Uniform Non-Deterministic Semantics for Ciuciura's $mb{C}^n$-Hierarchy

Abstract

We introduce a uniform non-deterministic semantics for the hierarchy of paraconsistent systems mbC^n introduced by Ciuciura. The proposed construction generalizes Omori's three-valued semantics for mbC^1 to all systems of the hierarchy. We prove soundness and completeness of the semantics with respect to the corresponding axiomatizations and show that the consequence relations of the systems mbC^n cannot be characterized by finite deterministic matrices.

arXiv commentIn Proceedings NCL'26, arXiv:2610.34489