Alternative Translation Techniques for Propositional and First-Order Modal Logics |
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Authors: | Angelo Montanari Alberto Policriti Matteo Slanina |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of Udine, Italy;(2) Department of Computer Science, Stanford University, Stanford, CA, U.S.A |
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Abstract: | We describe and analyze techniques, other than the standard relational/functional methods, for translating validity problems of modal logics into first-order languages. For propositional modal logics we summarize the -as-Pow method, a complete and automatic translation into a weak set theory, and then describe an alternative method, which we call algebraic, that achieves the same full generality of -as-Pow but is simpler and computationally more attractive. We also discuss the relationships between the two methods, showing that -as-Pow generalizes to the first-order case. For first-order modal logics, we describe two extensions, of different degrees of generality, of -as-Pow to logics of rigid designators and constant domains. |
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Keywords: | translation methods (first-order) modal logics computable set theories |
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