On the relationship between assumption-based framework and autoepistemic logic

Abstract

Assumption-based (AB) framework [BTK93] is a generalisation of abduction. It augments a theory with a set of admissible assumptions that it can defend against any attacks. Autoepistemic logic is a nonmonotonic logic about an ideal agent who reasons about her beliefs and ignorance introspectively. On the surface, these two formalisms look very different. A closer examination reveals many similarities. Indeed, BTK93 has shown that stable extensions in the AB framework of an autoepistemic theory correspond to the Moore's AE extensions of the theory. In this paper, we shall continue to establish some more relationships between the two formalisms. We first reformulate BTK's AB framework for AE logic with a modal approach. We then provide an AB framework for a revised preferred extension that neither subsumes nor being subsumed by Przymusinski's 3-valued AE logic. We then show that the AB framework for a revised complete extension of any consistent AE theory strictly subsumes Przymusinski's 3-valued AE logic. By exploiting the clear structure of the modally reformulated AB framework, we further define an AB framework for a reflexive preferred (cf. stable, complete) extension that integrates Schwarz 's reflexive AE logic with Przymusinski's 3-valued AE logic.