Applicative Abstract Categorial Grammar

10 pages•Published: July 7, 2015

Abstract

We present the grammar/semantic formalism of Applicative Abstract
Categorial Grammar (AACG), based on the recent techniques from
functional programming: applicative functors, staged languages and
typed final language embeddings. AACG is a generalization of
Abstract Categorial Grammars (ACG), retaining the benefits of ACG as a
grammar formalism and making it possible and convenient to express a
variety of semantic theories.

We use the AACG formalism to uniformly formulate Potts' analyses of
expressives, the dynamic-logic account of anaphora, and the
continuation tower treatment of quantifier strength, quantifier
ambiguity and scope islands. Carrying out these analyses in ACG
required compromises and the ballooning of parsing complexity, or was
not possible at all. The AACG formalism brings modularity, which comes
from the compositionality of applicative functors, in contrast to
monads, and the extensibility of the typed final embedding. The
separately developed analyses of expressives and QNP are used as they
are to compute truth conditions of sentences with both these features.

AACG is implemented as a `semantic calculator', which is the ordinary
Haskell interpreter. The calculator lets us interactively write
grammar derivations in a linguist-readable form and see their yields,
inferred types and computed truth conditions. We easily extend
fragments with more lexical items and operators, and experiment with
different semantic-mapping assemblies. The mechanization lets a
semanticist test more and more complex examples, making empirical tests
of a semantic theory more extensive, organized and systematic.

Keyphrases: acg, monads, staging, syntax semantic interface

In: Makoto Kanazawa, Lawrence S. Moss and Valeria de Paiva (editors). NLCS'15. Third Workshop on Natural Language and Computer Science, vol 32, pages 29-38.

Links:	https://easychair.org/publications/paper/RPN
	https://doi.org/10.29007/s2m4