Preferred extensions as stable models

Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t. AF. In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics.

[1]  Paolo Mancarella,et al.  Computing ideal sceptical argumentation , 2007, Artif. Intell..

[2]  Ulises Cortés,et al.  Defining new argumentation-based semantics by minimal models , 2006, 2006 Seventh Mexican International Conference on Computer Science.

[3]  Stefan Woltran,et al.  Reasoning in Argumentation Frameworks Using Quantified Boolean Formulas , 2006, COMMA.

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

[5]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[6]  Juan Carlos Nieves,et al.  Using Arguing Agents to increase the Human Organ Pool for Transplantation , 2003 .

[7]  Phan Minh Dung,et al.  Dialectic proof procedures for assumption-based, admissible argumentation , 2006, Artif. Intell..

[8]  Trevor J. M. Bench-Capon.  Value-based argumentation frameworks , 2002, NMR.

[9]  Yannis Dimopoulos,et al.  Graph Theoretical Structures in Logic Programs and Default Theories , 1996, Theor. Comput. Sci..

[10]  Rachel Ben-Eliyahu-Zohary.  An incremental algorithm for generating all minimal models , 2005, Artif. Intell..

[11]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

[12]  Claudette Cayrol,et al.  On Decision Problems Related to the Preferred Semantics for Argumentation Frameworks , 2003, J. Log. Comput..

[13]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games , 1995, Artif. Intell..

[14]  Francesco Ricca,et al.  The DLV Java Wrapper , 2003, APPIA-GULP-PRODE.

[15]  Philippe Besnard,et al.  Checking the acceptability of a set of arguments , 2004, NMR.

[16]  Dorian Gaertner,et al.  CaSAPI : a system for credulous and sceptical argumentation , 2007 .

[17]  Dirk van Dalen,et al.  Logic and structure , 1980 .

[18]  J. Pollock.  Cognitive Carpentry: A Blueprint for How to Build a Person , 1995 .

[19]  Trevor J. M. Bench-Capon,et al.  Complexity in Value-Based Argument Systems , 2004, JELIA.

[20]  Miroslaw Truszczynski,et al.  The First Answer Set Programming System Competition , 2007, LPNMR.

[21]  Phan Minh Dung,et al.  An Abstract, Argumentation-Theoretic Approach to Default Reasoning , 1997, Artif. Intell..

[22]  Georg Gottlob,et al.  The DLV System , 2002, JELIA.

[23]  Claudio Ulises Cortés García,et al.  Studying the grounded semantics by using a suitable codification , 2008 .

[24]  Henry Prakken,et al.  Logics for Defeasible Argumentation , 2001 .

[25]  Rachel Ben-Eliyahu – Zohary,et al.  An incremental algorithm for generating all minimal models , 2005 .

[26]  Mauricio Osorio,et al.  Applications of Intuitionistic Logic in Answer Set Programming , 2004, Theory Pract. Log. Program..