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Scientific Programming
Volume 2018, Article ID 4157030, 10 pages
Research Article

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

1Department of Computing Science, Umeå University, 901 87 Umeå, Sweden
2Departamento de Actuaría, Física y Matemáticas, Universidad de las Américas Puebla, Sta. Catarina Mártir, 72820 Cholula, PUE, Mexico

Correspondence should be addressed to Juan Carlos Nieves;

Received 28 June 2017; Revised 9 October 2017; Accepted 24 October 2017; Published 1 March 2018

Academic Editor: Fabrizio Riguzzi

Copyright © 2018 Juan Carlos Nieves and Mauricio Osorio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 on suitable integration 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 program is a D3-WFS-DCOM model of . 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 a operator, which is a generalization of the aggregation operator setof over arbitrary complete lattices.