Generalized relations in linguistics and cognition

Categorical compositional models of natural language exploit grammatical structure to calculate the meaning of phrases and sentences from the meanings of individual words. More recently, similar compositional techniques have been applied to conceptual space models of cognition. Compact closed categories, particularly the category of finite dimensional vector spaces, have been the most common setting for categorical compositional models. When addressing a new problem domain, such as conceptual space models of meaning, a key problem is finding a compact closed category that captures the features of interest. We propose categories of generalized relations as a source of new, practical models for cognition and NLP. We demonstrate using detailed examples that phenomena such as fuzziness, metrics, convexity, semantic ambiguity can all be described by relational models. Crucially, by exploiting a technical framework described in previous work of the authors, we also show how the above-mentioned phenomena can be combined into a single model, providing a flexible family of new categories for categorical compositional modelling.