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    Item type:Publication,
    Connexive arithmetic formulated relevantly
    (Oxford University Press (OUP), 2025-12-04)
    ;
    Luis Estrada-González
    <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>
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    Item type:Publication,
    Connexive logic: new old challenges
    (Oxford University Press (OUP), 2025-02-20)
    ;
    Luis Estrada-González