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Intuitionistic Sahlqvist Theory for Deductive Systems
Journal of Symbolic Logic 89 (4):1522-1580 (2024)
Abstract
Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic.Other Versions
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References found in this work
Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Logic and Implication: An Introduction to the General Algebraic Study of Non-classical Logics.Petr Cintula & Carles Noguera - 2021 - Cham: Springer Verlag.
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