Intuitionistic Sahlqvist theory for deductive systems

Authors :: Fornasiere, Damiano
Moraschini, Tommaso
Publication Year :: 2022
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.<br />Comment: 50 pages