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

Abstract

In this paper, we will prove that the logics of the family ${\text{Ciu}}^n$:=$\{Ci{u}^n{\}}_{n\in \omega }$ 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 $Ci{u}^n$-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.

18 pages