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CONNEXIVE IMPLICATIONS IN SUBSTRUCTURAL LOGICS
- Part of
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- Journal:
- The Review of Symbolic Logic / Volume 17 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 24 July 2023, pp. 878-909
- Print publication:
- September 2024
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- Article
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This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FL
${}_{\scriptsize\mbox{e}}$-algebras). In particular, we inquire into sufficient and necessary conditions under which generalizations of the connexive implication-like operation defined in [6] for Heyting algebras still satisfy connexive theses. It will turn out that, in most cases, connexive principles are equivalent to the equational Glivenko property with respect to Boolean algebras. Furthermore, we provide some philosophical upshots like, e.g., a discussion on the relevance of the above operation in relationship with G. Polya’s logic of plausible inference, and some characterization results on weak and strong connexivity.
