Applicative Abstract Categorial Grammars

We present the grammar/semantic formalism of Applicative Abstract Categorial Grammars (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 with the accompanying 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.