Mortensen Logics

Luis Estrada-González
(Institute for Philosophical Research, National Autonomous University of Mexico (UNAM))
Fernando Cano-Jorge
(Universidad Panamericana)

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.

In Andrzej Indrzejczak and Michał Zawidzki: Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications (NCL 2022), Łódź, Poland, 14-18 March 2022, Electronic Proceedings in Theoretical Computer Science 358, pp. 189–201.
Published: 14th April 2022.

ArXived at: https://dx.doi.org/10.4204/EPTCS.358.14 bibtex PDF
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