Generalized disjunctive well-founded semantics for logic programs: procedural semantics (original) (raw)

Comparisons and computation of well-founded semantics for disjunctive logic programs

ACM Transactions on Computational Logic, 2005

Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which semantics is the most intended. In this paper we look at disjunctive well-founded reasoning from different angles. We show that there is an intuitive form of the well-founded reasoning in disjunctive logic programming which can be characterized by slightly modifying some existing approaches to defining disjunctive well-founded semantics, including program transformations, argumentation, unfounded sets (and resolution-like procedure). By employing the techniques developed by Brass and Dix in their transformationbased approach, we also provide a bottom-up procedure for this semantics. The significance of our work is not only in clarifying the relationship among different approaches, but also shed some light on what is an intended well-founded semantics for disjunctive logic programs.

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.

A well-founded semantics with disjunction

2005

In this paper we develop a new semantics for disjunctive logic programs, called Well-Founded Semantics with Disjunction (WFS d), by resorting to a fixed point-based operator. Coinciding with the Well-Founded Semantics (WFS) for normal logic programs, our semantics is uniquely defined for every disjunctive logic program.

A Top-Down Procedure for Disjunctive Well-Founded Semantics

2001

Skepticism is one of the most important semantic intuitions in artificial intelligence. The semantics formalizing skeptical reasoning in (disjunctive) logic programming is usually named well-founded semantics. However, the issue of defining and computing the well-founded semantics for disjunctive programs and databases has proved to be far more complex and difficult than for normal logic programs. The argumentation-based semantics WFDS is among the most promising proposals that attempts to define a natural well-founded semantics for disjunctive programs. In this paper, we propose a top-down procedure for WFDS called D-SLS Resolution, which naturally extends the Global SLS-resolution and SLI-resolution. We prove that D-SLS Resolution is sound and complete with respect to WFDS. This result in turn provides a further yet more powerful argument in favor of the WFDS.

A Comparison of the Static and the Disjunctive Well-founded Semantics and its Implementation

1998

In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programs and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood the declarative and computational foundations of disjunctive programming proved to be much more elusive and difcult. Recently, two new and very promising semantics have been proposed for the class of disjunctive logic programs. Both of them extend the wellfounded semantics of normal programs. The rst one is the static semantics proposed by Przymusinski and the other is the disjunctive wellfounded semantics proposed by Brass and Dix. Although the two semantics are based on very di erent ideas, we show in this paper that they turn out to be very closely related. In fact, we show that it is possible to restrict the underlying language of STATIC to get D-WFS. We also show how to use this characterization for an implementation based a circumscriptive theorem prover.

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.

The Strong Semantics for Logic Programs

1991

Recently, the well-founded semantics of a logic program P has been strengthened to the well-founded semantics-by-case (WF C ) and then again to the extended well-founded semantics (WF E ). An important concept used in both WF C and WF E is that of derived rules. We extend the notion of derived rules by adding a new type of derivation and define the strong semantics of P, which has the following important property, known as the GCWA-property: if an atom p = false in all minimal models of P, then p = false in the strong semantics of P. In general, the WF C -semantics and the WF E -semantics do not have the GCWA-property. If we first apply the WF E -semantics to P and then apply the strong semantics to a suitably simplified form of P based on its WF E -semantics, then the resulting semantics is stronger than the WF E -semantics and has the GCWA-property.

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.