Genuine paracomplete logics

Abstract In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is paraconsistent if it rejects laws $\varphi ,\neg \varphi \vdash \psi $ and $\vdash \neg (\varphi \land )$. that paper, author analyzes, among three-valued logics, which them satisfy this property. If we consider multiple-conclusion consequence relations, dual properties those above-mentioned are , $\neg (\psi \vee ) $. We call paracomplete logics rejecting mentioned properties. present here an analysis logics. very natural twist structures semantics for these also found in systematic way. This produces automatically simple elegant Hilbert-style characterization all Finally, introduce LGP not paraconsistent, even cannot be characterized by single finite logical matrix.