## Journal of Symbolic Logic

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

Kazimierz Swirydowicz

#### 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

https://projecteuclid.org/euclid.jsl/1183745873

Mathematical Reviews number (MathSciNet)
MR1779754

Zentralblatt MATH identifier
0947.03029

JSTOR