Matrix characterisation of the hierarchy FiC n of bivaluated logics

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