Revisiting da Costa logic

In [25] Priest developed the da Costa logic (daC); this is a paraconsistent logic which is also a co-intuitionistic logic that contains the logic CωCω. Due to its interesting properties it has been studied by Castiglioni, Ertola and Ferguson, and some remarkable results about it and its extensions are shown in [8] and [11]. In the present article we continue the study of daC, we prove that a restricted Hilbert system for daC, named DC, satisfies certain properties that help us show that this logic is not a maximal paraconsistent system. We also study an extension of daC called PH1PH1 and we give different characterizations of it. Finally we compare daC and PH1PH1 with several paraconsistent logics.