# The Complexity of Reasoning for Fragments of Autoepistemic Logic - Computer Science > Logic in Computer Science

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Abstract: Autoepistemic logic extends propositional logic by the modal operator L. Aformula that is preceded by an L is said to be -believed-. The logic wasintroduced by Moore 1985 for modeling an ideally rational agent-s behavior andreasoning about his own beliefs. In this paper we analyze all Boolean fragmentsof autoepistemic logic with respect to the computational complexity of thethree most common decision problems expansion existence, brave reasoning andcautious reasoning. As a second contribution we classify the computationalcomplexity of counting the number of stable expansions of a given knowledgebase. To the best of our knowledge this is the first paper analyzing thecounting problem for autoepistemic logic.

Author: ** Nadia Creignou, Arne Meier, Michael Thomas, Heribert Vollmer**

Source: https://arxiv.org/