Constructive Tightly Grounded Autoepistemic Reasoning

The key concept of autoepistemic logic introduced by Moore is a stable expansion of a set of premises, i.e., a set of beliefs adopted by an agent with perfect introspection capabilities on the basis of the premises. Moore's formal-ization of a stable expansion, however, is non-constructive and produces sets of beliefs which are quite weakly grounded in the premises. A new more constructive definition of the sets of beliefs of the agent is proposed. It is based on classical logic and enumerations of formulae. Considering only a certain subclass of enumera-tions, L-hierarchic enumerations, an attractive class of expansions is captured to characterize the sets of beliefs of a fully introspective agent. These L-hierarchic expansions are stable set minimal, very tightly grounded in the premises and independent of the syntactic representation of premises. Furthermore, Reiter's default logic is shown to be a special case of autoepistemic logic based on L-hierarchic expansions .