A Closer Look at Some Subintuitionistic Logics

SERGIO ARTURO CELANI AND RAMON JANSANA

Notre Dame Journal of Formal Logic

Duke University Press

Año: 2001 vol. 42 p. 225 - 255

0029-4527

In the present paper we study systematically several consequence relationson the usual language of propositional intuitionistic logic that can bedened semantically by using Kripke frames and the same dening truth conditionsfor the connectives as in intuitionistic logic but without imposing some ofthe conditions on the Kripke frames that are required in the intuitionistic case.The logics so obtained are called subintuitionistic logics in the literature. We departfrom the perspective of considering a logic just as a set of theorems and alsodepart from the perspective taken by Restall in that we consider standard Kripkemodels instead of models with a base point. We study the relations betweensubintuitionistic logics and modal logics given by the translation considered byDošen. Moreover, we classify the logics obtained according to the hierarchyconsidered in Abstract Algebraic Logic.