A Variant of Material Connexive Logic

Alexander Belikov; Dmitry Zaitsev

doi:10.18778/0138-0680.2021.24

Authors

Alexander Belikov Lomonosov Moscow State University, Department of Logic, Faculty of Philosophy, 119234, Lomonosovskij prospekt, 27/4, Moscow, Russian Federation https://orcid.org/0000-0003-1395-8878
Dmitry Zaitsev Lomonosov Moscow State University, Department of Logic, Faculty of Philosophy, 119234, Lomonosovskij prospekt, 27/4, Moscow, Russian Federation https://orcid.org/0000-0002-9076-4658

DOI:

https://doi.org/10.18778/0138-0680.2021.24

Keywords:

many-valued logics, connexive logic, four-valued logic MC, informal reasoning

Abstract

The relationship between formal (standard) logic and informal (common-sense, everyday) 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’ (and thus, Aristotle’s) 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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