<i>C</i>-systems of da Costa and Aristotle’s theses

Abstract This paper demonstrates the impossibility of obtaining a non-trivial logic by extending any of da Costa’s paraconsistent calculi $C_{n}$, where $1 \le n &amp;lt; \omega $, with Aristotle’s theses. As a solution to this issue, we propose da Costa-like calculi with intuitionistic (and classical) implication, which, when extended by Aristotle’s theses, will retain their non-triviality. In contrast to connexive logic, we will accept consequentia mirabilis as a thesis for all the calculi analysed in this article. The calculi will be presented in a Hilbert-style formulation, where the sole rule of inference is detachment, and a non-deterministic bivaluational semantics will be employed in their analysis.