CONICET | Buscador de Institutos y Recursos Humanos

Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H.~P.~Sankappanavar as a generalization of Heyting algebras. We address the problem of determining sub-varieties of the variety of semi-Heyting algebras for which the implication operation is uniquely determined. In doing this, we shed some light on the close relationship between the intuitionistic and semi-intuitionistic propositional calculus. We present a different version of semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke models.