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A concise axiomatization of \(\text{RM}_\rightarrow\). (English) Zbl 1036.03016

Summary: A new axiomatization for the implicational fragment of Dunn’s system RM is given. The new axiomatization is considerably more concise than the axiomatization that was previously known. Specifically, we show that the two axioms CCpCpqCpq and CCCCCpqqprCCCCCqppqrr may be replaced with either CCCpCCCqprqrr or CCCCCpqrCqprr. Since the implicational fragment of RM coincides with the implicational fragment of Sobocinski’s system S, the new axiomatization provides a concise basis for that system as well.

MSC:

03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
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