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.     

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。     

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。     

缺省理论的简化

缺省理论△=(D,W)中的缺省规则集D,是该理论的不确定因素.如果能去掉一些缺省规则而又不影响该理论的延伸,则就在一定程度上简化了该理论.本文证明了关于规范缺省理论的延伸的若干性质,利用这些性质,我们可以把某些规范缺省理论在一定条件下得以化简,有的甚至可以把它们化为一阶逻辑理论.     

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.     

关于D.W.Etherington的扩充产生算法的一个注记

Ｄ．Ｗ．Ｅｔｈｅｒｉｎｇｔｏｎ提出了一类总是有扩充的缺省理论，即有限有序缺省理论，同时使用接连近似的方法给出产生这类缺省理论的所有扩充的算法，并证明该算法对有限有序网络缺省理论总是收敛到一扩充。本文首先举例说明Ｄ．Ｗ．Ｅｔｈｅｒｉｎｇｔｏｎｄ的算法对一般的有限有序缺省理论并非总是收敛，然后给出了该算法对
对一般的有限有序缺省理论收敛的一个充分条件。     

利用重写系统研究缺省逻辑

本文在布尔环重量写系统中研究了缺省逻辑。一个缺省理论等价于一个布尔环方程组。本文还分析了命题缺省理论外延的结构，证明了一个缺省理论的外延的模型集合就是对应的布尔环方程组的极大缺省解，从而为确定缺省理论的外延提供了一种简便实用的方法。     

一种基于Rough集的兴趣缺省规则挖掘算法

Rough集理论提供了一种新的处理不精确，不完全与不相容知识的数学方法，从不一致决策表中快速，有效地挖掘出缺省规则是决策规则挖掘研究的一个热点，文中引入了决策规则的相似度概念，并提出了基于Rough集的兴趣缺省规则挖掘算法（IDRMA），依据IDRMA算法对决策规则进行合理的分类，可获取用户的兴趣缺省规则。     

A proof procedure for normal default theories

Recent research by Delgrande [6] and Geffner and Pearl [10] suggests two different semantic interpretations for normal defaults with one single representation as conditional sentences. However, they both need additional formal mechanisms for handling irrelevant information when their approaches are applied to formalising default reasoning. Delgrande in [5, 6] suggests two meta-strategies which he considers to be adequately strong to handle the orderings of defaults, and he claims they are equivalent. Furthermore, each of Delgrande's strategies is defined in terms of all sentences of the object language. In this paper, we shall prove that Delgrande's claim that his meta-strategies are equivalent is incorrect and that one of his meta-strategies can be reformulated within the framework of First Order Predicate Calculus (FOPC) and without having to consider every sentence of the object language. One advantage of such a reformalisation is its computational simplicity: to give an extension of a default theory there is only a need to consider those sentences which occur in the default theory under consideration rather than every sentence in the object language; furthermore, to provide a proof procedure for Delgrande's system as based on the meta-strategy we have formalised, one need only employ a FOPC proof procedure, rather than a conditional one.     

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.     

Regular disjunction-free default theories

In this paper, the class of regular disjunction-free default theories is introduced and investigated.A transformation from regular default theories to normal default theories is established. The initial theory andthe transformed theory have the same extensions when restricted to old variables. Hence, regular default theoriesenjoy some similar properties (e.g., existence of extensions, semi-monotonicity) as normal default theories. Then,a new algorithm for credulous reasoning of regular theories is developed. This algorithm runs in a time not morethan 0(1.45~n), where n is the number of defaults. In case of regular prerequisite-free or semi-2CNF defaulttheories, the credulous reasoning can be solved in polynomial time. However, credulous reasoning for semi-Horndefault theories is shown to be NP-complete although it is tractable for Horn default theories. Moreover, skepticalreasoning for regular unary default theories is co-NP-complete.     

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。     

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.     

利用格论研究缺省推理

本文提出了一组转换规则,使用这组转换规则可以把缺省规则转换成扩展规则,然后使用这些扩展规则去扩展缺省理论的初始逻辑公式集合,在这些扩展规则的基础上,我们提出了缺省格(default lattice)的概念,证明了缺省理论的外延刚好对应于它的缺省格的相容性集合的D-极大值,因此可以使用缺省格求出缺省理论的所有外延.