Modal extension of ideal paraconsistent four-valued logic and its subsystem (Q2004955)

The paper starts from a paraconsistent four-valued logic 4CC and adds modal operators, thus defining a modal logic M4CC. This logic embeds in the modal logic S4. Moreover, for a certain subset M4CC* of M4CC, a converse embedding also exists. 4CC is both paraconsistent and paracomplete: both the principle of explosion and the law of excluded middle are rejected. Both M4CC and M4CC* are sequent calculi and enjoy Kripke completeness, cut elimination, decidability and finite model property. A further section introduces the modal diamond as a primitive operator.