A Frame-based Characterisation of the Paraconsistent Well-founded Semantics with Explicit Negation

In this work, we present Paraconsistent Well-Founded Semantics with eXplicit negation (WFSXp) by introducing a frame-based semantics. As far as we know, this is the first time that a declarative approach for WFSXp is effectively characterised in terms of a model theory. Dismissing usual techniques based on immediate consequence operators, our definition depicts WFSXp by minimising models satisfying particular criteria. Aware that WFSXp captures a large deal of logic programming semantics (including the main well-founded ones), our approach subsumes indirectly a semantics for them. Then assuming an illustrative tone, by adding some conditions, we also show how it can be adjusted to define Well-Founded Semantics with eXplicit negation (WFSX ), WellFounded Semantics (WFS) as well as Answer Sets. Given its declarative aspects, our work paves the way to define a logical representation of the family of well-founded semantics.

[1]  Robert A. Kowalski,et al.  The Semantics of Predicate Logic as a Programming Language , 1976, JACM.

[2]  V. Lifschitz,et al.  The Stable Model Semantics for Logic Programming , 1988, ICLP/SLP.

[3]  Teodor C. Przymusinski,et al.  Semantic Issues in Deductive Databases and Logic Programs , 1990 .

[4]  Teodor C. Przymusinski.  Extended Stable Semantics for Normal and Disjunctive Programs , 1990, ICLP.

[5]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[6]  Phan Minh Dung,et al.  Negations as Hypotheses: An Abductive Foundation for Logic Programming , 1991, ICLP.

[7]  Chiaki Sakama,et al.  Extended Well-Founded Semantics for Paraconsistent Logic Programs , 1992, FGCS.

[8]  José Júlio Alferes,et al.  Well Founded Semantics for Logic Programs with Explicit Negation , 1992, ECAI.

[9]  Vladimir Lifschitz.  Minimal Belief and Negation as Failure , 1994, Artif. Intell..

[10]  José Júlio Alferes,et al.  Reasoning with Logic Programming , 1996, Lecture Notes in Computer Science.

[11]  C. Damásio,et al.  A survey of paraconsistent semantics for logic programs , 1998 .

[12]  David Pearce,et al.  From Here to There: Stable Negation in Logic Programming , 1999 .

[13]  Greg Restall,et al.  An Introduction to Substructural Logics , 2000 .

[14]  C. Damásio,et al.  Antitonic Logic Programs , 2001, LPNMR.

[15]  Pedro Cabalar.  Well Founded Semantics as Two dimensional Here and There , 2001, Answer Set Programming.

[16]  José Júlio Alferes,et al.  A logic programming system for nonmonotonic reasoning , 1995, Journal of Automated Reasoning.

[17]  Michael Schroeder,et al.  A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics , 2005, Theory Pract. Log. Program..