On the Intertranslatability of Autoepistemic, Default and Priority Logics, and Parallel Circumscription

Abstract

This paper concentrates on comparing the relative expressive power of five non-monotonic logics that have appeared in the literature. The results on the computational complexity of these logics suggest that these logics have very similar expressive power that exceeds that of classical monotonic logic. A refined classification of non-monotonic logics by their expressive power can be obtained using translation functions that satisfy additional requirements such as faithfulness and modularity used by Gottlob. Basically, we adopt Gottlob’s framework for our analysis, but propose a weaker notion of faithfulness. A surprising result is deduced in light of Gottlob’s results: Moore’s autoepistemic logic is less expressive than Reiter’s default logic and Marek and Truszczyński’s strong autoepistemic logic. The expressive power of priority logic by Wang et al. is also analyzed and shown to coincide with that of default logic. Finally, we present an exact classification of the non-monotonic logics under consideration in the framework proposed in the paper.