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CONNEXIVE IMPLICATIONS IN SUBSTRUCTURAL LOGICS

Part of: General logic Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  24 July 2023

DAVIDE FAZIO  and
GAVIN ST. JOHN Open the ORCID record for GAVIN ST. JOHN [Opens in a new window]
DAVIDE FAZIO*
Affiliation:
DIPARTIMENTO DI SCIENZE DELLA COMUNICAZIONE UNIVERSITÀ DEGLI STUDI DI TERAMO CAMPUS “AURELIO SALICETI,” VIA R. BALZARINI 1, 64100 TERAMO (TE), ITALY
GAVIN ST. JOHN
Affiliation:
DIPARTIMENTO DI MATEMATICA UNIVERSITÀ DEGLI STUDI DI SALERNO VIA GIOVANNI PAOLO II, 132, 84084 FISCIANO (SA), ITALY E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

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.

Keywords

connexive logicresiduated latticesGlivenko propertysubstructural logicsweakly connexive logicstrong connexivity

MSC classification

Primary: 03A10: Logic in the philosophy of science 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) 03B55: Intermediate logics 03B60: Other nonclassical logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 3 , September 2024 , pp. 878 - 909
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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