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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| DOI | 10.2307/2275545 |
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References found in this work BETA
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 - 1973 - Journal of Symbolic Logic 38 (2):329-329.
On 2nd Order Intuitionistic Propositional Calculus with Full Comprehension.Dov M. Gabbay - 1974 - Archive for Mathematical Logic 16 (3-4):177-186.
View all 7 references / Add more references
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.
Quantified Multimodal Logics in Simple Type Theory.Christoph Benzmüller & Lawrence C. Paulson - 2013 - Logica Universalis 7 (1):7-20.
Uniform Interpolation and Propositional Quantifiers in Modal Logics.Marta Bílková - 2007 - Studia Logica 85 (1):1-31.
Expressivity of Second Order Propositional Modal Logic.Balder ten Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
View all 18 citations / Add more citations
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