The Strong Semantics for Logic Programs (original) (raw)

Generalized well-founded semantics for logic programs

1990

We extend the well-founded semantics of Van Gelder et al.[12] so that it is able to reason through clauses instead of single literals. This is necessary to infer p to be true in the program {pa; pb; a¬ b; b¬ a}. We call this generalized semantics, the generalized well-founded semantics. We present fixpoint and model theoretic definitions for generalized well-founded semantics and show their equivalence.

Well founded semantics for logic programs with explicit negation

European Conf. on Artificial Intelligence (ECAI'92), 1992

The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics 22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised 11]. This relationship improves the cross{fertilization between logic programs and default theories, since we generalize previous results concerning their relationship 3, 4, 7, 1, 2], and there is an increasing use of logic programming with explicit negation for nonmonotonic reasoning 7, 15, 16, 13, 23]. It also clari es the meaning of logic programs combining both explicit negation and negation by default. In particular, it shows that explicit negation corresponds exactly to classical negation in the default theory, and elucidates the use of rules in logic programs. Like defaults, rules are unidirectional, so their contrapositives are not implicit; the rule connective, , is not material implication, but has rather the avour of an inference rule, like defaults. It is worth noting that existing top{down procedures for well-founded semantics without explicit negation 24, 14] can be easily adapted to the semantics we are proposing for extended programs. This issue is only brie y considered here and will be the subject of a forthcoming report.

A logic for reasoning about well-founded semantics: preliminary report

2005

Abstract. The paper presents a preliminary solution to a long-standing problem in the foundations of well-founded semantics for logic programs. The problem addressed is this: which logic can be considered adequate for well-founded semantics (WFS) in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program?

Partial Deduction of Logic Programs wrt Well-Founded Semantics

1992

In this paper, we extend the partial deduction framework of [LS] to unfold non-ground negative literals [ST,CW] and to include loop checks [B2] during partial deduction. We show that the unified framework is sound and complete wrt well-founded model semantics, when certain conditions are satisfied.

Logical foundations of well-founded semantics

2006

Abstract We propose a solution to a long-standing problem in the foundations of well-founded semantics (WFS) for logic programs. The problem addressed is this: which (non-modal) logic can be considered adequate for well-founded semantics in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program?

Generalized disjunctive well-founded semantics for logic programs: procedural semantics

Methodologies For Intelligent Systems 5, 1991

Generalized disjunctive well-founded semantics (GDWFS) is a refined form of the generalized well-founded semantics (GWFS) of Baral, Lobo and Minker, to disjunctive logic programs. We describe fixpoint, model theoretic and procedural characterizations of GDWFS and show their equivalence. The fixpoint semantics is similar to the fix'point semantics of the GWFS, except that it iterates over state-pairs (a pair of sets; one a set of disjunctions of atoms and the other a pair of conjunctions of atoms), rather than partial interpretations. The model theoretic semantics is based on a dynamic stratification of the program. The procedural semantics is based on SLIS refutations, + trees and SLISNF trees.

Strong negation in well-founded and partial stable semantics for logic programs

2006

Abstract. A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT2. On logic programs partial equilibrium models coincide with Przymusinski's partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories.

On the equivalence of the static and disjunctive well-founded semantics and its computation

Theoretical Computer Science, 2001

In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programming and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood, the declarative and computational foundations of disjunctive logic programming proved to be much more elusive and di cult. Recently, two new and promising semantics have been proposed for the class of disjunctive logic programs. The ÿrst one is the static semantics STATIC, proposed by Przymusinski, and, the other is the disjunctive well-founded semantics D-WFS, proposed by Brass and Dix. Although the two semantics are based on very di erent ideas, both of them have been shown to share a number of natural and intuitive properties. In particular, both of them extend the well-founded semantics of normal logic programs. Nevertheless, since the static semantics employs a much richer underlying language than the D-WFS semantics, in general, the two semantics are di erent. The main result of this paper shows, however, that, when restricted to a common language, the two semantics in fact coincide. This important result provides additional and powerful argument in favor of the two semantics. It also allows us to use a recently developed minimal model theorem prover for an e cient implementation of the two semantics.

Well-founded semantics for semi-normal extended logic programs

In this paper we present a new approach for apply- ing well-founded semantics to extended logic programs. The main idea is not to fundamentally change the def- inition of well-founded semantics (as others have at- tempted) but rather to dene a few restrictions on the content of the extended logic program, that make it pos- sible to apply ìtraditionalî well-founded