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 Such reasoning is nonmonotonic in the sense that conclusions drawn may later be withdrawn when additional information is obtained.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.     

Issues in commonsense set theory

The success of set theory as a foundation for mathematics inspires its use in artificial intelligence, particularly in commonsense reasoning. In this survey, we briefly review classical set theory from an AI perspective, and then consider alternative set theories. Desirable properties of a possible commonsense set theory are investigated, treating different aspects like cumulative hierarchy, self-reference, cardinality, etc. Assorted examples from the ground-breaking research on the subject are also given.     

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.     

Intelligent handling of data by integration of commonsense reasoning

Any intelligent problem solving system should be able, given the known data on a case, to decide whether some item of information is true, false or unknown. In this paper the way in which various forms of commonsense reasoning can be integrated to provide such decisions is described. To this end three structural types of knowledge defined over data, and four strategies for exploiting these structures, are identified. ‘Decide-Status’ integrates the reasoning strategies into a task frame. This frame structure not only integrates the reasoning but also affords the appropriate facilities for providing strategic justifications for its conclusions, if required.     

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.     

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.     

Bilattices and Reasoning in Artificial Intelligence: Concepts and Foundations

The past few decades have seen a resurgence ofreasoning techniques in artificial intelligenceinvolving both classical and non-classical logics. Inhis paper, ``Multi-valued Logics: A Uniform Approach toReasoning in Artificial Intelligence', Ginsberg hasshown that through the use of bilattices,several reasoning techniques can be unified under asingle framework. A bilattice is a structure that canbe viewed as a class of truth values that canaccommodate incomplete and inconsistent informationand in certain cases default information. Inbilattice theory, knowledge is ordered along twodimensions: truth/falsity and certainty/uncertainty. By defining the corresponding bilattices as truthspaces, Ginsberg has shown that the same theoremprover can be used to simulate reasoning in firstorder logic, default logic, prioritized default logicand assumption truth maintenance system. Although thisis a significant contribution, Ginsberg's paper waslengthy and involved. This paper summarizes some ofthe essential concepts and foundations of bilatticetheory. Furthermore, it discusses the connections ofbilattice theory and several other existingmulti-valued logics such as the various three-valuedlogics and Belnap's four-valued logic. It is notedthat the set of four truth values in Belnap's logicform a lattice structure that is isomorphic to thesimplest bilattice. Subsequently, Fitting proposed aconflation operation that can be used to selectsub-sets of truth values from this and otherbilattices. This method of selecting sub-sets oftruth values provides a means for identifyingsub-logic in a bilattice.     

Notes on Ginsberg's multivalued logics

The use of multivalued logics for knowledge representation and nonmonotonic reasoning has often been advocated, in particular within the general framework proposed by Ginsberg in his paper "Multivalued logics: a uniform approach to reasoning in artificial intelligence." His system is based on a multivalued logic with an arbitrary number of truth values classified with respect to two partial orders, a truth order and a knowledge order. This classification is very interesting and gives an intuitive appeal to the framework. In this paper the work by Ginsberg is critically reviewed, pointing out some flaws and ways to overcome them. Moreover, we present some ideas on how to modify the original schema in order to obtain a more semantically well-founded framework.
L'utilisation de la Iogique multivalente pour la représentation des connaissances et le raisonnement non monotone a souvent été préconisée, en particulier à l'intérieur du cadre général proposé par Ginsberg dans son article intitulé〘 Multivalued logics: a uniform approach to reasoning in artificial intelligence 〙 Son système est basé sur une logique multivalente comportant un nombre arbitraire de valeurs de vérité classées selon deux ordres partiels: un ordre de vérité et un ordre de connaissances. Cette classification est très intéressante et donne un attrait intuitif au cadre. Dans cet article, l'auteur examine le travail de Ginsberg, y relève des lacunes et propose des moyens de les corriger. De plus, il expose certaines idées en vue de modifier le schéma original et ainsi obtenir un meilleur cadre du point de vue de la sémantique.     

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.     

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.     

A Survey of Commonsense Knowledge Acquisition

Collecting massive commonsense knowledge (CSK) for commonsense reasoning has been a long time standing challenge within artificial intelligence research. Numerous methods and systems for acquiring CSK have been developed to overcome the knowledge acquisition bottleneck. Although some specific commonsense reasoning tasks have been presented to allow researchers to measure and compare the performance of their CSK systems, we compare them at a higher level from the following aspects: CSK acquisition task (what CSK is acquired from where), technique used (how can CSK be acquired), and CSK evaluation methods (how to evaluate the acquired CSK). In this survey, we first present a categorization of CSK acquisition systems and the great challenges in the field. Then, we review and compare the CSK acquisition systems in detail. Finally, we conclude the current progress in this field and explore some promising future research issues.     

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.     

A different paradigm for expert systems: an introduction to logic programming and related knowledge representation issues

Abstract: Current expert system technology is 30 years old. Expert system shells find their origins in the work of early expert systems, most notably MYCIN which was developed at Stanford in the mid-1970s. Even Prolog programmers are settling for less robust reasoning power. The logic programming community (from which both expert systems and Prolog arose) has made notable advances since those times. These advances are lacking from current expert system technology. The advances include a well-developed theory of multiple forms of negation, an understanding of open domains and the closed world assumption, default reasoning with exceptions, reasoning with respect to time (i.e. a solution to the frame problem, and introspection with regard to previous beliefs), reasoning about actions, introspection, and maintaining multiple views of the world simultaneously.
The contribution of this paper is to discuss these developments in a singular, integrated, practical, digestible manner. Some of these ideas exist in a variety of papers spread across decades. They also exist in the minds of a very small community of researchers. Some of these ideas are unpublished. The presentation in this paper is from a different point of view, and intended to be more comprehensive and pedagogical. The presentation is also intended to be accessible to a much wider audience. Both the synthesis and the simplicity of this presentation are absent from the literature.     

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.     

Meta-path reasoning of knowledge graph for commonsense question answering

Commonsense question answering (CQA) requires understanding and reasoning over QA context and related commonsense knowledge, such as a structured Knowledge Graph (KG). Existing studies combine language models and graph neural networks to model inference. However, traditional knowledge graph are mostly concept-based, ignoring direct path evidence necessary for accurate reasoning. In this paper, we propose MRGNN (Meta-path Reasoning Graph Neural Network), a novel model that comprehensively captures sequential semantic information from concepts and paths. In MRGNN, meta-paths are introduced as direct inference evidence and an original graph neural network is adopted to aggregate features from both concepts and paths simultaneously. We conduct sufficient experiments on the CommonsenceQA and OpenBookQA datasets, showing the effectiveness of MRGNN. Also, we conduct further ablation experiments and explain the reasoning behavior through the case study.     

'Classical' Negation in Nonmonotonic Reasoning and Logic Programming

Gelfond and Lifschitz were the first to point out the need for a symmetric negation in logic programming and they also proposed a specific semantics for such negation for logic programs with the stable semantics, which they called 'classical'. Subsequently, several researchers proposed different, often incompatible, forms of symmetric negation for various semantics of logic programs and deductive databases. To the best of our knowledge, however, no systematic study of symmetric negation in non-monotonic reasoning was ever attempted in the past. In this paper we conduct such a systematic study of symmetric negation. We introduce and discuss two natural, yet different, definitions of symmetric negation: one is called strong negation and the other is called explicit negation. For logic programs with the stable semantics, both symmetric negations coincide with Gelfond–Lifschitz' 'classical negation'. We study properties of strong and explicit negation and their mutual relationship as well as their relationship to default negation 'not', and classical negation '¬'. We show how one can use symmetric negation to provide natural solutions to various knowledge representation problems, such as theory and interpretation update, and belief revision. Rather than to limit our discussion to some narrow class of nonmonotonic theories, such as the class of logic programs with some specific semantics, we conduct our study so that it is applicable to a broad class of non-monotonic formalisms. In order to achieve the desired level of generality, we define the notion of symmetric negation in the knowledge representation framework of AutoEpistemic logic of Beliefs, introduced by Przymusinski.     

面向对象逻辑语言SCKE中的限制推理

限制理论是形式化常识知识并进行常识推理的一种重要方法．本文主要研究将限制理论转化为面向对象逻辑语言的可能性，并实现了完成这个转换的编译器．按面向对象逻辑语言的语义运行编译后的程序，可得到与原限制理论相同的结果．将该编译器嵌入面向对象逻辑语言解释器中，可以大大提高该语言的表达能力，特别是可以实现对常识知识表示和常识推理的支持．