Focus and Higher-Order Unification

Pulman has shown that Higher-Order Unifcat ion (HOU) can be used to model the interpretation of focus. In this paper, we extend the unification based approach to cases which are often seen as a test-bed for focus theory: utterances with multiple focus operators and second occurrence expressions. We then show that the resulting analysis favourably compares with two prominent theories of focus (namely, Rooth's Alternative Semantics and Krifka's Structured Meano ings theory) in that it correctly generates interpretations which these alternative theories cannot yield. Finally, we discuss the formal properties of the approach and argue that even though HOU need not terminate, for the class of unification-problems dealt with in this paper, HOU avoids this shortcoming and is in fact computationally tractable. 1 I n t r o d u c t i o n In this paper, we argue that Higher Order Unification (HOU) provides a linguistically adequate tool for modeling the semantics of focus. Building up on (Pulman, 1995), we develop a unificationbased analysis of focus which we show favourably compares with two prominent theories of focus, Rooth's Alternative Semantics and Krifka's Structured Meanings theory. For data which is generally viewed as a test-bed for focus theory (utterances with multiple focus operators and second occurrence expressions), we show that contrary to Rooth's and Krifka's theories, the HOU treatment yields a transparent analysis while avoiding underand over-generation. Focus is a much debated notion. In this paper, we assume a simplifed version of Jackendoff's definition: a f o cu s is the semantic value of a prosoditally prominent element. We take the identification of prosodically prominent elements as given. To set the stage for this paper, we will briefly review the folklore, i.e. the main issues of focus theory. It is commonly agreed that focus triggers the formation of an additional semantic value which we will call the Focus S e m a n t i c Va lue (FSV). The name and definition of the FSV varies from author to author: Jackendoff (Jackendoff, 1972) calls it the presuppositional set, Rooth (Rooth, 1992) the Alternative Sct and Krifka (Krifka, 1992) the Ground. In this paper, we assume a definition of the FSV which is in essence Rooth's Alternative set, that is, tile set of semantic objects obtained by making an appropriate substitution in the focus position. For instance, the FSV of (la) is defined as (lb), the set of properties of the form like-lug y where y is an individual (in what follows, focus is indica~ted using upper-case; we also follow Montague's convention that for any type % D~ is the set of objects of type r and wff~ is the set of wits of type r). (1) a. Jon only likes M A R Y b. l y c It is also usuMly agreed that certain linguistic elements a s s o c i a t e w i t h focus in that the meaning of the utterance containing these elements varies depending on the choice of focus. For instance in (2a-b), the focus operator only associates with focus so that the difference in focus between (2a) and (2b) induces a difference in meaning between the two utterances: in a world where aon introduced Paul to Mary and Sarah, and no other introduction takes place, (2a) is necessarily