An Avron rule for fragments of R-mingle
George Metcalfe · Journal of Logic and Computation · 2013
Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle.In particular, it is shown that a "modus-ponens-like" rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication-fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set of rules.Indeed, this latter case provides an example of a three-valued logic with a finitely axiomatizable consequence relation that has no finite basis for its admissible rules.