On the complexity of propositional quantification in intuitionistic logic

Journal of Symbolic Logic 62 (2):529-544 (1997)
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Abstract

We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine

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10.2307/2275545

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Philip Kremer
University of Toronto at Scarborough

Citations of this work

A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
Logics for propositional contingentism.Peter Fritz - 2017 - Review of Symbolic Logic 10 (2):203-236.
Expressivity of second order propositional modal logic.Balder ten Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.

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References found in this work

Propositional quantifiers in modal logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 16 (1):72-73.
Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Journal of Symbolic Logic 38 (2):329-329.

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