The Weak Variable Sharing Property

Tore Fjetland Øgaard

doi:10.18778/0138-0680.2023.05

Authors

Tore Fjetland Øgaard University of Bergen, Department of Philosophy, Postboks 7805, 5020 Bergen, Bergen, Norway Author https://orcid.org/0000-0002-7082-991X

DOI:

https://doi.org/10.18778/0138-0680.2023.05

Keywords:

characteristic matrix, relevant logics, variable sharing properties

Abstract

An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all its odd-valued extensions \(\mathbf{RM}_{2n\mathord{-}1}\) satisfy the weak variable sharing property. It is also shown that a proof to the effect that the "fuzzy" version of the relevant logic R satisfies the property is incorrect.

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