Focus and Higher-Order Unification

Focus and Higher-Order Unification Claire Gardent Computational Linguistics Universitgt des Saarlandes, D 66041 Saarbr/icken claire~coli, uni- sb. de Michael Kohlhase Computer Science Universitgt des Saarlandes, D-66041 Saarbrficken kohlhase(~cs, uni-sb, de Abstract 2 Focus theory Pulman has shown that Higher-Order Unifcation (HOU) can be used to model the interpretation of focus. In this pa- per, we extend the unification based ap- proach 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 Se- mantics and Krifka's Structured Meano ings theory) in that it correctly gener- ates interpretations which these alter- native 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 Introduction In this paper, we argue that Higher Order Uni- fication (HOU) provides a linguistically adequate tool for modeling the semantics of focus. Building up on (Pulman, 1995), we develop a unification- based analysis of focus which we show favourably compares with two prominent theories of focus, Rooth's Alternative Semantics and Krifka's Struc- tured Meanings theory. For data which is gener- ally viewed as a test-bed for focus theory (utter- ances with multiple focus operators and second occurrence expressions), we show that contrary to Rooth's and Krifka's theories, the HOU treat- ment yields a transparent analysis while avoiding under- and over-generation. Focus is a much debated notion. In this paper, we assume a simplifed version of Jackendoff's defini- tion: a focus is the semantic value of a prosodi- tally prominent element. We take the identifica- tion 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 fo- cus theory. It is commonly agreed that focus triggers the formation of an additional seman- tic value which we will call the Focus Seman- tic Value (FSV). The name and definition of the FSV varies from author to author: Jackend- off (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 ap- propriate 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 con- vention 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 MARY b. lyc It is also usuMly agreed that certain linguis- tic elements associate with focus …

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