10 - Types and Constraints in the LKB

Summary

Introduction

This chapter describes – from a mathematical perspective – the system of typed feature structures used in the ACQUILEX Lexical Knowledge Base (LKB). We concentrate on describing the type system the LKB takes as input, making explicit the necessary conditions on the type hierarchy and explaining how – mathematically – our system of constraints works. It is assumed that the reader is familiar with basic unification-based formalisms like PATR-II, as explained in Shieber (1986). It must also be said from the start that our approach draws heavily on the work on typed feature structures by Carpenter (1990, 1992).

The LKB works basically through unification on (typed) feature structures. Since most of the time we deal with typed feature structures (defined in section 10.2) we will normally drop the qualifier and talk about feature structures. When necessary, to make a distinction, we refer to structures in PATR-II and similar systems as untyped feature structures. Feature structures are defined over a (fixed) finite set of features FEAT and over a (fixed) type hierarchy 〈TYPE, ⊑〉. Given FEAT and 〈TYPE, ⊑〉 we can define T the collection of all feature structures over FEAT and 〈TYPE, ⊑〉. But we are interested in feature structures which are well-formed with respect to a set of constraints. To describe constraints and well-formedness of feature structures we specify a function C: TYPE → F, which corresponds to an association of a constraint feature structure C(t_i) to each type t_i in the type hierarchy TYPE.