Computing Argumentation Semantics in Answer Set Programming

We propose a simple and generic method for computing Dung's standard argumentation semantics along with semi-stable semantics in Answer Set Programming (ASP). The different semantics captured by argumentation frameworks are all uniformly represented in our ASP setting. It is based on Caminada's reinstatement labellings for argumentation frameworks as well as our method of computing circumscription in ASP. In our approach, a given argumentation framework is translated into a single normal logic program w.r.t. the chosen semantics whose answer set (if exists) yields an argument-based extension expressed by means of a reinstatement labelling for the semantics. We show soundness and completeness theorems for our translation, which allow us not only to compute argument-based extensions but also to decide whether an argument is sceptically or credulously accepted w.r.t. the chosen semantics. Based on our theorems, the prototype argumentation system was implemented using the ASP solver, DLV, whose evaluation results verified correctness of our approach.

[1]  Katsumi Inoue,et al.  Compiling Prioritized Circumscription into Answer Set Programming , 2004, ICLP.

[2]  Ulises Cortés,et al.  Preferred extensions as stable models , 2008, Theory Pract. Log. Program..

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

[4]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[5]  Frank Wolter,et al.  Semi-qualitative Reasoning about Distances: A Preliminary Report , 2000, JELIA.

[6]  Chiaki Sakama,et al.  Prioritized logic programming and its application to commonsense reasoning , 2000, Artif. Intell..

[7]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

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

[9]  Toshiko Wakaki,et al.  Circumscriptive Theorem Prover based on Integration of Guess and Check Programs , 2007 .

[10]  Chiaki Sakama,et al.  Computing Preferred Answer Sets in Answer Set Programming , 2003, LPAR.

[11]  Vladimir Lifschitz,et al.  Computing Circumscription , 1985, IJCAI.

[12]  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..

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

[14]  Gerald Pfeifer,et al.  A Deductive System for Non-Monotonic Reasoning , 1997, LPNMR.

[15]  Paul E. Dunne,et al.  Semi-stable semantics , 2006, J. Log. Comput..

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

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

[18]  Ilkka Niemelä,et al.  Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP , 1997, LPNMR.

[19]  Thomas Eiter,et al.  Towards Automated Integration of Guess and Check Programs in Answer Set Programming , 2004, LPNMR.

[20]  Trevor J. M. Bench-Capon,et al.  Coherence in finite argument systems , 2002, Artif. Intell..

[21]  Martin Caminada,et al.  On the Issue of Reinstatement in Argumentation , 2006, JELIA.

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

[23]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

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