We present a new and general approach of defining semantics for disjunctive logic programs. Our framework consists of two parts: (1) a semantical , where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (2) a procedural, namely a bottom-up queryevaluation method based on operators working on conditional facts (introduced independently by Bry and Dung/Kanchansut for nondisjunctive programs). As to (1), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial evaluation property GPPE) and define a new semantics D-WFS. Our semantics coincides for normal programs with the well-founded semantics WFS. For positive disjunctive programs D-WFS coincides with the generalized closed world semantics GCWA. As a byproduct, we get new characterizations of WFS and GCWA. D-WFS is strongly related to Przymusinski's STATIC semantics: we conjecture that they coincide w.r.t. to the derivati...

Our goal is to derive bottom-up query-evaluation algorithms from abstract properties of the underlying negation semantics. In this paper, we demonstrate our approach for the disjunctive stable model semantics, but the ideas are applicable to many other semantics as well. Our framework also helps to understand and compare other proposed query evaluation algorithms. It is based on the notion of conditional facts, developed by Bry and Dung/Kanchansut. We start by computing a "residual program" and show that it is equivalent to the original program under very general conditions on the semantics (which are satisfied, e.g., by the well-founded, stable, stationary, and static semantics). Many queries can already be answered on the basis of the residual program. For the remaining literals, we propose to use an appropriate completion of the residual program, which syntactically characterizes the intended models. In the case of the stable model semantics, we utilize an interesting connection ...

Motivated by the possibilities of applying deductive database technology for efficient query answering in description logics, we present a translation operator µ that transforms non-recursive ALC ontologies into a disjunctive deductive database. Contrary to our previous work, in this paper we focus on handling negation, disjunction and existential quantifiers, which cannot be handled by deductive databases in a straightforward manner. We present a performance evaluation of our approach, confirming the intuition that techniques for optimizing query answering in disjunctive deductive databases may improve query answering in description logics. 1

. We propose a query-evaluation algorithm for database specifications consisting of overridable rules (defaults) and non-overridable rules (axioms). Both kinds of rules may contain disjunctions. Preferences among the defaults are given by a partial order which corresponds to a subclass relationship allowing multiple inheritance. We use a bottomup theorem proving procedure. It is applied to the set of (disjunctively) assumed default instances which essentially can again be computed by bottom-up evaluation. Our approach has two main advantages: First, it gives a simple foundation for bottom-up evaluation in the presence of defaults; this can be taken as a basis for different optimizations. Second, in contrast to other deduction algorithms, it is able to handle partially ordered defaults with a skeptical / minimal model semantics. 1 Introduction Our goal is to extend deductive databases [14, 10, 20] by overridable rules in order to increase the reusability of such specifications. This cl...

Our aim is to clarify which nonmonotonic consequence relation given by a set of "supernormal " defaults, i.e. defaults of the form There are in fact a number of proposals for (e.g. the skeptical and the credulous semantics). In this paper we look at the space of all possible default semantics and try to characterize the known ones by their properties, especially the valid deduction rules. For instance, it seems reasonable to require that any useful semantics should coincide with the original CWA if this is consistent. We might also want to allow proofs by case analysis. Then we get the skeptical semantics (assuming some other very natural deduction rules). Our results are in fact completeness proofs for "natural deduction systems " based on different default semantics. 1

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...

The goal of this paper is to explain the usage and semantics of hierarchical defaults in logical specifications. We discuss the usefulness of defaults for different specification scenarios like specialization, aggregation, explanation, revision, etc. To understand defaults formally, we introduce a general framework parameterized on the underlying logical institution extended by an instantiation mechanism for formulae. It is shown that hierarchical defaults have intended models if the extended institution is compact. As an example for a non-standard logic, we give the semantics of defaults in the multi-modal object calculus of the is-core project. To structure and compose specifications with defaults, default-preserving specification morphisms are defined and corresponding colimit constructions are sketched. 1 Introduction In this paper, we want to explain the usage and semantics of defaults in logic-based system specifications, particularly in specifications having an object-oriented ...

It is known that bottom-up query evaluation can be extended to work with disjunctive facts, but there seems to be the common assumption that it is much too inefficient for practical applications. In this paper, we improve the extended bottom-up evaluation by making the resolvable literal in a disjunctive fact unique. In many cases, this reduces an exponential behaviour to a polynomial one. We introduce the notion of "disjunction types" formalizing which predicates can appear together in a disjunction. This information is needed to generalize implementation techniques based on the predicate dependency graph, e.g. to determine a sequence for the evaluation of the rules. These two ideas are utilized in a translation of disjunctive rules into Horn clauses with some list-valued arguments. This shows that at least the addition of a few disjunctive rules to an otherwise Horn database does not destroy the possibility of efficient query evaluation. 1 Introduction The theory of deductive databa...

Abstract. We prove that negative hyper-resolution is a sound and complete procedure for answering queries in disjunctive logic programs. In our formulation, answers of queries are defined using disjunctive substitutions, which are more flexible than answer literals used in theorem proving systems. 1

ABSTRACT. We present a language for specifying structure and behavior of objects in information systems. This language is restricted to a set of core concepts for conceptual modeling. But it includes powerful concepts for specifying constraints and derived data. We present an algorithm for deciding on safe computation of derived information and demonstrate how this algorithm works with an example.