Sets, heads, and spreading in LFG

Lexical Functional Grammar (LFG) uses abstract syntactic representation (f-structures) that tend to provide less hierarchical structure for certain constructions than those employed in other formal frameworks. This produces some good results, such as a very straightforward account of feature-sharing between phrases and their heads, but also certain difficulties, especially in cases where the semantic interpretation seems to be determined by the hierarchical c-structure rather than the flatter f-structure. These are unproblematic for all other major generative frameworks, but have been troublesome for standard versions of LFG. Here I will consider two such cases: scoping adjectival modification in noun phrases; and Romance 'complex' (or 'restructuring') predicates. Problems with the semantic interpretation of these constructions were first discussed by Andrews (1983) and Alsina (1997), respectively, and by others subsequently. Both constructions exhibit the problem of apparent concentricity, and a fully satisfactory and accepted LFG solution has not yet been found. My proposal is to use the hybrid objects and distribution convention of Dalrymple and Kaplan (2000), but with singleton rather than multi-member sets, along with a facility to stipulatively suppress distribution in individual constructions. This provides an analysis which explains scope-determination and helps with certain other problems, with far less change to the theory than in previous attempts such as Andrews and Manning (1993, 1999).