Functional Identity and Resource-Sensitivity in Control

Glue semantics provides a semantics for Lexical Functional Grammar (LFG) that is expressed using linear logic and provides an interpretation for the f(unctional)-structure level of syntactic representation, connecting it to the level of s(emantic)-structure in LFG's parallel projection architecture. Due to its use of linear logic for meaning assembly, Glue is resource-sensitive: semantic resources contributed by lexical entries and resulting f-structures must each be used in a successful proof exactly once. In this paper, I will examine the tension between a resource-sensitive semantics which interprets f-structures and structure-sharing in f-structures as expressed by functional control resulting from lexical functional identity equations. The empirical phenomenon I concentrate on is equi, also known as obligatory control. Although at first blush it seems that structure-sharing poses a serious problem for Glue semantics, I will show that this is not so. In fact, this tension leads to a very restrictive theory, and the analysis I present here solves several long-standing problems in the semantics of equi, by exploiting LFG's grammatical architecture.

In this paper I will:
1. Give a Glue semantics for equi.
2. Show how the analysis can yield either a propositional or property denotation for the clausal complement of an equi verb. This flexibility arises naturally from the architecture of the theory.
3. Adopt the property theory of equi complements, which has been argued for independently by Chierchia (1984).
4. Counter previous objections to the property theory from anaphoric binding and typological data by exploiting LFG's architecture.
5. Argue that a previous solution to the structure-sharing/resource-sensitivity problem (Kehler et al., 1999) can only yield a propositional denotation. The Kehler et al. proposal is rejected for empirical and theoretical reasons.
6. Show several empirical predictions of the analysis.