On Structured Argumentation with Conditional Preferences

We study defeasible knowledge bases with conditional preferences (DKB). A DKB consists of a set of undisputed facts and a rule-based system that contains different types of rules: strict, defeasible, and preference. A major challenge in defining the semantics of DKB lies in determining how conditional preferences interact with the attack relations represented by rebuts and undercuts, between arguments. We introduce the notions of preference attack relations as sets of attacks between preference arguments and the rebuts or undercuts among arguments as well as of preference attack relation assignments which map knowledge bases to preference attack relations. We present five rational properties (referred to as regular properties), the inconsistency-resolving, effective rebuts, context-independence, attack monotonicity and link-orientation properties generalizing the properties of the same names for the case of unconditional preferences. Preference attack relation assignment are defined as regular if they satisfy all regular properties. We show that the set of regular assignments forms a complete lower semilattice whose least element is referred to as the canonical preference attack relation assignment. Canonical attack relation assignment represents the semantics of preferences in defeasible knowledge bases as intuitively, it could be viewed as being uniquely identified by the regular properties together with the principle of minimal removal of undesired attacks. We also present the normal preference attack relation assignment as an approximation of the canonical attack relation assignment.

[1]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

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

[3]  Phan Minh Dung,et al.  Fundamental properties of attack relations in structured argumentation with priorities , 2018, Artif. Intell..

[4]  Gerhard Brewka,et al.  Preferred Subtheories: An Extended Logical Framework for Default Reasoning , 1989, IJCAI.

[5]  Thomas Eiter,et al.  Preferred Answer Sets for Extended Logic Programs , 1999, Artif. Intell..

[6]  Grigoris Antoniou.  Defeasible logic with dynamic priorities , 2002, NMR.

[7]  Henry Prakken,et al.  The ASPIC+ framework for structured argumentation: a tutorial , 2014, Argument Comput..

[8]  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..

[9]  Dov M. Gabbay.  Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview , 2009, Stud Logica.

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

[11]  Henry Prakken,et al.  A general account of argumentation with preferences , 2013, Artif. Intell..

[12]  Leila Amgoud,et al.  Postulates for logic-based argumentation systems , 2014, Int. J. Approx. Reason..

[13]  Hans Tompits,et al.  A framework for compiling preferences in logic programs , 2002, Theory and Practice of Logic Programming.

[14]  Simon Parsons,et al.  Instantiating Metalevel Argumentation Frameworks , 2018, COMMA.

[15]  Martin Caminada,et al.  On the evaluation of argumentation formalisms , 2007, Artif. Intell..

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

[17]  Phan Minh Dung,et al.  Inductive Defense for Sceptical Semantics of Extended Argumentation , 2011, J. Log. Comput..

[18]  Phan Minh Dung,et al.  An axiomatic analysis of structured argumentation with priorities , 2016, Artif. Intell..

[19]  Guillermo Ricardo Simari,et al.  On Acceptability in Abstract Argumentation Frameworks with an Extended Defeat Relation , 2006, COMMA.

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

[21]  Pietro Baroni,et al.  AFRA: Argumentation framework with recursive attacks , 2011, Int. J. Approx. Reason..