Minimal Belief and Negation as Failure: A Feasible Approach

Abstract

Lifschitz introduced a logic of minimal belief and negation as failure, called mbnf, in order to provide a theory of epistemic queries to nonmonotonic databases. We present a feasible subsystem of mbnf which can be translated into a logic built on first order logic and negation as failure, called fonf. We give a semantics for fonf along with an extended connection calculus. In particular, we demonstrate that the obtained system is still more expressive than other approaches. Introduction Lifschitz [ 1991; 1992 ] 1 introduced a logic of minimal belief and negation as failure, mbnf, in order to provide a theory of epistemic queries to nonmonotonic databases. This approach deals with self-knowledge and ignorance as well as default information. From one perspective, mbnf relies on concepts developed by Levesque [ 1984 ] and Reiter [ 1990 ] for database query evaluation. In these approaches, databases are treated as first order theories, whereas queries may also contain an epistemic mo...