An axiomatic approach to feature term generalization

Abstract

This paper presents a missing link between Plotkin’s least general generalization formalism and generalization on the Order Sorted Feature (OSF) foundation. A feature term (or ψ-term) is an extended logic term based on ordered sorts and is a normal form of an OSF-term. An axiomatic definition of ψ-term generalization is given as a set of OSF clause generalization rules and the least generality of the axiomatic definition is proven in the sense of Plotkin’s least general generalization (lgg). The correctness of the definition is given on the basis of the axiomatic foundation. An operational definition of the least general generalization of clauses based on ψ-terms is also shown as a realization of the axiomatic definition.