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Propositional Quantification in Bimodal S5

Fritz, Peter
Journal article; AcceptedVersion; Peer reviewed
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final+draft.pdf (691.8Kb)
Year
2018
Permanent link
http://urn.nb.no/URN:NBN:no-68122

CRIStin
1599771

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Appears in the following Collection
  • Institutt for filosofi, ide- og kunsthistorie og klassiske språk [319]
  • CRIStin høstingsarkiv [15979]
Original version
Erkenntnis: An International Journal of Scientific Philosophy. 2018, DOI: http://dx.doi.org/10.1007/s10670-018-0035-3
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.
 
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