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Published in:
2012 | OriginalPaper | Chapter
On the Parameterized Complexity of Default Logic and Autoepistemic Logic
Authors : Arne Meier, Johannes Schmidt, Michael Thomas, Heribert Vollmer
Published in: Language and Automata Theory and Applications
Publisher: Springer Berlin Heidelberg
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We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. in the context of the implication problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems.
On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XP
nu
), unless P=NP.