Well Founded Semantics is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model of a program P as a (possibly incomplete) view of the world. Thus the Well Founded model may be accepted to be a definite view of the world and the extended stable models as alternative enlarged consistent belief models an agent may have about the world. Our purpose is to exhibit a modular systematic method of representing nonmonotonic problems with the Well Founded semantics of logic programs. In this paper we use this method to represent and solve some classical nonmonotonic problems. This leads us to consider our method quite generic. 1 Introduction Well Founded Semantics (WFS) [15] is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model (WFM) of a program P as a (possibly incomplete) view of the world. Thus the WFM may be accepted to be a definite view of the world and the eXtended Stable Models (XSMs) as alternative enlarged consistent belief mo...

In Reiter's default logic, the parameters of a default are treated as metavariables for ground terms. We propose an alternative definition of an extension for a default theory, which handles parameters as genuine object variables. The new form of default logic may be preferable when the domain closure assumption is not postulated. It stands in a particularly simple relation to circumscription. Like circumscription, it can be viewed as a syntactic transformation of formulas of higher order logic. 1 Introduction Default logic [Reiter, 1980] is one of the most expressive and most widely used nonmonotonic formalisms. In one respect, however, the main definition of default logic, that of an extension, is not entirely satisfactory. Recall that a default ff : fi 1 ; : : : ; fi m =fl (1) is open if it contains free variables, and closed otherwise. The concept of an extension is defined in two steps: It is first introduced, by means of a fixpoint construction, for default theories without op...

Our purpose is to exhibit a modular systematic method of representing non-- monotonic reasoning problems with the Well Founded Semantics WFS of extended logic programs augmented with eXplicit negation (WFSX), augmented by its Contradiction Removal Semantics (CRSX) when needed. We apply this semantics, and its contradiction removal semantics counterpart, to represent non-monotonic reasoning problems. We show how to cast in the language of logic programs extended with explicit negation such forms of non-monotonic reasoning as defeasible reasoning, abductive reasoning and hypothetical reasoning and apply them to such different domains of knowledge representation as hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in a logic programming semantics comprising two forms of negation avoiding some drawbacks of other proposals, with which we relate our work.

The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...

This article discusses the problems and difficulties, the results so far, and some improvements in logic and logical languages that may be required to formalize common sense. Fundamental conceptual advances are almost certainly required. The object of the paper is to get more help for AI from philosophical logicians. Some of the requested help will be mostly philosophical and some will be logical. Likewise the concrete AI approach may fertilize philosophical logic as physics has repeatedly fertilized mathematics.

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.

Learning and reasoning are both aspects of what is considered to be intelligence. Their studies within AI have been separated historically, learning being the topic of machine learning and neural networks, and reasoning falling under classical (or symbolic) AI. However, learning and reasoning are in many ways interdependent. This paper discusses the nature of some of these interdependencies and proposes a general framework called FLARE, that combines inductive learning using prior knowledge together with reasoning in a propositional setting. Several examples that test the framework are presented, including classical induction, many important reasoning protocols and two simple expert systems. 1. Introduction Induction and deduction are both underlying processes in intelligent agents. Induction "involves intellectual leaps from the particular to the general" (D'Ignazio & Wold, 1984). It plays an important part in knowledge acquisition or learning. D'Ignazio and Wold (1984) claim that in...

Introduction The frame problem, the problem of efficiently determining which things remain the same in a changing world, 1 has been with us for over a quarter of a century -- ever since the publication of McCarthy and Hayes's famous essay, "Some Philosophical Problems from the Standpoint of Artificial Intelligence," in 1969. A quarter of a century is a very long time in the time frame of computer science, and especially in the history of Artificial Intelligence (AI), which has itself been around for only about 40 years. Indeed, it is not much younger than the advent of logicist AI (McCarthy, 1958), that brand of AI which attempts to formalize reasoning, particularly common-sense reasoning, within mathematical logic. Present since the early years of AI, the frame problem has festered within the AI community. It has drawn, and continues to draw, manpower and talent from the pool of AI researchers, particularly from the logicist community. It has pitted logicists a

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A self-organizing incremental learning model that attempts to combine inductive learning with prior knowledge and default reasoning is described. The inductive learning scheme accounts for useful generalizations and dynamic priority allocation, and effectively supplements prior knowledge. New rules may be created and existing rules modified, thus allowing the system to evolve over time. By combining the extensional and intensional approaches to learning rules, the model remains self-adaptive, while not having to unnecessarily suffer from poor (or atypical) learning environments. By combining rulebased and similarity-based reasoning, the model effectively deals with many aspects of brittleness. 1. INTRODUCTION Much effort has been devoted to understanding learning and reasoning in artificial intelligence [6, 19, 22]. However, very few models attempt to integrate these two complementary processes. Rather, there is a vast body of research in machine learning, often focusing on inductive...