On the existence and multiplicity of extensions in dialectical argumentation

In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of extensions in terms of the notion of dialectical justification, a close cousin of the notion of admissibility. The characterization is given in the context of the particular logic for dialectical argumentation DEFLOG. The results are of direct relevance for several well-established models of defeasible reasoning (like default logic, logic programming and argumentation frameworks), since elsewhere dialectical argumentation has been shown to have close formal connections with these models.

[1]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (vol. 1) , 1993 .

[2]  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..

[3]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[4]  Christos H. Papadimitriou,et al.  Default Theories that Always Have Extensions , 1994, Artif. Intell..

[5]  Ana Gabriela Maguitman,et al.  Logical models of argument , 2000, CSUR.

[6]  David W. Etherington.  Formalizing Nonmonotonic Reasoning Systems , 1987, Artif. Intell..

[7]  Bart Verheij.  Dialectical Argumentation As A Heuristic For Courtroom Decision Making , 2000 .

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

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

[10]  Bart Verheij,et al.  Automated argument assistance for lawyers , 1999, ICAIL '99.

[11]  Jürgen Dix,et al.  Nonmonotonic Reasoning: An Overview , 1997, CSLI Lecture Notes.

[12]  P. J. van Koppen,et al.  Rationality, information and progress in law and psychology , 2000 .

[13]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[14]  S. Toulmin.  The uses of argument , 1960 .

[15]  Bart Verheij.  DefLog - a logic of dialectical justification and defeat , 2000 .

[16]  Bart Verheij.  Evaluating Arguments Based on Toulmin’s Scheme , 2005 .