Expressing generalizations in unification-based grammar formalisms

This paper shows how higher levels of generalization can be introduced into unification grammars by exploiting methods for typing grammatical objects. We discuss the strategy of using global declarations to limit possible linguistic structures, and sketch a few unusual aspects of our typechecking algorithm. We also describe the sort system we use in our semantic representation language and illustrate the expressive power gained by being able to state global constraints over these sorts. Finally, we briefly illustrate the sort system by applying it to some agreement phenomena and to problems of adjunct resolution. 1 I n t r o d u c t i o n Since Kay's seminal work (Kay 1979), the utility of unification as a general tool in computational linguistics has gained widespread recognition. One major point on which the methodology of unification grammars differs radically from that assumed by linguistic theories lies in the way they deal with generalizations that hold over the domain of description. In unification-based theories, such generalizations are typically implicit, or extremely limited in their import. The reasons for this are easy to pinpoint. First, in such theories one has to be explicit about the feature structures that the grammar manipulates, and these structures have to be described more or less directly. In PATR-II for example (Shieber et al 1983) the only means of expressing a generalization is via the notion of template, a structure which merely represents recurring information--i.e, information that *The work reported here was carried out ae part of ESPRIT project P393 ACORD. A longer version of this paper can be found in Calder et a! (1988a). recurs in different lexical items, combination rules, lexical rules or other templates. A second reason why unification-based theories do not lend themselves easily to the expression of general statements is that there is no explicit quantification in unification formalisms. In fact, every statement in these formalisms represents a simple existential constraint, never a universal generalization. The work reported here is an a t tempt to introduce higher levels of organization into unification grammars. The notions we employ to do this come from sorted logics and from strong data typing in programming language theory. We will show that the typing of grammatical objects offers a way of stating structural constraints on, or equivalently universal properties of, the objects that constitute the grammar. The grammatical framework in which these ideas have been implemented is Uaificatioa Categorial Grammar (UCG) and its semantic representation language InL, both developed as part of the ESPRIT-funded project ACORD. Introductions to UCG and InL can be found in Calder et al (1988b) and Zeevat (1988). For present purposes it is sufficient to note that UCG uses a sorted logic which requires being able to express complex constraints over clusters of features. While there is no real distinction between this technique and that of data typing mentioned above, we will nevertheless continue to use the term typing only to refer to constraints on the global s tructure of an object and reserve the term sort to refer to constraints that hold of a variable in InL. In the following sections, we will first discuss our strategy of using global declarations to limit possible linguistic structures. We will briefly describe some of the type declarations currently implemented in UCG and discuss the unusual aspects of our type-checking algorithm. We will also infor-