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Solving Set Optimization Problems by Cardinality Optimization with an Application to Argumentation

Faber, Wolfgang, Vallati, Mauro, Cerutti, Federico and Giacomin, Massimiliano (2016) Solving Set Optimization Problems by Cardinality Optimization with an Application to Argumentation. In: 22nd European Conference on Artificial Intelligence (ECAI2016). Frontiers in Artificial Intelligence and Applications, 285 (285). IOS Press, pp. 966-973. ISBN 978-1-61499-671-2

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Abstract

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.

Item Type: Book Chapter
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Schools: School of Computing and Engineering
School of Computing and Engineering > High-Performance Intelligent Computing > Planning, Autonomy and Representation of Knowledge
School of Computing and Engineering > High-Performance Intelligent Computing > Planning, Autonomy and Representation of Knowledge
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Depositing User: Wolfgang Faber
Date Deposited: 02 Sep 2016 13:20
Last Modified: 02 Dec 2016 15:03
URI: http://eprints.hud.ac.uk/id/eprint/29318

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