Agreement Modalities

Recently, several extensions to the Lambek calculus have been proposed that incorporate important aspects of the expressivity offered by feature structures as used in constraint-based grammars. In this paper we focus on a specific extension using unary modal operators to express feature information. We compare this to a constraint-based approach, like categorial unification grammar, and an extension of the Lambek calculus that uses layering of a categorial logic over a feature logic. We illustrate the approach with a simple example of agreement relations between adjectives and nouns in Dutch. In the first section we highlight a number of aspects of feature structures, their logic and their use as descriptive devices in theories of grammar. In the second section we present the formal details of a multimodal type-logical grammar and extensions to categorial grammars that include means to express some aspects of feature structures. In the last section we illustrate their use. 1 Feature St..