Ernst, Fitelson, Harris, and Wos [A
concise axiomatization of RM→,
Bulletin of the Section of Logic
(University of Lódź), vol. 30 (2001), pp. 191-194] discovered two three-bases for the implicational fragment of
Dunn's system R-Mingle, {CCpqCCqrCpr, CpCCpqq,
CCCCCpqrCqprr} and
{CCpqCCqrCpr, CpCCpqq, CCCpCCCqprqrr}.
Each of their bases has a total
length of 31 (counting occurrences of sentential variables and of the
connective). Wos later asks [as Open Question OQ29.RM in L. Wos and G. Pieper, Automated Reasoning and the Discovery of Missing and Elegant Proofs, Rinton Press, Paramus, 2003] if there exists an equivalent two-base, and [as Open Question OQ30.RM] if there exists a single axiom for this system. |
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ANSWER TO OQ29.RM
CCCCpqqrCCrsCps |
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