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First-order expressivity for S5-models: Modal vs. two-sorted languages. (English) Zbl 0990.03014
Summary: Standard models for modal 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.

03B45 Modal logic (including the logic of norms)
03B20 Subsystems of classical logic (including intuitionistic logic)
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