On non-alethic logic

Non-alethic logic was introduced in da Costa [3]. In this kind of logic the principles of tertium non datur and of contradiction are not valid; furthermore, non-alethic logic constitutes a generalization of both paraconsistent and paracomplete logics. Nowadays, paraconsistent and paracomplete logics constitutes an important subject among non-classical logics, being studied in many countries, especially in Brazil, Australia, Italy and the U.S.A. In this note we present one propositional system of non-alethic logic N-1 and its corresponding first-order predicate system N-1(=).