Matrix characterisation of the hierarchy FiC n of bivaluated logics

Abstract

In this paper, we define the family FiCn:={FiCn}n∈ω of logics bymeans of semantics of bivaluations. This family is a variant of the familyof paraconsistent bivaluated Ciun-logics, defined and studied byJ. Ciuciura. We will show that every logic in FiCn can be alternativelydefined by means of finite matrices. This result arises from the characterisationof the truth-values of the involved matrices (relative toeach FiCn-logic) as being specific finite sequences of elements of theset 2 := {0, 1}.Moreover,we will showin this paper that such characterisationis related to the well-known standard Fibonacci Sequence,which is presented here by means of its binary expansion.