On nonmonotonic reasoning with the method of sweeping presumptions

Reasoning almost always occurs in the face of incomplete information. Such reasoning is nonmonotonic in the sense that conclusions drawn may later be withdrawn when additional information is obtained. There is an active literature on the problem of modeling such nonmonotonic reasoning, yet no category of method-let alone a single method-has been broadly accepted as the right approach. This paper introduces a new method, called sweeping presumptions, for modeling nonmonotonic reasoning. The main goal of the paper is to provide an example-driven, nontechnical introduction to the method of sweeping presumptions, and thereby to make it plausible that sweeping presumptions can usefully be applied to the problems of nonmonotonic reasoning. The paper discusses a representative sample of examples that have appeared in the literature on nonmonotonic reasoning, and discusses them from the point of view of sweeping presumptions.     

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.     

The epistemic basis of defeasible reasoning

This article argues that: (i) Defeasible reasoning is the use of distinctive procedures for belief revision when new evidence or new authoritative judgment is interpolated into a system of beliefs about an application domain. (ii) These procedures can be explicated and implemented using standard higher-order logic combined with epistemic assumptions about the system of beliefs. The procedures mentioned in (i) depend on the explication in (ii), which is largely described in terms of a Prolog program, EVID, which implements a system for interactive, defeasible reasoning when combined with an application knowledge base. It is shown that defeasible reasoning depends on a meta-level Closed World Assumption applied to the relationship between supporting evidence and a defeasible conclusion based on this evidence. Thesis (i) is then further defended by showing that the EVID explication of defeasible reasoning has sufficient representational power to cover a wide variety of practical applications of defeasible reasoning, especially in the context of decision making.     

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.     

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.     

DEFAULT LOGICS: A UNIFIED VIEW

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.     

线性支持向量机优化问题的极大熵方法

支特向量机是一种新的机器学习方法，已成功地应用于模式分类、回归分析和密度估计等问题中．本文依据统计学习理论和最优化理论建立了线性支特向量机的无约束优化模型，并给出了一种有效的近似解法一极大熵方法,为求解支持向量机优化问题提供了一种新途径,本文方法特别易于计算机实现。数值实验结果表明了模型和算法的可行性和有效性．     

基于最大熵方法的统计语言模型

针对现有统计语言模型中存在计算量过大和系统负担过重的问题,该文提出了一种基于最大熵方法的统计语言模型。模型在参数估计阶段,引入约束最优化理论中拉格朗日乘数定理和牛顿迭代算法,以确保模型在多个约束条件中可求出最优化参数值;在特征选择阶段,采用计算近似增益的平行算法,解决模型计算量过大和系统开销问题。将该模型用于汉语句子分析的软件实验中表明:模型具有较高的计算效率和鲁棒性。     

Modal logic for default reasoning

In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agent's initial assumptions and do not depend on their syntactic representation.Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion — weak iterative expansion — and we show that there is an important class of theories, that we call -programs, for which iterative and weak iterative expansions coincide. Thus, for -programs, iterative expansions can be equivalently defined by semantic means.This work was partially supported by Army Research Office under grant DAAL03-89-K-0124, and by National Science Foundation and the Commonwealth of Kentucky EPSCoR program under grant RII 8610671.     

Considerations on default logic: an alternative approach1

In the following paper we analyze Reiter's default logic and suggest modifying the notion of an extension for default theories. This modification leads to two important properties which are not guaranteed in Reiter's formalism: the existence of extensions and semimonotonicity.