Affiliation:
1. Aix-Marseille Université
2. Gottfried Wilhelm Leibniz Universität Hannover
3. TWT GmbH
Abstract
Autoepistemic logic extends propositional logic by the modal operator
L
. A formula
φ
that is preceded by an
L
is said to be “believed.” The logic was introduced by Moore in 1985 for modeling an ideally rational agent’s behavior and reasoning about his own beliefs. In this article we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of checking that a given set of formulae characterizes a stable expansion and that of counting the number of stable expansions of a given knowledge base. We improve the best known
Δ
2
p
-upper bound on the former problem to completeness for the second level of the Boolean hierarchy. To the best of our knowledge, this is the first paper analyzing counting problem for autoepistemic logic.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
9 articles.
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