On the problem of expressibility operations of characteristic matrices of paraconsistent and paracomplete logics

Abstract

The following expressibilities are constructed: (1) implication of every logical matrix $M_{PCont}$, $M_{PCont(1)}$ and $M_{PComp(1)}$ in terms of the operations of the logical matrix $M_{LPF}$, (2) implication of every logical matrix $M_{PCont}$, $M_{LPF}$ and $M_{PComp(1)}$ in terms of the operations of the logical matrix $M_{PCont(1)}$, (3) implication of every logical matrix $M_{PCont}$, $M_{LPF}$ and $M_{PCont(1)}$ in terms of the operations of the logical matrix $M_{PComp(1)}$. Also it’s proven that the implications of the logical matrices $M_{LPF}$, $M_{PCont(1)}$ and $M_{PComp(1)}$ are not expressible in terms of the operations of the logical matrix $M_{PCont}$.