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

TL;DR

This paper demonstrates that the paraconsistent Ciuciura's hierarchy logics can be characterized using finite matrices, with truth-values linked to Fibonacci sequences, providing a new algebraic perspective.

Contribution

It introduces a matrix-based characterization of Ciuciura's hierarchy of paraconsistent logics, connecting truth-values to finite sequences and Fibonacci numbers.

Findings

Logics of the family Ciu^n can be defined by finite matrices.

Truth-values are finite sequences of 0s and 1s.

Characterization relates to the Fibonacci sequence.

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.