A Variant of Material Connexive Logic

Bulletin of the Section of Logic 51 (2):227-242 (2022)
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Abstract

The relationship between formal logic and informal reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius’ Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.

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Author Profiles

Alexander Belikov
Moscow State University
Dmitry Zaitsev
Lomonosov Moscow State University

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References found in this work

The Propositional Logic of Ordinary Discourse.William S. Cooper - 1968 - Inquiry: An Interdisciplinary Journal of Philosophy 11 (1-4):295 – 320.
Negation as Cancellation, Connexive Logic, and qLPm.Heinrich Wansing - 2018 - Australasian Journal of Logic 15 (2):476-488.
The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.

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