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.     

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.     

若干限制形式的缺省推理的复杂性

该文研究判定一文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是一集Horn缺省规则,而W是definite Horn公式或者Bi-Horn公式.     

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。     

一种基于多重支持度的缺省规则挖掘算法

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而有效地挖掘出缺省规则是决策规则挖掘研究的一个热点。MDRBR算法采用单一的规则支持度阈值进行缺省规则的挖掘,这不利于有效地挖掘出用户感兴趣的缺省规则。为此,该文对MDRBR算法进行了改进,并提出了一种基于多重支持度的的缺省规则挖掘算法-MSMDRBR算法,MSMDRBR算法可依据多重支持度阈值合理地取舍决策规则,因而具有一定的实用意义。     

贪婪缺省逻辑

提出一种贪婪缺省逻辑,旨在构造扩展的过程中尽可能的保留缺省规则当中的信息.给出了贪婪缺省逻辑的推演系统-GD系统和贪婪缺省的GD-扩展的定义.并且证明了对于缺省理论 的一个扩展,必定存在一个贪婪缺省理论的GD-扩展使得缺省逻辑的扩展是贪婪缺省逻辑扩展的子集.并且存在贪婪缺省理论 的某一GD-扩展,该GD-扩展不包含缺省理论的任一扩展.因此缺省逻辑和贪婪缺省逻辑是两种不同的逻辑.     

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.     

一种基于Rough集的缺省规则挖掘算法

Rough集方法是一种处理不确定或模糊知识的重要工具,对基于Rough集理论的缺省规则挖掘算法进行研究,在引入规则支持度概念后,提出了一种基于Rough集的缺省规则挖掘算法MDRBR。实验结果表明,该算法能较好地过滤噪音,提高规则的挖掘效率。     

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。     

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。     

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.     

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。     

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.     

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.     

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。     

Reasoning about Actions and Planning with Preferences Using Prioritized Default Theory

This paper shows how action theories, expressed in an extended version of the language     , can be naturally encoded using Prioritized Default Theory . We also show how prioritized default theory can be extended to express preferences between rules . This extension provides a natural framework to introduce different types of preferences in action theories— preferences between actions and preferences between final states . In particular, we demonstrate how these preferences can be expressed within extended prioritized default theory. We also discuss how this framework can be implemented in terms of answer set programming.     

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.     

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。     

基于模态缺省理论的多Agent系统的知识更新

基于模态缺省理论，建立多Agent系统的模态缺省逻辑，给出了每个主体 对应的模态缺省理论 的新知识和知识冲突的概念及其意义，主要讨论在多Agent环境下，当一个Agent的知识不足以完成推理时，可以从其它Agent处获得新的知识，从而对自身的信念集进行更新。当Wi发生变化(如遇到新的知识或出现与原信念集冲突的知识)时扩充Ei的性质和变化规律，提出了获取新扩充的较简单的求解方法，并证明了相关的定理，给出了多Agent系统的关于知识的一个动态描述过程。