An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...

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...

Recent research on applications of nonmonotonic reasoning to the semantics of logic programs demonstrates that some nonmonotonic formalisms are better suited for such use than others. Circumscription is applicable as long as the programs under consideration are stratified. To describe the semantics of general logic programs without the stratification assumption, one has to use autoepistemic logic or default logic. When Gelfond and Lifschitz extended this work to programs with classical negation, they used default logic, because it was not clear whether autoepistemic logic could be applied in that wider domain. In this paper we show that programs with classical negation can be, in fact, easily represented by autoepistemic theories. We also prove that an even simpler embedding is possible if reflexive autoepistemic logic is used. Both translations are applicable to disjunctive programs as well. 1 Introduction Recent research on applications of nonmonotonic reasoning to the semantics of ...

This paper completes an investigation of the logical expressibility of finite, locally stratified, general logic programs. We show that every hyperarithmetic set can be defined by a suitably chosen locally stratified logic program (as a set of values of a predicate over its perfect model). This is an optimal result, since the perfect model of a locally stratified program is itself an implicitly definable hyperarithmetic set (under a recursive coding of the Herbrand base); hence to

vii Chapter 1 Introduction 1 1.1 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Research Approach and Significance : : : : : : : : : : : : : : : : : : : : 1 1.3 Overview of Contributions : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.4 Organization : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 Chapter 2 Motivation and Background 4 2.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2 Reasoning About Actions : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Temporal Formalisms for Reasoning About Actions : : : : : : : : : : : : 5 2.3.1 Situation Calculus : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3.2 Other Formalisms : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.4 Problems in Reasoning About Actions : : : : : : : : : : : : : : : : : : : 6 2.4.1 The Frame, Qualification and Ramification Problems : : : : : : : 6 2.4.2 Different Aspects of Reasoning About Actions : : : : :...

We present a framework for default reasoning which has its roots in Reiter's Default Logic. Contrary to Reiter, however, we do not consider defaults as inference rules used to generate extensions of a classical set of facts. In our approach defaults are elements of the logical language, and we will define inference rules on defaults. This has several advantages. First of all, we can reason about defaults, not just with defaults. This makes it easy to include different intuitions about the right behaviour of a default logic in an explicit form. Secondly, we can show how some of the problems of Reiter's logic and of some recent proposals to solve them can be handled adequately by exploiting the dependency information contained in derived defaults. ii 1 Background and Motivation Reiter's Default Logic DL [14] is currently one of the most popular and most widely used formalizations of default reasoning. There are at least two reasons for this popularity. Firstly, although the technical ...

The correspondence between Reiter's default reasoning and logic programming has been exhaustively studied (e.g. [1], [2], [3]). A Contrario the relation with the many variants of the initial theory of Reiter seems far less known. This paper aims to present a preliminary investigation on applying a variant of default reasoning proposed by Witold L/ukaszewicz [5] to extended logic programs. We show that the modification made to the notion of extension by L/ukaszewicz has its counterpart as a relaxed notion of answer set of an extended logic program. As can be expected from this correspondence: (1) any extended logic program has always at least one relaxed answer set; (2) classical answer sets can be completely characterized among the set of relaxed answer sets of an extended logic program.