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    Item type:Publication,
    Connexive arithmetic formulated relevantly
    (Oxford University Press, 2025)
    Cano-Jorge, Fernando  
    ;
    Luis Estrada-González
    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, cRM3⁠, cRM⁠, cRMn⁠, and cRM⁠. We compare these with their counterparts RM3⁠, RM and that extend relevant arithmetic. ©The authors ©Oxford University Press.