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There exist exactly two maximal strictly relevant extensions of the relevant logic R

Published online by Cambridge University Press:  12 March 2014

Kazimierz Swirydowicz
Kazimierz Swirydowicz*
Affiliation:
Faculty of Mathematics and Computer Science, Of Adam Mickiewicz University, Poznan, Poland E-mail: swirydow@math.amu.edu.pl
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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 → B the formulas A and B do not have a common variable then there exists a valuation v such that v (A → 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 → B is provable in such a logic then A and B have a common propositional variable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1125 - 1154
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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