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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Sturm, H., Wolter, F. First-order Expressivity for S5-models: Modal vs. Two-sorted Languages. Journal of Philosophical Logic 30, 571–591 (2001). https://doi.org/10.1023/A:1013360121031
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DOI: https://doi.org/10.1023/A:1013360121031