Abstract
We provide an answer to the three questions asked by H.J.Levesque during his AAAI-84 presentation: 1. How to distinguish between local and global inconsistencies i.e. between Believe(p) & Believe(¬p) and Belicve(p&¬p) ? 2. How to introduce quantifiers to the logic of beliefs ? 3. Is it possible to determine whether an agent explicitly believes in a statement p in a time better then O(KB*p) ? We introduce a logic of explicit and implicit beliefs B#L, which allows local inconsistencies, but forbids global ones. We prove its soundness and completeness. The semantics for the B#L logic is given by a Kripke model. We show how to introduce quantifiers to this logic and discuss its computational properties.The paper is organized as follows 1. Introduction. 2. The logics of explicit beliefs. 3. Implication in E fde , and E x . 4. Implicit and Explicit Beliefs. 5. The semantics of beliefs. 6. Tractability of implication. 7. Final remarks. 8. References.
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