The Handling of Loops in Talmudic Logic, with Application to Odd and Even Loops in Argumentation

The Talmud is a body of arguments and discussions about all aspects of the human agent’s social, legal and religious life. It was completed over 1500 years ago and its argumentation and debates contain many logical principles and examples very much relevant to today’s research in logic, artificial intelligence, law and argumentation. In a series of books on Talmudic Logic, the authors have studied the logical prinicples involved in the Talmud, one by one, devoting a volume to each major principle We have just finished writing Volume 5, entitled Resolution of Conflicts and Normative Loops in the Talmud, and the present paper describes how the Talmud deals with even and odd loops and compares the results with open issues in argumentation. For other English papers corresponding to previous books, see [1, 2, 3, 4, 5, 6]. We start by looking at two typical loops, as in Figures 1 and 2.

[1]  Martin Caminada,et al.  Preferred semantics as socratic discussion , 2014, J. Log. Comput..

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

[3]  D. M. Gabbaya.  Equational approach to argumentation networks , 2012 .

[4]  Dov M. Gabbay,et al.  Logical Analysis of the Talmudic Rules of General and Specific (Klalim-u-Pratim) , 2011 .

[5]  Toshiko Wakaki.  Preference-Based Argumentation Capturing Prioritized Logic Programming , 2010, ArgMAS.

[6]  Dov M. Gabbay,et al.  Obligations and prohibitions in Talmudic deontic logic , 2011, Artificial Intelligence and Law.

[7]  Martin Caminada,et al.  On the Limitations of Abstract Argumentation , 2011 .

[8]  Stefan Woltran,et al.  Strong Equivalence for Argumentation Semantics Based on Conflict-Free Sets , 2011, ECSQARU.

[9]  Dov M. Gabbay,et al.  Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction , 2009, Stud Logica.

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

[11]  Dov M. Gabbay,et al.  Contrary to time conditionals in Talmudic logic , 2012, Artificial Intelligence and Law.

[12]  Dov M. Gabbay,et al.  Future determination of entities in Talmudic public announcement logic , 2013, J. Appl. Log..

[13]  Martin Caminada.  A labelling approach for ideal and stage semantics , 2011, Argument Comput..

[14]  Henry Prakken,et al.  An abstract framework for argumentation with structured arguments , 2010, Argument Comput..

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

[16]  Fernando A. Tohmé,et al.  Two approaches to the problems of self-attacking arguments and general odd-length cycles of attack , 2009, J. Appl. Log..