Brief study of G'₃ logic

Abstract

We present a Hilbert-style axiomatization of a recently introduced logic, called G'₃ G'₃ is based on a 3-valued semantics. We prove a soundness and completeness theorem. The replacement theorem holds in G'₃. As it has already been shown in previous work, G'3 can express some non-monotonic semantics. We prove that G'₃can define the same class of functions as Lukasiewicz 3 valued logic. Moreover, we identify some normal forms for this logic.

Keywords:

• paraconsistent
• axiomatization
• G'₃ logic