Default Logic and Autoepistemic Logic: Fixed Points and Common Semantic Framework

When we work with information from multiple sources, the formats of the knowledge bases may not be uniform. It would be desirable to be able to combine a knowledge base of default rules with one containing autoepistemic formulas. Previous works on relating default logic and autoepistemic logic mostly impose some constraints on autoepistemic logic, and thus are not suitable for combining the two logics. We first present a fixed point formulation of autoepistemic logic analogous to that of default logic. Then we introduce a possible world framework with a partition structure, which corresponds to our intuitive notion of accessibility as linking alternate ``possible'' worlds. We show that both default logic and autoepistemic logic can be characterized using this framework, and the constraints imposed on the possible world structures correspond to the requirements in the fixed point formulations. Casting both default logic and autoepistemic logic in a common framework is important for developing a semantics applicable to the two logics, both separately and combined.