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     

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．     

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.     

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。     

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.     

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.     

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。     

基于DFL的缺省假设推理研究

日常生活中人们可以在信息不完全的情况下进行推理并得出较好的推理结论,而且在推理过程中,很多对象都是具有动态模糊性(DF Character)。因此文中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)的缺省假设推理,并给出了缺省假设推理的框架描述、动态模糊(DF)知识的表示以及推理算法等。     

基于DFL的缺省假设推理研究

日常生活中人们可以在信息不完全的情况下进行推理并得出较好的推理结论，而且在推理过程中，很多对象都是具有动态模糊性（DF Character）。因此文中针对研究对象以及它们之问的动态模糊性，提出了基于动态模糊逻辑（DFL）的缺省假设推理，并给出了缺省假设推理的框架描述、动态模糊（DF）知识的表示以及推理算法等。     

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.     

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.     

A Default Logic Based Framework for Context-Dependent Reasoning with Lexical Knowledge

Lexical knowledge is increasingly important in information systems—for example in indexing documents using keywords, or disambiguating words in a query to an information retrieval system, or a natural language interface. However, it is a difficult kind of knowledge to represent and reason with. Existing approaches to formalizing lexical knowledge have used languages with limited expressibility, such as those based on inheritance hierarchies, and in particular, they have not adequately addressed the context-dependent nature of lexical knowledge. Here we present a framework, based on default logic, called the dex framework, for capturing context-dependent reasoning with lexical knowledge. Default logic is a first-order logic offering a more expressive formalisation than inheritance hierarchies: (1) First-order formulae capturing lexical knowledge about words can be inferred; (2) Preferences over formulae can be based on specificity, reasoning about exceptions, or explicit priorities; (3) Information about contexts can be reasoned with as first-order formulae formulae; and (4) Information about contexts can be derived as default inferences. In the dex framework, a word for which lexical knowledge is sought is called a query word. The context for a query word is derived from further words, such as words in the same sentence as the query word. These further words are used with a form of decision tree called a context classification tree to identify which contexts hold for the query word. We show how we can use these contexts in default logic to identify lexical knowledge about the query word such as synonyms, antonyms, specializations, meronyms, and more sophisticated first-order semantic knowledge. We also show how we can use a standard machine learning algorithm to generate context classification trees.     

An Interpretation of Default Logic in Minimal Temporal Epistemic Logic

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours.     

What Should Default Reasoning be,by Default?

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain.     

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.     

Default Reasoning and Generics

There are numerous logical formalisms capable of drawing conclusions using default rules. Such systems, however, do not normally determine where the default rules come from; i.e., what it is that makes Birds fly a good rule, but Birds drive trucks a bad one.
Generic sentences such as Birds fly are often used informally to describe default rules. I propose to take this characterization seriously, and claim that a default rule is adequate if the corresponding generic sentence is true. Thus, if we know that Tweety is a bird, we may conclude by default that Tweety flies, just in case Birds fly is a true sentence.
In this paper, a quantificational account of the semantics of generic sentences is presented. It is argued that a generic sentence is evaluated not in isolation, but with respect to a set of relevant alternatives. For example, Mammals bear live young is true because among mammals that bear live young, lay eggs, undergo mitosis, or engage in some alternative form of procreation, the majority bear live young. Since male mammals do not procreate in any form, they do not count. Some properties of alternatives are presented, and their interactions with the phenomena of focus and presupposition is investigated.
It is shown how this account of generics can be used to characterize adequate default reasoning systems, and several desirable properties of such systems are proved. The problems of the automatic acquisition of rules from natural language are discussed. Because rules are often explicitly expressed as generics, it is argued that the interpretation of generic sentences plays a crucial role in this endeavor, and it is shown how the theory presented here can facilitate such interpretation.