Justifications and Blocking Sets in a Rule-Based Answer Set Computation

Notions of justifications for logic programs under answer set semantics have been recently studied for atom-based approaches or argumentation approaches. The paper addresses the question in a rule-based answer set computation: the search algorithm does not guess on the truth or falsity of an atom but on the application or non application of a non monotonic rule. In this view, justifications are sets of ground rules with particular properties. Properties of these justifications are established; in particular the notion of blocking set (a reason incompatible with an answer set) is defined, that permits to explain computation failures. Backjumping, learning, debugging and explanations are possible applications. 1998 ACM Subject Classification D.1.6 Logic Programming, I.2.3 Logic Programming

[1]  Grigoris Antoniou,et al.  Justifications for Logic Programming , 2013, LPNMR.

[2]  Hans Tompits,et al.  A Meta-Programming Technique for Debugging Answer-Set Programs , 2008, AAAI.

[3]  Torsten Schaub,et al.  Graphs and Colorings for Answer Set Programming with Preferences , 2003, Fundam. Informaticae.

[4]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[5]  Miroslaw Truszczynski,et al.  Logic programs with abstract constraint atoms: The role of computations , 2007, Artif. Intell..

[6]  Pascal Nicolas,et al.  ASPeRiX, a first-order forward chaining approach for answer set computing* , 2009, Theory and Practice of Logic Programming.

[7]  Igor Stéphan,et al.  ASPeRiX, a first-order forward chaining approach for answer set computing , 2017, Theory Pract. Log. Program..

[8]  Antonius Weinzierl,et al.  OMiGA : An Open Minded Grounding On-The-Fly Answer Set Solver , 2012, JELIA.

[9]  Carlos Viegas Damásio,et al.  Unifying Justifications and Debugging for Answer-Set Programs , 2015, ICLP.

[10]  Martin Gebser,et al.  Conflict-Driven Answer Set Solving , 2007, IJCAI.

[11]  Pascal Nicolas,et al.  The First Version of a New ASP Solver : ASPeRiX , 2009, LPNMR.

[12]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[13]  Alessandro Dal Palù,et al.  Answer Set Programming with Constraints Using Lazy Grounding , 2009, ICLP.

[14]  V. S. Costa,et al.  Theory and Practice of Logic Programming , 2010 .

[15]  Hans Tompits,et al.  Stepping through an Answer-Set Program , 2011, LPNMR.

[16]  Antonius Weinzierl,et al.  Finding explanations of inconsistency in multi-context systems , 2010, Artif. Intell..

[17]  Enrico Pontelli,et al.  Under Consideration for Publication in Theory and Practice of Logic Programming Justifications for Logic Programs under Answer Set Semantics , 2022 .

[18]  Francesca Toni,et al.  Justifying answer sets using argumentation , 2016, Theory Pract. Log. Program..