There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R
Swirydowicz, Kazimierz
J. Symbolic Logic, Tome 64 (1999) no. 1, p. 1125-1154 / Harvested from Project Euclid
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.
Publié le : 1999-09-14
Classification: 
@article{1183745873,
     author = {Swirydowicz, Kazimierz},
     title = {There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 1125-1154},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745873}
}
Swirydowicz, Kazimierz. There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  1125-1154. http://gdmltest.u-ga.fr/item/1183745873/