The Complexity of Reasoning for Fragments of Autoepistemic Logic

Circuits, Logic, and Games

计算机科学;物理学;数学

Nadia Creignou ; Arne Meier ; Michael Thomas ; Heribert Vollmer

Others  :  http://drops.dagstuhl.de/opus/volltexte/2010/2523/pdf/10061.ThomasMichael.Paper.2523.pdf
PID  :  44029

学科分类：计算机科学（综合）

来源: CEUR

【 摘 要 】

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 1985 for modeling an ideally rational agent’s behavior and reasoning about his own beliefs. In this paper 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 counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic.