Journal of Philosophical Logic

, Volume 35, Issue 2, pp 209–223 | Cite as

Expressivity of Second Order Propositional Modal Logic



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.

Key Words

bounded fragment expressivity modal logic propositional quantifiers 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.ISLA, Universiteit van AmsterdamAmsterdamThe Netherlands

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