In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities

We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sd-DNNF), then for any consistent set of literals S, we can simultaneously count, in time linear in the size of , the models of: [ S; [ S [ flg: for every literal l 62 S; [ S n flg: for every literal l 2 S; [ S n flg [ f:lg: for every literal l 2 S.

INTRODUCTION In nonmonotonic reasoning conflicts among defaults are ubiquitous. For instance, more specific rules may be in conflict with more general ones, a problem which has been studied intensively in the context of inheritance networks (Poole,1985; Touretzky, 1986; Touretzky et al., 1991). When defaults are used for representing design goals in configuration tasks conflicts naturally arise. The same is true in model based diagnosis where defaults are used to represent the assumption that components typically are ok. In legal reasoning conflicts among rules are very common (Prakken, 1993) and keep many lawyers busy (and rich). The standard nonmontonicformalisms handle such conflicts by generating multiple belief sets. In default logic (Reiter, 1980) and autoepistemic logic (Moore, 1985) these sets are called extensions or expansions, respectively. In circumscription (McCarthy, 1980) the belief sets correspond to different classes of preferred models. Usually, not all of the beli

We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of atoms of the form s t where s and t are names. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed program correspond with the preferred answer sets of the original program. Our approach allows the specification of dynamic orderings, in which preferences can appear arbitrarily within a program. Static orderings (in which preferences are external to a logic program) are a trivial restriction of the general dynamic case. First, we develop a specific approach to reasoning with preferences, wherein the preference ordering specifies the order in which rules are to be applied. We then demonstrate the wide range of applicability of our framework by showing how other approaches, among them that of Brewka and Eiter, can be captured within our framework. Since the result of each of these transformations is an extended logic program, Affiliated with the School of Computing Science at Simon Fraser University, Burnaby, Canada.

Description logic reasoners are able to detect incoherences (such as logical inconsistency and concept unsatisfiability) in knowledge bases, but provide little support for resolving them. We propose to recast techniques for propositional inconsistency management into the description logic setting. We show that the additional structure afforded by description logic statements can be used to refine these techniques. Our focus in this paper is on the formal semantics for such techniques, although we do provide high-level decision procedures for the knowledge integration strategies discussed.

In this tutorial-overview, which resulted from a lecture course given by the authors at

We investigate the space e#ciency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space e#ciency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space e#ciency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms ...

In this paper we show that a particular construction of belief revision operator is equivalent to the standard method for computing consistency-based diagnosis. We show how a diagnosis problem can be translated into a problem of belief revision and show how kernel constructions for revision operators can be used for computing diagnosis. We also show how Reiter's algorithm for computing diagnosis can be adapted for being used in belief revision. 1 Introduction Belief revision (for an overview, see [ Gardenfors, 1988; Gardenfors and Rott, 1995 ] ) deals with the problem of how to accommodate new assertions into an existent body of knowledge. Traditionally, the body of knowledge is represented by a belief set, a set of formulas closed under logical implication. Instead of belief sets we are going to use belief bases to represent belief states. A belief base is a set not closed under logical consequence [ Fuhrmann, 1991; Hansson, 1989; Nebel, 1992 ] . For every belief base B...

Possibilistic logic is a logic for reasoning with uncertain and partially inconsistent knowledge bases. Its standard version consists in ranking propositional formulas according to their certainty or priority level, by assigning them lower bounds of necessity values. We give a survey of automated deduction techniques for standard possibilistic logic, together with complexity results. We focus on the extensions of resolution (Section 3) and of the Davis and Putnam procedure (Section 4). In Section 5 we consider extended versions and variants of possibilistic logic. We conclude by listing the related research topics, the applicative impact of this work and further research issues. 1 Introduction Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete and partially inconsistent knowledge. At the syntactical level it handles formulae of propositional or firstorder classical logic, to which are attached lower bounds of so-called degrees of necessity and possib...

Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default ! , does KB entail ! ? We classify the complexity of this problem for a number of well-known approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literal-Horn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedback-free Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to q-Horn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional know...