Narrowing in Partial Conditional Equational Theories (Abstract)

We extend the "Conditional Narrowing Algorithm" of H.Hussmann (MIF-8502, Universlt~t Passau 1985) to partial conditional equational theories. Without loss of generality it is assumed that the partial conditional equational theory IMP be canonical, i.e. for every conditional existence equation (X : G -> t @ t') E IMP holds Var(G)=X, and that for every term r E Term(t,t') \ Term(G) there exists a conditional existence equation (Y : H -> p ~ p') E IMP and a substitution u wit~ Hu = G and p~ = r.