An axiomatic analysis of structured argumentation with priorities

Several systems of semantics have been proposed for structured argumentation with priorities. As the proposed semantics often sanction contradictory conclusions (even for skeptical reasoners), there is a fundamental need for guidelines for understanding and evaluating them, especially their conceptual foundation and relationship.In this paper, we present an axiomatic analysis of the semantics of structured defeasible argumentation both with and without preferences by introducing a class of ordinary attack relations satisfying a set of simple and intuitive properties. We show that there exists a "normal form" for ordinary attack relations in the sense that stable extensions wrt any ordinary attack relation are stable extensions wrt the normal attack relations.We relate the ordinary semantics to other approaches, especially to the ASPIC+ framework and the prioritized approaches in logic programming.

[1]  Miroslaw Truszczynski,et al.  Preferences and Nonmonotonic Reasoning , 2008, AI Mag..

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

[3]  A.R.C.S. A. H. Loveless.  What is an abstract ? , 1990 .

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

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

[6]  Phan Minh Dung,et al.  An Axiomatic Analysis of Structured Argumentation for Prioritized Default Reasoning , 2014, ECAI.

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

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

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

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

[11]  Gerhard Brewka.  Cumulative Default Logic: In Defense of Nonmonotonic Inference Rules , 1991, Artif. Intell..

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

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

[14]  Philippe Besnard,et al.  Bridging the Gap between Abstract Argumentation Systems and Logic , 2009, SUM.

[15]  Tran Cao Son,et al.  An argument-based approach to reasoning with specificity , 2001, Artif. Intell..

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

[17]  Tran Cao Son,et al.  Reasoning with Prioritized Defaults , 1997, LPKR.

[18]  Anthony Hunter,et al.  Instantiating abstract argumentation with classical logic arguments: Postulates and properties , 2011, Artif. Intell..

[19]  Phan Minh Dung,et al.  Closure and Consistency In Logic-Associated Argumentation , 2014, J. Artif. Intell. Res..

[20]  Donald Nute,et al.  Defeasible Logic , 1994, INAP.

[21]  Torsten Schaub,et al.  A Comparative Study of Logic Programs with Preference: Preliminary Report , 2001, Answer Set Programming.

[22]  Ronald Prescott Loui,et al.  Defeat among arguments: a system of defeasible inference , 1987, Comput. Intell..

[23]  Michael Gelfond,et al.  Logic programming and knowledge representation—The A-Prolog perspective , 2002 .

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

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

[26]  James P. Delgrande,et al.  A First-Order Conditional Logic for Prototypical Properties , 1987, Artif. Intell..

[27]  Michael Gelfond,et al.  Classical negation in logic programs and disjunctive databases , 1991, New Generation Computing.

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

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

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

[31]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[32]  Gerard Vreeswijk,et al.  Abstract Argumentation Systems , 1997, Artif. Intell..

[33]  Chitta Baral,et al.  Logic Programming and Knowledge Representation , 1994, J. Log. Program..

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

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

[36]  Stefan Woltran,et al.  Structural Properties for Deductive Argument Systems , 2013, ECSQARU.

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

[38]  Raymond Reiter,et al.  SOME REPRESENTATIONAL ISSUES IN DEFAULT REASONING , 1980 .

[39]  Danny De Schreye,et al.  Answer Set Planning , 1999 .

[40]  Hector Geffner,et al.  Conditional Entailment: Bridging two Approaches to Default Reasoning , 1992, Artif. Intell..

[41]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[42]  Jussi Rintanen.  Lexicographic Priorities in Default Logic , 1998, Artif. Intell..

[43]  Dov M. Gabbay,et al.  Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems , 1989, Logics and Models of Concurrent Systems.

[44]  Anthony Hunter,et al.  Aggregating evidence about the positive and negative effects of treatments , 2012, Artif. Intell. Medicine.

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