Journal of Symbolic Logic

There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R

Kazimierz Swirydowicz

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Abstract

In [60] N. Belnap presented an 8-element matrix for the relevant logic R with the following property: if in an implication A $\rightarrow$ B the formulas A and B do not have a common variable then there exists a valuation v such that v(A $\rightarrow$ B) does not belong to the set of designated elements of this matrix. A 6-element matrix of this kind can be found in: R. Routley, R.K. Meyer, V. Plumwood and R.T. Brady [82]. Below we prove that the logics generated by these two matrices are the only maximal extensions of the relevant logic R which have the relevance property: if A $\rightarrow$ B is provable in such a logic then A and B have a common propositional variable.

Article information

Source
J. Symbolic Logic, Volume 64, Issue 3 (1999), 1125-1154.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745873

Mathematical Reviews number (MathSciNet)
MR1779754

Zentralblatt MATH identifier
0947.03029

JSTOR
links.jstor.org

Citation

Swirydowicz, Kazimierz. There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R. J. Symbolic Logic 64 (1999), no. 3, 1125--1154. https://projecteuclid.org/euclid.jsl/1183745873


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