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Expressivity of Second Order Propositional Modal Logic

Balder Ten Cate
Journal of Philosophical Logic
Vol. 35, No. 2 (Apr., 2006), pp. 209-223
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226866
Page Count: 15
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Expressivity of Second Order Propositional Modal Logic
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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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