Mortensen Logics

TL;DR

This paper systematically analyzes and compares the connexive variants of closed set logic and P2 logic obtained by adding Mortensen's M3V conditional, revealing differences in inconsistency and stability.

Contribution

It provides a systematic comparison of connexive variants of CSL and P2 with M3V, highlighting their differing behaviors in inconsistency and connexive stability.

Findings

Inconsistency is exacerbated in connexive CSL but attenuated in connexive P2.

M3V conditional remains connexively stable when combined with paraconsistent negations.

Abstract

Mortensen introduced a connexive logic commonly known as 'M3V'. M3V is obtained by adding a special conditional to LP. Among its most notable features, besides its being connexive, M3V is negation-inconsistent and it validates the negation of every conditional. But Mortensen has also studied and applied extensively other non-connexive logics, for example, closed set logic, CSL, and a variant of Sette's logic, identified and called 'P2' by Marcos. In this paper, we analyze and compare systematically the connexive variants of CSL and P2, obtained by adding the M3V conditional to them. Our main observations are two. First, that the inconsistency of M3V is exacerbated in the connexive variant of closed set logic, while it is attenuated in the connexive variant of the Sette-like P2. Second, that the M3V conditional is, unlike other conditionals, "connexively stable", meaning that it remains connexive when combined with the main paraconsistent negations.