Abstract
RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.
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Mares, E.D. The Incompleteness of RGL. Studia Logica 65, 315–322 (2000). https://doi.org/10.1023/A:1005283629842
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DOI: https://doi.org/10.1023/A:1005283629842