Approximate reasoning in strength logic

The author defines a modal logic SL (strength logic) to reason about beliefs in an AI system. SL is a refinement of J. Halpern and M. Rabin´s likelihood logic (LL) (1987). As in LL, the powers of a modal operator S are used in SL to denote various degrees of certainty of beliefs. However, the axiomatization of SL is different from that of LL. Formulas in SL admit normal forms, and decision procedures of SL can be effectively constructed. The author defines a model of SL as an extension of Herbrand models for the propositional logic. This interpretation of SL is sharply different from the conventional semantics of modal logics. The thrust behind this research is to provide a natural and rigorous logic for designing, implementing, and verifying AI systems capable of approximate reasoning