Connexive arithmetic formulated relevantly
Journal
Logic Journal of the IGPL
ISSN
1367-0751
1368-9894
Publisher
Oxford University Press (OUP)
Date Issued
2025-12-04
Author(s)
Luis Estrada-González
Type
text::journal::journal article
Abstract
<jats:title>Abstract</jats:title>
<jats:p>Following the strategy in [15] to develop inconsistent models for relevant arithmetics, we formulate a connexive variant of arithmetic by replacing the conditional of RM3 with the Belikov–Loginov conditional. We obtain thus the connexive logic cRM3 which serves as a base logic for arithmetics cRM3$^{i}$, cRM3$^{i\sharp }$, cRM$^{\sharp }$, cRMn$^{i}$, and cRM$^\omega $. We compare these with their counterparts RM3$^{i\sharp }$, RM$^{\sharp }$ and $\mathbf{RM}^\omega$ that extend relevant arithmetic $\mathbf{R}^\sharp$.</jats:p>
<jats:p>Following the strategy in [15] to develop inconsistent models for relevant arithmetics, we formulate a connexive variant of arithmetic by replacing the conditional of RM3 with the Belikov–Loginov conditional. We obtain thus the connexive logic cRM3 which serves as a base logic for arithmetics cRM3$^{i}$, cRM3$^{i\sharp }$, cRM$^{\sharp }$, cRMn$^{i}$, and cRM$^\omega $. We compare these with their counterparts RM3$^{i\sharp }$, RM$^{\sharp }$ and $\mathbf{RM}^\omega$ that extend relevant arithmetic $\mathbf{R}^\sharp$.</jats:p>