subsumption for structural matching

Structural matching originally introduced by Steven Vere in the mid seventies was a popular sub eld of inductive concept learning in the late seventies and early eighties Despite various attempts to formalize and implement the notion of most speci c generalisation of two productions several problems remained These include using background knowledge the non uniqueness of most speci c generalisations and handling in equalities We show how Gordon Plotkin s notions of least general generalisation and rela tive least general generalisation de ned on clauses can be adapted for use in structural matching such that the remaining problems disappear De ning clauses as universally quanti ed disjunctions of literals and productions as existentially quanti ed conjunc tions of literals it is shown that the lattice on clauses imposed by subsumption is order isomorphic to the lattice on productions needed for structural matching The mapping also shows the relation between the older work on structural matching and the fashionable inductive logic programming paradigm