based on the semantic tableaux method and works for default theories with a finite set of defaults that are formulated over a decidable subset of first-order logic. We prove that all extensions (if any) of a default theory can be produced by constructing the semantic tableau ofone formula built from the general laws and the default consequences. This result allows us to describe an algorithm that provides extensions if there are any, and to decide if there are none. Moreover, the method gives a necessary and sufficient criterion for the existence of extensions of default theories with finitely many defaults provided they are formulated on a decidable subset of FOL.This work was completed while the author was at CNRS, Marseille.     

可能性缺省逻辑及其应用

本文分析了Yager用可能性理论框架来表示缺省知识的形式化方法,并测试了三类不同的应用方案,得到的结果与Reiter的缺省逻辑得到的结果相比较,表明只在具有严格的约束的缺省逻辑下,Yager的形式化方法才与Reiter的缺省逻辑具有一定的相关性,我们指出了它们在一般缺省理论下的不匹配处,并给出了以不动点机制抽改进方来消除这
些不匹配。     

A Correct Logic Programming Computation of Default Logic Extensions

We present a method of representing some classes of default theories as normal logic programs. The main point is that the standart semantics (i.e., SLDNF-resolution) computes answer substitutions that correspond exactly to the extensions of the represented default theory. This means that we give a correct implementation of default logic. We explain the steps of constructing a logic program LogProg(P, D) from a given default theory (P, D), give some examples, and derive soundness and completeness results.     

Embedding defaults into terminological knowledge representation formalisms

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are applied only to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable. We describe an algorithm for computing extensions and show how the inference procedures of terminological systems can be modified to give optimal support to this algorithm.This is a revised and extended version of a paper presented at the3rd International Conference on Principles of Knowledge Representation and Reasoning, October 1992, Cambridge, MA.     

Characterization of an auto-compatible default theory

In this paper,an equivalence condition for deciding whether a default theory is an auto-compatible default one is presented.Under the condition,the existence of extension of an auto-compatible default theory is a natural result.By introducing a well-ordering over the set D of default rules,the extensions of an auto-compatible default theory(D,W) can be computed directly.The condition represents clearly the characterization of an auto-compatible default theory,and some properties about auto-compatible default theory,such as semi-monotonicity,become natural corollaries.Based on the characterization,the revision of default beliefs is discussed to ensure the existence of extension of the default theory,and the methos is applied to investigate stable models of a general logic program.