A four-valued modal logic arising from Monteiro's last algebras

Abstract

We study the class of abstract logics projectively generated by the class of tetravalent modal algebras. They are modal logics and they turn out to be four-valued in the sense that they can be characterized using the natural logic on the four-element tetravalent modal algebra which generates this variety together with sorne special class of homomorphisms. We also characterize them by their abstract properties and prove a completeness theorem.