Expressivity of Second Order Propositional Modal Logic

Journal of Philosophical Logic 35 (2):209-223 (2006)
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Abstract

We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.

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10.1007/s10992-005-9012-9

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Citations of this work

A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
A Modal Loosely Guarded Fragment of Second-Order Propositional Modal Logic.Gennady Shtakser - 2023 - Journal of Logic, Language and Information 32 (3):511-538.
On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.

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