The Complexity of Reasoning for Fragments of Autoepistemic Logic

TL;DR

This paper analyzes the computational complexity of reasoning tasks and counting stable expansions in Boolean fragments of autoepistemic logic, providing a comprehensive complexity classification for these problems.

Contribution

It offers the first complexity analysis of counting stable expansions in autoepistemic logic and classifies the complexity of common reasoning problems across Boolean fragments.

Findings

Complexity classifications for expansion, brave, and cautious reasoning.

First analysis of counting stable expansions in autoepistemic logic.

Identification of tractable and intractable fragments.

Abstract

Autoepistemic logic extends propositional logic by the modal operator L. A formula 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.