In LFG syntactic structure is represented in terms of two levels of syntactic description: c-structure and f-structure. Context-free PS rules with f-descriptions define the functional correspondence between c- and f-structure. Subcategorisation and long-distance dependencies are represented in f-structure, while the functional mapping between c- and f-structure accounts for properties like word order variation. LFG semantics is driven by linear logic based meaning construction from f-structure (Dalrymple 1999), and allows for flexible coupling of syntax and compositional semantics.

An LTAG grammar (Joshi and Shabes 1997) consists of a set of lexicalised elementary trees, which are composed by two operations: substitution and adjunction. The syntactic representation consists of the resulting constituent tree (derived tree), and the derivation tree, which records dependencies between elementary trees established by substitution and adjunction operations in parsing. LTAG semantics is traditionally based on the structure of derivation trees.

In our paper we review existing appoaches to semantics construction in LTAG (Shieber and Schabes(1990), Schabes and Shieber(1994), Kallmeyer and Joshi (1999)), 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 between the syntactic operations of adjunction and substitution – which determine the derivation structures - on the one hand, and the semantic operations of modification and complementation, on the other (see also Rambow et al (1995)).

We investigate the application of LL-based ''glue'' semantics construction to LTAG ¹ taking as underlying structure the derived tree, which is most appropriate for principle-based semantics construction. We show how linear logic semantics construction helps to bridge the non-isomorphism between syntactic and semantic operations in LTAG. The glue approach also allows to bridge non-tree local dependencies in control structures, which are otherwise problematic in LTAG. On a more general perspective, the exercise is instructive in that it elucidates the role that f-structure plays in LFG syntax and semantics, and helps clarify the relation between the two syntactic frameworks in terms of their similarities and differences.

We introduce LL-based semantics construction for LTAG starting with constructions involving tree-local dependencies. We label argument nodes in LTAG elementary trees with metavariables ¯ _1, ¯ ₂, etc. Lexical anchors are labelled with ­ metavariables. The metavariables are referred to in the glue part of meaning constructors. The meaning constructors of auxiliary (i.e. adjunction) trees which correspond to semantic complementation encode skeleton-type meanings, thereby bridging the non-isomorphism that proved problematic for semantics construction from derivation trees. For auxiliary trees that correspond to modifiers in semantics, both foot and root node are labelled with metavariables *. Finally, the anchor's variable ­ is projected to all tree nodes that are not marked by ¯ _i or * metavariables. Labelling of tree-internal nodes is crucial, e.g., for the analysis of VP modifying adverbs. The labelled trees look LFG-like, but do not introduce additional linguistic assumptions into LTAG, although tree internal labelling is largely equivalent to LFG's head projection chains. The metavariables are instantiated in parsing; the instantiated meaning constructors are assembled, and used to derive a meaning for the tree's root variable.

The analysis of VP modifying adverbs and control verb constructions both involve non-tree local dependencies, which leads to a refinement of LTAG tree representations to avoid indeterminacy in LL-based semantic composition. Tree labelling now encodes argument metavariables ¯ _1, ¯ ₂ as arguments of the lexical anchor ­ , for example (­ :¯ ₁) which comes close to LFG's functional description (­ SUBJ), ¯ ₁ being LTAG's equivalent of LFG's subject function. This encoding allows for successful analysis of VP modifiers. Following the analysis of control verbs in Ash(2001), glue semantics can now also bridge the missing control relation, which in LFG is encoded both in syntax and glue semantics. This provides an interesting comparison between tree-based analysis in LTAG, as opposed to f-structure based analysis in LFG, as well as between a syntactic+semantic (LFG+Glue) vs. a purely semantic (LTAG+Glue) account of functional control.

Finally, we propose a glue-based analysis of long-distance dependencies, which in LTAG are driven by tree adjunction. The tree labelling therefore crucially differs from LFG f-structures, which are defined via functional uncertainty. However, LTAGs analysis of long-distance dependencies is severely restricted by the formal power of the tree adjunction operation. It does not extend to languages with special word order properties, as for example Kashmiri, where wh-words end up in sentence-second position, preceded by a topic from the matrix clause (Rambow et al 1995) ... A case for (uncertainty in) f-structure.

In sum we argue (i) that derivations in LTAG are problematic for semantic composition, show (ii) that non-isomorphism between syntactic and semantic operations can be bridged by glue semantics, (iii) that LTAGs restriction to only ``talk about'' adjunction and substitution nodes leads to unsatisfactory indeterminacy, which (iv) can be avoided by explicitly recording local dependencies between head and arguments (i.e. those internal to elementary trees) at a level of representation which is appropriate for semantics construction, i.e. a projection from, or labelling of the derived tree. Finally, (v) glue semantics bridges the missing non-tree local control relation in LTAG, and is applied to the adjunction-based analysis of long-distance dependencies, which is, however, formally and empirically more restricted than LFG's analysis in terms of functional uncertainty.

1 Hepple(1999) sketches LL-based semantics for D-Trees, to overcome problems faced by categorial semantics in the analysis of quantification. It is not yet clear whether his D-Trees analysis extends to problematic constructions in LTAG, like VP modifiers, control or coordination.

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