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

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.
Keywords bounded fragment  expressivity  modal logic  propositional quantifiers
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DOI 10.1007/s10992-005-9012-9
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References found in this work BETA

Admissible Sets and Structures: An Approach to Definability Theory.Jon Barwise - 1975 - Berlin, Heidelberg, and New York: Springer Verlag.
Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.

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Citations of this work BETA

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 Perspective on Monadic Second-Order Alternation Hierarchies.Antti Kuusisto - 2008 - In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 231-247.
On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.

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