Cooperative combination of default logic and autoepistemic logic

Abstract

When we work with information from multiple sources, the formats of the knowledge bases may not be uniform. It is desirable to be able to combine a knowledge base of default rules with one containing autoepistemic formulas. “Cooperative combination” refers to the integration of knowledge bases in different formats, in a way that retains as much of the individual characteristics of the component formalisms as possible. Previous work on relating default logic and autoepistemic logic mostly imposes some constraints on autoepistemic logic, and thus is 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 common framework, which is important for developing a semantics applicable to the two logics, both separately and combined. We show one way of cooperatively integrating the two logics, and provide both a syntactic fixed point and a semantic possible partition sequence characterization.