We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.

This paper surveys the main results appeared in the literature on the computational complexity of non-monotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on non-monotonic formalisms, like default logic, autoepistemic logic, circumscription, closed-world reasoning and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursion-theoretic results are surveyed. Work partially supported by the ESPRIT Basic Research Action COMPULOG and the Progetto Finalizzato Informatica of the CNR (Italian Research Council). The first author is supported by a CNR scholarship 1 Introduction Non-monotonic logics and negation as failure in logic programming have been defined with the goal of providing formal tools for the representation of default information. One of the ideas und...

One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the non-monotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of non-monotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per...

this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in Sections 4 and 5, we discuss model theory and fixed points, which play a crucial role in the definition of semantics. Section 6 is the main section of the paper and is entirely devoted to a systematic exposition and comparison of various proposed semantics. In Section 7 we discuss the relationship between declarative semantics of deductive databases and logic programs and non-monotonic reasoning. Section 8 contains concluding remarks. 2 Deductive Databases

Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce non-determinism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation. Keywords: prioritized logic programs, abduction, default reasoning, prioritized circumscription 1 Introduction In commonsense reasoning a theory is usually assumed incomplete and may contain indefinite or conflicting knowledge. Under such circumstances, priority information is useful to select appropriate know...

Circumscription appears to be the most powerful and well-studied technique used in formalizing common-sense reasoning. The general form of predicate circumscription allows for fixed and varying (floating) predicates. We show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates. In fact, we transform this problem even into circumscription without fixed and varying predicates, that is where all predicates are minimized. Thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription. As a consequence, algorithms that compute circumscription for an inference task can be simplified. Mailing address: Via Salaria 113, I-00198 Roma, Italia. E-mail: cadoli@vaxrma.infn.it y Mailing address: Paniglgasse 16, A-1040 Wien, Austria. Internet e-mail: feiter,gottlobg@vexper...

. This paper presents a method of embedding circumscriptive theories in general disjunctive programs. In a general disjunctive program, negation as failure occurs not only in the body but in the head of a rule. In this setting, minimized predicates of a circumscriptive theory are specified using the negation in the body, while fixed and varying predicates are expressed by the negation in the head. Moreover, the translation implies a close relationship between circumscription and abductive logic programming. That is, fixed and varying predicates in a circumscriptive theory are also viewed as abducible predicates in an abductive disjunctive program. Our method of translating circumscription into logic programming is fairly general compared with the existing approaches and exploits new applications of logic programming for representing commonsense knowledge. 1 Introduction It is well-known that logic programming semantics have close relationships to circumscription. In early studies, Rei...

The purpose of this paper is to compare three types of non-monotonic semantics: (a) proof-theoretic semantics based on the closed world assumption, (b) model-theoretic semantics based on the notion of a minimal model and (c) model-theoretic semantics based on the notion of a minimal Herbrand model. All of these semantics capture the non-monotonicity of common sense reasoning, i.e. the ability to withdraw conclusions after some new information is added to the original theories, and proved to be powerful enough to handle most examples of such reasoning presented in the literature. However, since these formalizations are based on different intuitions and often produce different results, the problem of understanding the relationship between them is especially important. In the first part of the paper we concentrate on the class of positive logic programs, also called definite theories. Although the three semantics usually differ for universal sentences, our main result shows that they alwa...

This paper presents SLGCN for effective query evaluation with constructive

We discuss several abstract semantics for nonmonotonic logics. We present their motivations, their development and some historical origins, and show that the three systems considered are essentially equivalent: (a) the coherent systems of filters of S.Ben-David and R.Ben-Eliahu, (b) the coherent systems of filters developed by the author, (c) the partial order semantics of N.Friedman and J.Halpern. Keywords: nonmonotonic reasoning, nonmonotonic logics, preferential models 1 Introduction 1.1 Overview We first present a quite abstract introduction to abstract semantics (Section 1.2). This part is for the reader familiar with or uninterested in the details of their motivation by nonmonotonic logics. Sections 1.3 and 1.4 provide this motivation, and trace the origins and developments of the abstract ideas from more concrete examples of nonmonotonic reasoning. In particular, we discuss the well-examined preferential model semantics, the weak filter semantics developed by the author, and v...