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.
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Keywords | bounded fragment expressivity modal logic propositional quantifiers |
Categories | (categorize this paper) |
ISBN(s) | |
DOI | 10.1007/s10992-005-9012-9 |
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References found in this work BETA
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Admissible Sets and Structures: An Approach to Definability Theory.Jon Barwise - 1975 - Berlin, Heidelberg, and New York: Springer Verlag.
Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.
Quantifying Over Propositions in Relevance Logic: Nonaxiomatisability of Primary Interpretations of $\forall P$ and $\exists P$.Philip Kremer - 1993 - Journal of Symbolic Logic 58 (1):334-349.
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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.
Pure Extensions, Proof Rules, and Hybrid Axiomatics.Patrick Blackburn & Balder Ten Cate - 2006 - Studia Logica 84 (2):277-322.
Second-Order Propositional Modal Logic and Monadic Alternation Hierarchies.Antti Kuusisto - 2015 - Annals of Pure and Applied Logic 166 (1):1-28.
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.
View all 7 citations / Add more citations
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