A General Axiomatization for the logics of the Hierarchy ${\mathbb{I}}^n{\mathbb{P}}^k$

Abstract

In this paper, the logics of the family ${\mathbb{I}}^n{\mathbb{P}}^k$:=$\{I^n{P}^k{\}}_{(n,k)\in {\omega }^2}$ are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic $I^1$ and of the paraconsistent logic $P^1$. It is proved that this family can be naturally ordered, and it is shown an adequate axiomatics for each logic of the form $I^n{P}^k$.

20 pages