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Propositional quantification in Bimodal S5
Fritz, Peter
Fritz, Peter
Author
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.
Keywords
Date
2020
Type
Journal article
Journal
Erkenntnis
Book
Volume
85
Issue
Page Range
455-465
Article Number
ACU Department
Dianoia Institute of Philosophy
Faculty of Theology and Philosophy
Faculty of Theology and Philosophy
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Open Access Status
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Controlled