Minimal Coverings of Maximal Partial Clones

A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minimal covering.

• Type: Conference
• Year: 2009
• Where: ISMVL
• Authors: Karsten Schölzel
• Keywords: Artificial Intelligence, ISMVL 2009, Maximal Partial Clones, Partial Function, Partial Sheffer Functions