Matrix characterization of Ciuciura's paraconsistent hierarchy $\textsf{Ciu}^n$

Abstract

In this paper, we will prove that the logics of the family $\textsf{Ciu}^n$:=$\{Ciu^n\}_{n \in \omega}$ of paraconsistent Ciuciura{'}s Logics (defined by means of bivaluations) can be alternatively defined by means of finite matrices. This result arises from the characterization of the truth-values of the involved matrices (relative to each $Ciu^n$-logic) as being specific finite sequences of elements of the set $2$ := $\{0,1\}$. Moreover, we will show along the paper that this characterization is related to the well-known standard Fibonacci Sequence, which is presented here by means of its binary expansion.