Compositional Semantics of Coordination using Synchronous Tree Adjoining Grammar

In this paper, we propose a compositional semantics for DP coordination and VP coordination, using Synchronous Tree Adjoining Grammar (STAG). We take advantage of STAG’s capacity to provide an isomorphic derivation of semantic trees in parallel to syntactic ones, using substitution and adjoining in both syntax and semantics. In addition, we use unreduced λ-expressions in semantic elementary trees, as in Han (2007). This allows us to build the logical forms by applying λ-conversion and other operations defined on λexpressions to the semantic derived tree. DP meanings cannot be directly conjoined in an STAG approach that does not make use of unreduced λ-expressions in semantic trees as in Shieber (1990) and Nesson and Shieber (2006; 2007). In this approach, a quantified DP introduces an argument variable and a formula consisting of a quantifier, restriction and scope. The argument variables cannot be conjoined as conjunction is defined on formulas. Although the formula components can be conjoined in principle, it is not clear how the conjoined formulas can compose with the meaning coming from the rest of the sentence. In our analysis, we redefine the semantics of DPs as Generalized Quantifiers (GQ) (Barwise and Cooper, 1981), enabling the DP meanings to be directly conjoined. GQs can be conjoined through the application of the Generalized Conjunction Rule, and the conjoined GQs can compose with the meaning coming from the rest of the sentence through λ-conversion. Our approach is in contrast to previous works on DP coordination (Babko-Malaya, 2004) and VP coordination (Banik, 2004) that use featureunification-based TAG semantics (Kallmeyer and Romero, 2008). While the two accounts handle DP and VP coordination separately, they cannot together account for sentences with both DP and VP coordination, such as Every boy and every girl jumped and played, without adding new features. Furthermore, due to the recursive nature of coordination, an indefinite number of such features would potentially need to be added. We first present a new STAG approach to quantification and scope ambiguity in section 2, using GQs. We then extend the proposed GQ analysis to DP coordination in section 3 and VP coordination in section 4. It will also be shown how sentences with both DP and VP coordination can be handled under the proposed analysis.