Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 64, Issue 3 (1999), 1125-1154.
There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R
In  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 . 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.
J. Symbolic Logic, Volume 64, Issue 3 (1999), 1125-1154.
First available in Project Euclid: 6 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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