Default reasoning and belief revision: A syntax-independent approach

As an important variant of Reiter‘s default logic.Poole(1988) developed a nonmonotonic reasoning framework in the classical first-order language,Brewka and Nebel extended Poole‘s approach in order to enable a representation of priorities between defaults.In this paper a general framework for default reasoning is presented,which can be viewed as a generalization of the three approaches above.It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al.(1997).This esult provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case .As a by-product,an answer to the the question,raised by Mankinson and Gaerdenfors(1991),is also given about whether there is a counterpart contraciton in nonmonotonic logic.     

The Nature of Nonmonotonic Reasoning

Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard logics are monotonic. Much recent research in AI has been devoted to the attempt to develop nonmonotonic logics. After some motivational material, we give four formal proofs that there can be no nonmonotonic consequence relation that is characterized by universal constraints on rational belief structures. In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. We give several examples of how nonmonotonic reasoning systems may be based on monotonic logics.     

Operational Concepts of Nonmonotonic Logics Part 2: Autoepistemic Logic

The subject of nonmonotonic reasoning is reasoning with incompleteinformation. One of the main approaches is autoepistemic logic inwhich reasoning is based on introspection. This paper aims at providing a smooth introduction to this logic,stressing its motivation and basic concepts. The meaning (semantics)of autoepistemic logic is given in terms of so-called expansionswhich are usually defined as solutions of a fixed-point equation. Thepresent paper shows a more understandable, operational method fordetermining expansions. By improving applicability of the basicconcepts to concrete examples, we hope to make a contribution to awider usage of autoepistemic logic in practical applications.     

Strategies in Human Nonmonotonic Reasoning

Although humans seem adept at drawing nonmonotonic conclusions, the nonmonotonic reasoning systems that researchers develop are complex and do not function with such ease. This paper explores people's reasoning processes in nonmonotonic problems. To avoid the problem of people's conclusions being based on knowledge rather than on some reasoning process, we developed a scenario about life on another planet. Problems were chosen to allow the systematic study of people's understanding of strict and nonstrict rules and their interactions. We found that people had great difficulty reasoning and we identified a number of negative factors influencing their reasoning. We also identified three positive factors which, if used consistently, would yield rational and coherent reasoning—but no subject achieved total consistency. (Another possible positive factor, specificity, was considered but we found no evidence for its use.) It is concluded that nonmonotonic reasoning is hard. When people need to reason in a domain where they have no preconceived ideas, the foundation for their reasoning is neither coherent nor rational. They do not use a nonmonotonic reasoning system that would work regardless of content. Thus, nonmonotonic reasoning systems that researchers develop are expected to do more reasoning than humans actually do!     

常识问题——常识推理的逻辑基础

本文主要讨论常识推理的逻辑基础，基于一条从非单调推理到常识推理的技术途径，由此指出在更一般意义上形式化常识推是的一些结果，它建立常识逻辑和解决常识问题提供了有用的基础工具。     

Minimal Belief and Negation as Failure in Multi-Agent Systems

We propose an epistemic, nonmonotonic approach to the formalization of knowledge in a multi-agent setting. From the technical viewpoint, a family of nonmonotonic logics, based on Lifschitz's modal logic of minimal belief and negation as failure, is proposed, which allows for formalizing an agent which is able to reason about both its own knowledge and other agents' knowledge and ignorance. We define a reasoning method for such a logic and characterize the computational complexity of the major reasoning tasks in this formalism. From the practical perspective, we argue that our logical framework is well-suited for representing situations in which an agent cooperates in a team, and each agent is able to communicate his knowledge to other agents in the team. In such a case, in many situations the agent needs nonmonotonic abilities, in order to reason about such a situation based on his own knowledge and the other agents' knowledge and ignorance. Finally, we show the effectiveness of our framework in the robotic soccer application domain.     

Process and Policy: Resource-Bounded NonDemonstrative Reasoning

This paper investigates the appropriateness of formal dialectics as a basis for nonmonotonic reasoning and defeasible reasoning that takes computational limits seriously. Rules that can come into conflict should be regarded as policies, which are inputs to deliberative processes. Dialectical protocols are appropriate for such deliberations when resources are bounded and search is serial.
AI, it is claimed here, is now perfectly positioned to correct many misconceptions about reasoning that have resulted from mathematical logic's enormous success in this century: among them, (1) that all reasons are demonstrative, (2) that rational belief is constrained, not constructed, and (3) that process and disputation are not essential to reasoning. AI mainly provides new impetus to formalize the alternative (but older) conception of reasoning, and AI provides mechanisms with which to create compelling formalism that describes the control of processes.
The technical contributions here are: the partial justification of dialectic based on controlling search; the observation that nonmonotonic reasoning can be subsumed under certain kinds of dialectics; the portrayal of inference in knowledge bases as policy reasoning; the review of logics of dialogue and proposed extensions; and the preformal and initial formal discussion of aspects and variations of dialectical systems with nondemonstrative reasons.     

基于标记逻辑的非单调推理（Ⅰ）

我们把标记逻辑定义在一个特殊双格上,通过比较标记选取结论,从而同时捕捉超协调（容错）推理和非单调推理．本文介绍标记逻辑程序的句法与语义构造,提出诱导序列及其极限的概念,给出极限存在的等价条件,并证明一个重要结果：诱导序列基本定理,它是后续讨论的基础．     

基于自动推理技术的智能规划方法

对几种智能规划方法中利用的逻辑演绎与推理技术予以分析,分别介绍利用命题逻辑的基于可满足性的规划方法与规划系统,利用模态逻辑与析取推理的Conformant规划方法与规划系统,利用非单调逻辑的规划方法和利用模糊描述逻辑的Flexible规划方法,并结合国际规划竞赛和相关论文等的实验结论说明上述方法的有效性和可行性.最后,提出目前基于自动推理技术的智能规划方法所面临的挑战、可能的处理方法以及与之相关的研究热点与趋势.     

Preorder-based triangle: a modified version of bilattice-based triangle for belief revision in nonmonotonic reasoning

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle cannot handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover, the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.     

Programming in temporal-nonmonotonic reasoning

Nonmonotonic reasoning has been proposed as an extension to classical first-order logic. Now people are interested in temporal reasoning with nonmonotonic logic [6]. We combine the monotonic logic [7] with a temporal logic to get a more general reasoning language. We discuss a monotonic logic TML which has predicate formulas, temporal formulas and a special modal formula, and give a completeness theorem of it. We use TH() to designate the set of theorems of a temporal-nonmonotonic theory which has the same language with TML. The completeness theorem of the temporal-nonmonotonic logic naturally arises. Like the relationship between predicate logic with a practical logic programming language PROLOG, we propose a useful temporal-nonmonotonic reasoning language TN for the temporal-nonmonotonic logic. As an appendix we supply an algorithm for the programming language TN.     

经验逻辑：一种非单调逻辑的统一形式

人的常识推理是一种充满经验性知识的累积过程,而经验推理具有非单调性。本文提出一种关于典型与例外的经验逻辑,特别研究它的非单调性,它提供了一个现存的主要非单调逻辑的统一基础,这是通过一种类似的规则把它们翻译成经验逻辑获得的。因此,经验逻辑给出了一类更一般而且直观的非单调推理形式。     

N-SHOQ(D):描述逻辑SHOQ(D)的一个非单调扩展

描述逻辑SHOQ(D)给出了Web本体语言DAML OIL的语义,但SHOQ(D)只能处理严格成立的完备知识,不能处理在实际情况中经常出现的不完备知识．对描述逻辑SHOQ(D)进行扩展,提出了能够处理不完备知识的非单调描述逻辑N—SHOQ(D)．给出了N—SHOQ(D)的语法和语义,定义了N—SHOQ(D)中的蕴涵推理关系,研究了N—SHOQ(D)所具有的性质．N—SHOQ(D)为扩展DAML OIL语言到能够处理不完备知识的情形提供了语义支持．     

Autoepistemic logic of first order and its expressive power

We study the expressive power of first-order autoepistemic logic. We argue that full introspection of rational agents should be carried out by minimizing positive introspection and maximizing negative introspection. Based on full introspection, we propose the maximal well-founded semantics that characterizes autoepistemic reasoning processes of rational agents, and show that breadth of the semantics covers all theories in autoepistemic logic of first order, Moore's AE logic, and Reiter's default logic. Our study demonstrates that the autoepistemic logic of first order is a very powerful framework for nonmonotonic reasoning, logic programming, deductive databases, and knowledge representation.This research is partially supported by NSERC grant OGP42193.     

A Critical Reexamination of Default Logic, Autoepistemic Logic, and Only Knowing

Fifteen years of work on nonmonotonic logic has certainly increased our understanding of the area. However, given a problem in which nonmonotonic reasoning is called for, it is far from clear how one should go about modeling the problem using the various approaches. We explore this issue in the context on two of the best–known approaches, Reiter's default logic and Moore's autoepistemic logic, as well as two related notions of "only knowing," due to Halpern and Moses and to Levesque. In particular, we return to the original technical definitions given in these papers and examine the extent to which they capture the intuitions they were designed to capture.     

A Classification and Survey of Preference Handling Approaches in Nonmonotonic Reasoning

In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles.     

非单调推理的研究现状

一、引言 早在1959年,McCart~[1]就发现常识和常识推理很难处理,因为在常识推理中当前得出的结论,可能会由于以后新事实的加入而被取消.这就是所谓的“非单调性”。     

双析取逻辑程序设计基础（Ⅰ）

析取逻辑程序设计是传统逻辑程序设计最重要的扩充之一，本文通过一些实例说明，现存语义无法充分 表示信息的不完全性。为此，本文提出了双析取逻辑程序设计的概念，我们不仅从句法上将正规则析取逻辑程序推广为双析取逻辑程序。而且建立了一种高度直观，灵活的辩论语义框架ＢＤＡＳ。     

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．