Paracomplete Logics Dual to the Genuine Paraconsistent Logics: The Three-valued Case

In 2016 Béziau, introduce a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws φ,¬φ ⊢ ψ and ⊢ ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are ⊢ φ,¬φ and ¬(ψ∨¬ψ) ⊢. We call genuine paracomplete logics those rejecting the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics.