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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Montanari, A., Policriti, A. & Slanina, M. Alternative Translation Techniques for Propositional and First-Order Modal Logics. Journal of Automated Reasoning 28, 397–415 (2002). https://doi.org/10.1023/A:1015849504706
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DOI: https://doi.org/10.1023/A:1015849504706