Extending Well-Founded Semantics with Clark’s Completion for Disjunctive Logic Programs

Juan Carlos Nieves,Mauricio Osorio

doi:10.1155/2018/4157030

Juan Carlos Nieves, Mauricio Osorio

Open Access

https://doi.org/10.1155/2018/4157030

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Abstract

In this paper, we introduce new semantics (that we call D3-WFS-DCOMP) and compare it with the stable semantics (STABLE). For normal programs, this semantics is based onsuitableintegration of the well-founded semantics (WFS) and the Clark’s completion. D3-WFS-DCOM has the following appealing properties: First, it agrees with STABLE in the sense that it never defines a nonminimal model or a nonminimal supported model. Second, for normal programs it extends WFS. Third, every stable model of a disjunctive programPis a D3-WFS-DCOM model ofP. Fourth, it is constructed using transformation rules accepted by STABLE. We also introduce second semantics that we call D2-WFS-DCOMP. We show that D2-WFS-DCOMP is equivalent to D3-WFS-DCOMP for normal programs but this is not the case for disjunctive programs. We also introduce third new semantics that supports the use of implicit disjunctions. We illustrate how these semantics can be extended to programs including explicit negation, default negation in the head of a clause, and aluboperator, which is a generalization of the aggregation operatorsetofover arbitrary complete lattices.

Highlights

One of the most well-known semantics for logic programming is the stable semantics (STABLE) [1, 2]
Since c does not appear in the head of any clause of P1, we can derive ¬c and so we can delete ¬c in the last clause to get a semantically equivalent program P3. (Note that what we have done so far in this example is accepted by the STABLE semantics.) since we have that a←b a ← ¬b are clauses in P3 and by reasoning by cases, we derive a. (Reasoning by cases is not accepted in STABLE.) we derive b by simple modus ponens
D3-well-founded semantics (WFS)-DCOMP is the first logic programming semantics that we aim to introduce in this paper

Summary

Introduction

One of the most well-known semantics for logic programming is the stable semantics (STABLE) [1, 2]. The obtained semantics, that we call D3-WFS-DCOMP, satisfies the following main properties: First, it agrees with STABLE in the sense that it never defines a nonminimal model or a nonminimal supported model. Every stable model of a disjunctive program P is a D3-WFS-DCOM model of P Fourth, it is constructed using logic program transformations accepted by STABLE. In the last part of our paper, we highlight that the introduced logic programming semantics are suitable for modeling the setof operator of PROLOG using negation as failure.

Background

Logic Programming Semantics

Applications

Conclusion and Future Work