Treating Coordination with Datalog Grammars

In previous work we studied a new type of DCGs, Datalog grammars, which are inspired on database theory. Their efficiency was shown to be better than that of their DCG counterparts under (terminating) OLDT-resolution. In this article we motivate a variant of Datalog grammars which allows us a meta-grammatical treatment of coordination. This treatment improves in some respects over previous work on coordination in logic grammars, although more research is needed for testing it in other respects

Context Update for Lambdas and Vectors

Vector models of language are based on the contextual aspects of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, the denotations of phrases, and their compositional properties. In the latter approach the denotation of a sentence determines its truth conditions and can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In this short paper, we develop a vector semantics for language based on the simply typed lambda calculus. Our semantics uses techniques familiar from the truth conditional tradition and is based on a form of dynamic interpretation inspired by Heim's context updates

From compositional to systematic semantics

We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is required to be "systematic" (that is, the meaning function cannot be arbitrary, but must belong to some class), it is possible to distinguish between compositional and non-compositional semantics. As a result, we believe that the paper clarifies the concept of compositionality and opens a possibility of making systematic formal comparisons of different systems of grammars.Comment: 11 pp. Latex.

The Grail theorem prover: Type theory for syntax and semantics

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available

Type-driven semantic interpretation and feature dependencies in R-LFG

Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As Dalrymple and her colleagues note, LFG's f-structure completeness and coherence constraints fall out as a by-product of the linear logic machinery they propose for semantic interpretation, thus making those f-structure mechanisms redundant. Given that linear logic machinery or something like it is independently needed for semantic interpretation, it seems reasonable to explore the extent to which it is capable of handling feature structure constraints as well. R-LFG represents the extreme position that all linguistically required feature structure dependencies can be captured by the resource-accounting machinery of a linear or similiar logic independently needed for semantic interpretation, making LFG's unification machinery redundant. The goal is to show that LFG linguistic analyses can be expressed as clearly and perspicuously using the smaller set of mechanisms of R-LFG as they can using the much larger set of unification-based mechanisms in LFG: if this is the case then we will have shown that positing these extra f-structure mechanisms is not linguistically warranted.Comment: 30 pages, to appear in the the ``Glue Language'' volume edited by Dalrymple, uses tree-dvips, ipa, epic, eepic, fullnam