The Implicative Conditional Eric Raidl & Gilberto Gomes https://link.springer.com/article/10.1007/s10992-023-09715-6
This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent.p ⇒ q is thus defined as p ⇒ q as ¬à (p ∧ ¬q)∧ à p∧à ¬q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. On Mon, Jul 15, 2024 at 4:10 AM jean-yves beziau <jyb.logic...@gmail.com> wrote: > LoCa - Seminário Interuniversitário de Lógica no Rio de Janeiro > "O condicional implicativo" > Gilberto Lourenco Gomes, Universidade Estadual do Norte Fluminense, RJ, > Brasil > Quarta-feira dia 17 de Julho de 2024 às 17h30 > https://www.rio-logic.org/2024-1.html > -- LOGICA-L Lista acadêmica brasileira dos profissionais e estudantes da área de Lógica <logica-l@dimap.ufrn.br> --- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para logica-l+unsubscr...@dimap.ufrn.br. Para acessar esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAF2zFLC%3De3G%3DoJrJbFQcT1bUeMxC9%3D%2BZorVQ9kTfa%2Bvw08krjQ%40mail.gmail.com.
