Paracomplete Logics Dual To The Genuine Paraconsistent Logics: The Three-Valued Case

In 2016 Beziau, introduce a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws phi, (sic) phi proves psi and proves (sic) (phi boolean AND(sic) phi). In that paper the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multipleconclusion consequence relations, the dual properties of those above mentioned are proves phi, (sic) phi and (sic) (psi boolean OR (sic)psi) proves. We call genuine paracomplete logics those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics.