Intuitionistic Sahlqvist Theory for Deductive Systems

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Journal of Symbolic Logic 89 (4):1522-1580 (2024)
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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.

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10.1017/jsl.2023.7

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Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.

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