Classification of three-valued logical functions preserving 0 (Q750422)

Let \(P_ 3\) be the set of all functions f: \(E^ n\to E\) where \(E=\{0,1,2\}\). F \((\subset P_ 3)\) is called \(P_ 3\)-maximal if F is closed and there is no closed G such that \(F\subset G\subset P_ 3\). Denote by \(T_ 0\) the set of zero-preserving functions (in \(P_ 3)\). Let \(P_ 3\) be partitioned in such a manner that \(f_ 1\), \(f_ 2\) \((\in P_ 3)\) are in a common class exactly when, for any \(P_ 3\)- maximal set \(F_ i\), the formulae \(f_ 1\in F_ i\) and \(f_ 2\in F_ i\) are equivalent. A detailed survey is obtained on the classes of \(P_ 3\) which are included in \(T_ 0\). This enables one to determine the \(T_ 0\)-bases, i.e., the sets H such that H generates \(T_ 0\) but no proper subset of H does the same.