This article introduces the three-valuedweakly-intuitionistic logicI1 as a counterpart of theparaconsistent calculusP1 studied in .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. ) in a way very similar to the algebraization ofP1 given in .
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.
KeywordsMathematical Logic Computational Linguistic Classical Logic Intrinsic Interest Proper Extension
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