Expressivity of second order propositional modal logic

Journal of Philosophical Logic 35 (2):209-223 (2006)
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
J. F. A. K. van Benthem (1983). Modal Logic and Classical Logic. Distributed in the U.S.A. By Humanities Press.

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Tero Tulenheimo (2009). Hybrid Logic Meets If Modal Logic. Journal of Logic, Language and Information 18 (4):559-591.

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