Journal of Symbolic Logic 67 (3):1039-1054 (2002)
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A propositional system of modal logic is second-order if it contains quantifiers ∀p and ∃p, which, in the standard interpretation, are construed as ranging over sets of possible worlds (propositions). Most second-order systems of modal logic are highly intractable; for instance, when augmented with propositional quantifiers, K, B, T, K4 and S4 all become effectively equivalent to full second-order logic. An exception is S5, which, being interpretable in monadic second-order logic, is decidable
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DOI | 10.2178/jsl/1190150147 |
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References found in this work BETA
Reasoning About Knowledge.Ronald Fagin, Joseph Y. Halpern, Yoram Moses & Moshe Vardi - 1995 - MIT Press.
Solvable Cases of the Decision Problem.Paul Bernays - 1957 - Journal of Symbolic Logic 22 (1):68-72.
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 Simple Embedding of T Into Double S.Steven Kuhn - 2004 - Notre Dame Journal of Formal Logic 45 (1):13-18.
On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.
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