The Complexity of Reasoning for Fragments of Autoepistemic Logic.

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 Δ2p-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.