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

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Philip Kremer
University of Toronto at Scarborough
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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DOI 10.2307/2275545
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References found in this work BETA

Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
Completeness in the Theory of Types.Leon Henkin - 1951 - Journal of Symbolic Logic 16 (1):72-73.
Propositional Quantifiers in Modal Logic.Kit Fine - 1973 - Journal of Symbolic Logic 38 (2):329-329.

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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.
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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