In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ffl-semantics, possibilistic structures, and -rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:

Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

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...

Abstract. We argue for the usefulness of abductive reasoning in the context of ontologies. We discuss several applicaton scenarios in which various forms of abduction would be useful, introduce corresponding abductive reasoning tasks, give examples, and begin to develop the formal apparatus needed to employ abductive inference in expressive description logics. 1

Our goal is to generalize the well known bottom-up, set-oriented query evaluation for deductive databases in two aspects: First, we consider arbitrary clauses as rules in the database, not only Horn clauses or clauses with stratified negation. This allows to represent disjunctive information, in the database as well as in answers to queries. We utilize NF 2 relations for modelling sets of disjunctive facts and operations of the corresponding relational algebra for computing consequences and answers. Thus our algorithm should be of practical importance for applying database techniques in generalized deductions. Second, we parameterize the implicit database completion which underlies query evaluation. The classical rule for Horn clause databases, which only assumes the negation of facts not implied by the database, is not applicable to disjunctive databases. Moreover, the choice of completion often depends on the intended application. Therefore we allow the specification of arbitrary clauses as defaults, and we extend our algorithm to consider such general defaults. 1

: This paper deals with computing circumscription in the case of Horn data with addi ional protection (indefinite data), an intermediate investigation between Reiter's result on predicate a c completion and Lifschitz's efforts to make general (formula) circumscription more efficient as omputational tool. Reiter has shown a close tie between McCarthy's circumscription and Clark's - t predicate completion. Here we investigate a similar tie between an extended version of circumscrip ion involving protected data, and an extended version of predicate completion. When we have a e u fully ground atomic protected theory, we show that an extension to the relational algebra can b sed to obtain all (and only) correct answers. When general Horn axioms are added to the protected e c theory, we show that Horn axioms also can be used to compute sound answers; however, som orrect answers will not be found. 1. Introduction During the past several years, a number of notions have been developed surroundi...

In this paper we consider supernormal defaults [Poo88] with a strict partial order defining their priorities [Bre91]. We investigate their relation to minimal or preferential entailment and show that the semantics given in [Bre91] has to be modified in order to be equivalent to a preferential model approach. Concering the multiple extension problem, we introduce the careful view as an alternative to the credulous and skeptical one, which is needed to handle the generalized closed world assumption [Min82] within this framework. Given this "declaritive semantics" of such default theories, we will present a deduction algorithm for query answering. Compared to other approaches, the algorithm is quite efficient and general. Especially, it is able to generate disjunctive answers, to support the credulous, skeptical and careful view; and to cut fruitless search paths early. In order to check the applicability of defaults as soon as possible, we introduce the notion of a partial extension. 1 I...

In this paper the classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then the whole model is placed into the framework of the Dempster-Shafer theory of evidence. Laskey, Lehner [1] and Provan [2] have already proposed a similar point of view but these papers do not emphasize the mathematical foundations of the probabilistic assumptionbased reasoning paradigm. These foundations are thoroughly exposed in the rst part of this paper. Then we address the computational problems related to the assumption-based model. The idea is to translate evidence theory problems into propositional logic problems and then use the powerful techniques of logic to solve them. In particular, advanced consequence nding algorithms developed by Inoue [3] and Siegel [4] will be used. These logic-based techniques can be considered as alternatives to the classical method of local propagation in Markov trees. Finally, we switch back from logic to the theory of evidence in order to compute degrees of support of hypotheses. We show that some recently proposed methods for computing simple disjunctive normal forms can be used to compute these degrees of support.