The stable model semantics had been recently generalized to nonHerbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of normal and disjunctive programs under the general stable model semantics. A translation from disjunctive programs to normal programs is proposed for infinite s...

Department of Computer Science The Wichita State University Wichita, Kansas 67260-0083, USA e-mail: [email protected] Abstract. We introduce the notion of conditional facts in deductive databases. The language used to express the conditions in the basic facts does not involve constructs used to describe the database and is motivated by its potential usefulness in expressing disjunctive facts and ...

The stable model semantics of disjunctive logic programs is based on minimal models which assign atoms false by default. While this feature is highly useful and leads to concise problem encodings, it occasionally makes knowledge representation with disjunctive rules difficult. Lifschitz’ parallel circumscription provides a remedy by introducing atoms that are allowed to vary or to have fixed va...

Multiple convergence is proposed as a method for acquiring disjunctive concept descriptions. Disjunctive descriptions are necessary when the concept representation language is insufficiently expressive to satisfy the completeness and consistency requirements of inductive learning with a single conjunction of generalized features. Multiple convergence overcomes this insufficiency by allowing the...

Abductive logic programming has been widely used to declaratively specify a variety of problems in AI including updates in data and knowledge bases, belief revision, diagnosis, causal theory, and default reasoning. One of the most signi cant issues in abductive logic programming is to develop a reasonable method for knowledge assimilation, which incorporates obtained explanations into the curre...

This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is proposed and then proved to be sound over infinite structures. The equivalence of expressive power of two kinds of logic programs over arbitrary structures ...

Disjunctive Deductive Databases (DDDBs) | function-free disjunctive logic programs with negation in rule bodies allowed | have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a tho...

We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods, for our approach neither a conjunctive nor a disjunctive normal form is expected. Applying existing lower level reformulations for the corresponding semi-infinite program we derive conjunctive nonlinear problems without any logical expressions, which c...

The well-founded model for any general deductive database computed using the paraconsistent relational model, based on four-valued logic, does not support inference rules such as disjunctive syllogism. In order to support disjunctive syllogism, we utilize the generalization of the relational model to quasi-classic (QC) logic, whose inference power is much closer to classical logic. As the parac...

In this paper we investigate relationships between top-down and bottomup approaches to computation with disjunctive logic programs (DLPs). The bottom-up calculus considered, hyper tableaux, is depicted in its ground version and its relation to fixed point approaches from the literature is investigated. For the top-down calculus we use restart model elimination (RME) and show as our main result ...