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Solving set optimization problems by cardinality optimization with an application to argumentation. (English) Zbl 1403.68236

Kaminka, Gal A. (ed.) et al., ECAI 2016. 22nd European conference on artificial intelligence, The Hague, Netherlands, August 29 – September 2, 2016. Proceedings. Including proceedings of the accompanied conference on prestigious applications of intelligent systems (PAIS 2016). In 2 volumes. Amsterdam: IOS Press (ISBN 978-1-61499-671-2/pbk; 978-1-61499-672-9/ebook). Frontiers in Artificial Intelligence and Applications 285, 966-973 (2016).
Summary: Optimization – minimization or maximization – in the lattice of subsets is a frequent operation in artificial intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subset-optimal solutions. It is based on the relationship between cardinality-optimal and subset-optimal solutions, and the fact that many logic-based declarative programming systems provide constructs for finding cardinality-optimal solutions, for example maximum satisfiability (MaxSAT) or weak constraints in answer set programming (ASP). Clearly each cardinality-optimal solution is also a subset-optimal one, and if the language also allows for the addition of particular restricting constructs (both MaxSAT and ASP do) then all subset-optimal solutions can be found by an iterative computation of cardinality-optimal solutions. As a showcase, the computation of preferred extensions of abstract argumentation frameworks using the proposed method is studied.
For the entire collection see [Zbl 1352.68013].

MSC:

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
68T27 Logic in artificial intelligence
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