Maximal weakly-intuitionistic logics

This article introduces the three-valuedweakly-intuitionistic logicI¹ as a counterpart of theparaconsistent calculusP¹ studied in [11].I¹ is shown to be complete with respect to certainthree-valued matrices. We also show that in the sense that any proper extension ofI¹ collapses to classical logic.The second part shows thatI¹ is algebraizable in the sense of Block and Pigozzi (cf. [2]) in a way very similar to the algebraization ofP¹ given in [8].In the last part of the paper we suggest the definition of certain hierarchies of finite-valued propositional paraconsistent and weakly-intuitionistic calculi, and comment on their intrinsic interest.