Complexity of semi-stable and stage semantics in argumentation frameworks

Authors:
Wolfgang Dvořák;Stefan Woltran
Affiliations:
Institute for Information Systems 184/2, Technische Universität Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria;Institute for Information Systems 184/2, Technische Universität Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria
Venue:
Information Processing Letters
Year:
2010

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Abstract

In this work, we answer two questions about the complexity of semi-stable semantics for abstract argumentation frameworks: we show @P"2^P-completeness for the problem of deciding whether an argument is skeptically accepted, and respectively, @S"2^P-completeness for the problem of deciding whether an argument is credulously accepted under the semi-stable semantics. Furthermore, we extend these complexity bounds to the according decision problems for stage semantics and discuss two approaches towards tractability.