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

The class of abstract logics projectively generated by the class of logics defined on tetravalent modal algebras by the family of their filters is studied. These logics are four-valued in the sense that they can be characterized by a generalized matrix on the four-element tetravalent modal algebra which generates this variety together with a family of homomorphisms. They can be called modal since this four-element algebra can be given a nice epistemic interpretation as an extension of Belnap´s four-valued logic. The authors also characterize them by their abstract properties and prove a completeness theorem with respect to a sequent calculus suggested by the abstract version