Towards a Common Framework for Dialectical Proof Procedures in Abstract Argumentation

We present a common framework for dialectical proof procedures for computing credulous, grounded, ideal and sceptical preferred semantics of abstract argumentation. The framework is based on the notions of dispute derivation and base derivation. Dispute derivation is a dialectical notion first introduced for computing credulous semantics in assumption-based argumentation, and adapted here for computing credulous semantics and grounded semantics. Base derivation is introduced for two purposes: (i) to characterize all preferred extensions containing a given argument, and (ii) to represent backtracking in the search for a dispute derivation. We prove the soundness of the proof procedures for any argumentation frameworks and their completeness for general classes of finitary or finite-branching argumentation frameworks containing the class of finite argumentation frameworks as a subclass.We also discuss related results.

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

[2]  Antonis C. Kakas,et al.  Computing the Acceptability Semantics , 1995, LPNMR.

[3]  Trevor J. M. Bench-Capon,et al.  A model of legal reasoning with cases incorporating theories and values , 2003, Artif. Intell..

[4]  Paul E. Dunne,et al.  The Computational Complexity of Ideal Semantics I: Abstract Argumentation Frameworks , 2008, COMMA.

[5]  Trevor J. M. Bench-Capon,et al.  Persuasion and Value in Legal Argument , 2005, J. Log. Comput..

[6]  Sarit Kraus,et al.  Reaching Agreements Through Argumentation: A Logical Model and Implementation , 1998, Artif. Intell..

[7]  Nicholas Rescher,et al.  Dialectics: A Controversy-Oriented Approach to the Theory of Knowledge , 1977 .

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

[9]  C. Reed.  Agreeing to Differ: Modelling Persuasive Dialogue Between Parties With Different Values , 2001 .

[10]  Phan Minh Dung,et al.  An Argumentation-Theoretic Foundations for Logic Programming , 1995, J. Log. Program..

[11]  Michael J. Maher,et al.  Argumentation Semantics for Defeasible Logic , 2004, J. Log. Comput..

[12]  Fangzhen Lin,et al.  Argument Systems: A Uniform Basis for Nonmonotonic Reasoning , 1989, KR.

[13]  Sylvie Doutre,et al.  Preferred Extensions of Argumentation Frameworks: Query Answering and Computation , 2001, IJCAR.

[14]  Dirk Vermeir,et al.  Dialectic semantics for argumentation frameworks , 1999, ICAIL '99.

[15]  Bart Verheij,et al.  A Labeling Approach to the Computation of Credulous Acceptance in Argumentation , 2007, IJCAI.

[16]  Barbara Messing,et al.  An Introduction to MultiAgent Systems , 2002, Künstliche Intell..

[17]  Paolo Mancarella,et al.  Abductive Logic Programming , 1992, LPNMR.

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

[19]  Sanjay Modgil,et al.  Proof Theories and Algorithms for Abstract Argumentation Frameworks , 2009, Argumentation in Artificial Intelligence.

[20]  Martin Caminada.  An Algorithm for Computing Semi-stable Semantics , 2007, ECSQARU.

[21]  Phan Minh Dung,et al.  Assumption-Based Argumentation , 2009, Argumentation in Artificial Intelligence.

[22]  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..

[23]  Henry Prakken,et al.  Relating Protocols For Dynamic Dispute With Logics For Defeasible Argumentation , 2000, Synthese.

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

[25]  Sanjay Modgil,et al.  Reasoning about preferences in argumentation frameworks , 2009, Artif. Intell..

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

[27]  Phan Minh Dung,et al.  Towards an Argument-based Model of Legal Doctrines in Common Law of Contracts , 2008 .

[28]  Nicholas R. Jennings,et al.  Agents That Reason and Negotiate by Arguing , 1998, J. Log. Comput..

[29]  L. Liverpool.  Two Party Immediate Response Disputes: Properties and Efficiency , 2001 .

[30]  Henry Prakken,et al.  Credulous and Sceptical Argument Games for Preferred Semantics , 2000, JELIA.

[31]  Claudette Cayrol,et al.  A Reasoning Model Based on the Production of Acceptable Arguments , 2002, Annals of Mathematics and Artificial Intelligence.

[32]  Pietro Baroni,et al.  On principle-based evaluation of extension-based argumentation semantics , 2007, Artif. Intell..

[33]  Pietro Baroni,et al.  Solving Semantic Problems with Odd-Length Cycles in Argumentation , 2003, ECSQARU.

[34]  Henry Prakken,et al.  Argument-Based Extended Logic Programming with Defeasible Priorities , 1997, J. Appl. Non Class. Logics.

[35]  Guillermo Ricardo Simari,et al.  A Mathematical Treatment of Defeasible Reasoning and its Implementation , 1992, Artif. Intell..

[36]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[37]  Pierre Marquis,et al.  Prudent semantics for argumentation frameworks , 2005, 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'05).

[38]  Frank Dignum,et al.  Towards interest-based negotiation , 2003, AAMAS '03.

[39]  Henry Prakken,et al.  A System for Defeasible Argumentation, with Defeasible Priorities , 1996, Artificial Intelligence Today.

[40]  Pietro Baroni,et al.  SCC-recursiveness: a general schema for argumentation semantics , 2005, Artif. Intell..

[41]  Antonis C. Kakas,et al.  Computing Argumentation in Logic Programming , 1999, J. Log. Comput..

[42]  Francesca Toni,et al.  Hybrid argumentation and its properties , 2008, COMMA.

[43]  Gerard Vreeswijk.  An algorithm to compute minimally grounded and admissible defence sets in argument systems , 2006, COMMA.

[44]  Phan Minh Dung,et al.  A Sound and Complete Dialectical Proof Procedure for Sceptical Preferred Argumentation , 2007 .

[45]  Pietro Baroni,et al.  A systematic classification of argumentation frameworks where semantics agree , 2008, COMMA.

[46]  Phan Minh Dung,et al.  Towards argumentation-based contract negotiation , 2008, COMMA.

[47]  Christos H. Papadimitriou,et al.  Elements of the Theory of Computation , 1997, SIGA.

[48]  Trevor J. M. Bench-Capon,et al.  Legal Case-based Reasoning as Practical Reasoning , 2005, Artificial Intelligence and Law.

[49]  John L. Pollock,et al.  Defeasible Reasoning , 2020, Synthese Library.

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

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

[52]  N. Iyadrahwa,et al.  Argumentation-based negotiation , 2004 .

[53]  Guillermo Ricardo Simari,et al.  Defeasible logic programming: an argumentative approach , 2003, Theory and Practice of Logic Programming.

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

[55]  Henry Prakken,et al.  Coherence and Flexibility in Dialogue Games for Argumentation , 2005, J. Log. Comput..

[56]  Trevor J. M. Bench-Capon.  Persuasion in Practical Argument Using Value-based Argumentation Frameworks , 2003, J. Log. Comput..

[57]  Maxime Morge,et al.  Computing Argumentation for Decision Making in Legal Disputes , 2008, Computable Models of the Law, Languages, Dialogues, Games, Ontologies.