Erkenntnis 85 (2):455-465 (2020)

Peter Fritz
Australian Catholic University
Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions.
Keywords propositional quantifiers  bimodal logic  S5
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Reprint years 2020
DOI 10.1007/s10670-018-0035-3
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Possible Worlds.Robert Stalnaker - 1976 - Noûs 10 (1):65-75.
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Diamonds Are Forever.Cian Dorr & Jeremy Goodman - 2020 - Noûs 54 (3):632-665.

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