Propositional quantification in Bimodal S5

Journal article


Fritz, Peter 2020. Propositional quantification in Bimodal S5. Erkenntnis. 85, pp. 455 - 465. https://doi.org/10.1007/s10670-018-0035-3
AuthorsFritz, Peter
Abstract

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.

Year2020
JournalErkenntnis
Journal citation85, pp. 455 - 465
PublisherSpringer Netherlands
ISSN0165-0106
Digital Object Identifier (DOI)https://doi.org/10.1007/s10670-018-0035-3
Page range455 - 465
Research GroupDianoia Institute of Philosophy
Place of publicationNetherlands
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