Conflict-free and conflict-tolerant semantics for constrained argumentation frameworks

In this paper we incorporate integrity constraints in abstract argumentation frameworks. Two types of semantics are considered for these constrained frameworks: conflict-free and conflict-tolerant. The first one is a conservative extension of standard approaches for giving coherent-based semantics to argumentation frameworks, where in addition certain constraints must be satisfied. A primary consideration behind this approach is a dismissal of any contradiction between accepted arguments of the constrained frameworks. The second type of semantics preserves contradictions, which are regarded as meaningful and sometimes even critical for the conclusions. We show that this approach is particularly useful for assuring the existence of non-empty extensions and for handling contradictions among the constraints, in which cases conflict-free extensions are not available.Both types of semantics are represented by propositional sets of formulas and are evaluated in the context of three-valued and four-valued logics. Among others, we show a one-to-one correspondence between the models of these theories, the extensions, and the labelings of the underlying constrained argumentation frameworks.

[1]  Dirk Vermeir,et al.  Robust Semantics for Argumentation Frameworks , 1999, J. Log. Comput..

[2]  Ofer Arieli.  Towards Constraints Handling by Conflict Tolerance in Abstract Argumentation Frameworks , 2013, FLAIRS Conference.

[3]  Ofer Arieli.  Conflict-Tolerant Semantics for Argumentation Frameworks , 2012, JELIA.

[4]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[5]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning and Logic Programming , 1993, IJCAI.

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

[7]  Charles A. Baylis,et al.  Der volle Dreiwertige Aussagenkalkul. , 1937 .

[8]  Pietro Baroni,et al.  Semantics of Abstract Argument Systems , 2009, Argumentation in Artificial Intelligence.

[9]  Claudette Cayrol,et al.  Change in Abstract Argumentation Frameworks: Adding an Argument , 2010, J. Artif. Intell. Res..

[10]  Dov M. Gabbay,et al.  Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming , 2009, Stud Logica.

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

[12]  Arnon Avron,et al.  The Value of the Four Values , 1998, Artif. Intell..

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

[14]  Claudette Cayrol,et al.  Inferring from Inconsistency in Preference-Based Argumentation Frameworks , 2002, Journal of Automated Reasoning.

[15]  Newton C. A. da Costa,et al.  On the theory of inconsistent formal systems , 1974, Notre Dame J. Formal Log..

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

[17]  Ofer Arieli,et al.  Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae , 2007, TOCL.

[18]  Pierre Marquis,et al.  Constrained Argumentation Frameworks , 2006, KR.

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

[20]  Arnon Avron,et al.  Natural 3-valued logics—characterization and proof theory , 1991, Journal of Symbolic Logic.

[21]  Dov M. Gabbay,et al.  A Logical Account of Formal Argumentation , 2009, Stud Logica.

[22]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[23]  Pietro Baroni,et al.  An introduction to argumentation semantics , 2011, The Knowledge Engineering Review.

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

[25]  Leon van der Torre,et al.  A Logical Theory about Dynamics in Abstract Argumentation , 2013, SUM.

[26]  Ofer Arieli,et al.  On the acceptance of loops in argumentation frameworks , 2016, J. Log. Comput..

[27]  Martin Caminada,et al.  A QBF-based formalization of abstract argumentation semantics , 2013, J. Appl. Log..

[28]  Henry Prakken,et al.  AI & Law, Logic and Argument Schemes , 2005 .