Predicate transformations in a k-valued logic
Let \({\mathcal M}_{R_ k}^{(n)}\) be a class of (n-ary) functions over k- valued logic preserving the predicate \(R_ k(x_ 1,...,x_ h)\). Then the basic result of the paper states that the semigroup of endomorphisms of \({\mathcal M}_{R_ k}^{(n)}\) coincides with the semigroup of endomorphisms of a certain hypergraph \&\({}^ nG_{R_ k}\). It follows that also the automorphism groups coincide and that for specific relations \(R_ k\) the hypergraph can be replaced by a directed graph or a graph.
scientific article; zbMATH DE number 4106809