First-order expressivity for s5-models: Modal vs. two-sorted languages

Journal of Philosophical Logic 30 (6):571-591 (2001)
Abstract
Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented
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