We present initial work on a theory of coordination and parallelism in Glue Semantics (GLUE; Dalrymple 1999, 2001). We will explore points of convergence and divergence between our approach to coordination and similar Categorial Grammar (CG) approaches. We also compare our approach to a previous GLUE approach to coordination (Kehler et al. 1995, 1999) and argue that our approach is superior on the grounds that it preserves a very strong notion of resource-sensitivity (Dalrymple et al. 1993). We conclude by discussing parallelism in connection with the Coordinate Structure Constraint (CSC; Ross 1967). The CSC is a putatively robust condition on extraction which has been argued to be a feature of the CG approach to coordination and of other related approaches. It is standardly assumed to have two parts, the Conjunct Constraint and the Element Constraint (Grosu 1973). The Conjunct Constraint is quite robust, but the Element Constraint has been challenged repeatedly, most recently by Kehler (2002), who argues that the CSC is not a syntactic condition, but rather follows from conditions on discourse coherence and parallelism. We discuss a constraint language on the structure of GLUE derivations, and show how Kehler’s theory of discourse cohesion can be related to parallelism in such derivations.

Linear Logic based Semantics for LTAG – and what it teaches us about LFG and LTAG – We review existing appoaches to semantics construction in LTAG (Lexicalised Tree Adjoining Grammar) based on the notion of derivation (tree)s. We argue that derivation structures in LTAG are not appropriate to guide semantic composition, due to a non-isomorphism, in LTAG, between the syntactic operation of adjunction on the one hand, and the semantic operations of complementation and modification, on the other. Linear Logic based “glue semantics”, as developed within the LFG framework (cf. Dalrymple (1999)), allows for flexible coupling of syntactic and semantic structure. We investigate application of glue semantics to LTAG syntax, using as underlying structure the derived tree, which is more appropriate for principle-based semantics construction. We show how Linear Logic based semantics construction helps to bridge the non-isomorphism between syntactic and semantic operations in LTAG. The glue approach captures non-tree local dependencies in control and modification structures, and extends to the treatment of scope ambiguity with quantified NPs and VP modifiers. Finally, glue semantics applies successfully to the adjunction-based analysis of long-distance dependencies in LTAG, which differs significantly from the f-structure based analysis in LFG. 1

In this paper we review existing appoaches to semantics construction in LTAG (Lexicalised Tree Adjoining Grammar) which are all based on the notion of derivation (tree)s. We argue that derivation structures in LTAG are not appropriate to guide semantic composition, due to a non-isomorphism, in LTAG, between the syntactic operation of adjunction on the one hand, and the semantic operations of complementation and modification, on the other. Linear Logic based "glue" semantics, by now the classical approach to semantics construction within the LFG framework (cf. Dalrymple (1999)) allows for flexible coupling of syntactic and semantic structure. We investigate application of "glue semantics" to LTAG syntax, using as underlying structure the derived tree, which is more appropriate for principle-based semantics construction. We show how linear logic semantics construction helps to bridge the nonisomorphism between syntactic and semantic operations in LTAG. The glue approach allows to capture non-tree local dependencies in control and modification structures, and extends to the treatment of scope ambiguity with quantified NPs and VP adverbials. Finally, glue semantics applies successfully to the adjunction-based analysis of long-distance dependencies in LTAG, which di#ers significantly from the f-structure based analysis in LFG. 1

this paper outlines how it can be applied to HPSG. As well as providing an alternative form of semantics for HPSG, we believe that the benefits of HPSG glue include the following: (1) simplification of the Semantics Principle (Pollard and Sag, 1994); (2) a simple and elegant treatment of modifier scope, including empirical phenomena like quantifier scope ambiguity, the interaction of scope with raising, and recursive modification; (3) an analysis of control that handles agreement between controlled subjects and their coarguments while allowing for a property denotation for the controlled clause (Chierchia, 1984a,b); (4) re-use of highly efficient techniques for semantic derivation already implemented for LFG, and which target problems of ambiguity management also addressed by Minimal Recursion Semantics (Copestake et al., 1995, 1999). Glue semantics embodies a notion of `interpretation as deduction' closely related to categorial grammar's `parsing as deduction'. Syntactic analysis of a sentence yields a set of glue premises, which essentially state how bits of lexical meaning attach to words and phrases. Deduction in (linear) logic then combines the premises to derive a conclusion that attaches a meaning to the sentence as a whole. The innovation in this paper is to sketch how glue premises can be obtained from HPSG analyses; the subsequent stage of linear logic deduction is the same as when premises are obtained from LFG analyses. The paper is organized as follows. Section 2 briefly reviews the way in which linear logic / glue deduction assembles sentence meanings given a set of lexical glue premises. Section 3 describes the adjustments to HPSG's feature geometry necessary for it to construct sets of glue premises. Section 4 show how these adjustments give rise to sema...