Journal of Symbolic Logic 67 (3):1039-1054 (2002)

G. Aldo Antonelli
University of California, Davis
Richmond Thomason
University of Michigan, Ann Arbor
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

Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Solvable Cases of the Decision Problem.Paul Bernays - 1957 - Journal of Symbolic Logic 22 (1):68-72.
Undecidable Theories.Martin Davis - 1959 - Journal of Symbolic Logic 24 (2):167-169.

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Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
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.
The Logic of Sequence Frames.Fabio Lampert - 2022 - Review of Symbolic Logic 15 (1):101-132.

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