Inheritance hierarchies: Semantics and unification

Inheritance hierarchies are introduced as a means of representing taxonomicallyorganized data. The hierarchies are built up from so-called feature types that are ordered by subtyping and whose elements are records. Every feature type comes with a set of features prescribing fields of its record elements. So-called feature terms are available to denote subsets of feature types. Feature unification is introduced as an operation that decides whether two feature terms have a nonempty intersection and computes a feature term denoting the intersection.We model our inheritance hierarchies as algebraic specifications in ordersortedequational logic using initial algebra semantics. Our framework integrates feature types whose elements are obtained as records with constructor types whose elements are obtained by constructor application. Unification in these hierarchies combines record unification with order-sorted term unification and is presented as constraint solving. We specify a unitary unification algorithm by a set of simplification rules and prove its soundness and completeness with respect to the model-theoretic semantics

Conditional Descriptions in Functional Unification Grammar

A grammatical description often applies to a linguistic object only when that object has certain features. Such conditlonal descriptions can be indirectly modeled in Kay's Functional Unification Grammar (FUG) using functional descrlptions that are embedded within disjunctive alternatlves. An extension to FUG is proposed that allows for a direct representation of condltional descriptions. This extension has been used to model the input condltlons on the systems of systemlc grammar. Conditional descriptions are formally defined in terms of logical implicatlon and negatlon. This formal deftnltlon enables the use of conditional descrlptions as a general notatlonal extension to any of the unification-based gram mar representation systems currently used in computational linguistics