Abstract
In modal logics, less theories are decidable. The first undecidability results were obtained by Kripke, for the modal predicate calculus of S4.3., With two unary predicate letters. The result was obtained by interpreting in this modal logic the classically undecidable theory of a binary relation. Slomson interpreted the classically undecidable theory of one classical reflexive and symmetric relation in monadic S5 with one monadic letter. In Section 47 we shall obtain undecidability results for monadic fragments of one letter and also for certain theories of pure equality in modal logics by systematically interpreting the classical undecidable theory of symmetric and reflexive relation.
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