Characterization of Partial Sheffer Functions in 3-Valued Logic
Lucien Haddad, Dietlinde Lau · Proceedings/Proceedings - International Symposium on Multiple-Valued Logic · 2007
partial function f on a k-element set k is a partial Sheffer function if every partial function on k is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on k, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on k. We present minimal coverings of maximal partial clones on k for k = 2 and k = 3 and deduce criteria for partial Sheffer functions on a 2-element and a 3-element set.