39th International Symposium on Multiple-Valued Logic, ISMVL 2009
21 May 2009 through 23 May 2009
Naha, Okinawa
[en] Partial clones ; Partial functions ; Sheffer function ; Cloning ; Many valued logics
[en] A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. We show that for each κ ≥ 3 there exists a unique minimal covering.
Graduate School of Information Sciences of Tohoku University;IEEE Computer Society;Japan MVL Research Group