Information Flow in Pregroup Models of Natural Language

This paper is about pregroup models of natural languages, and how they relate to the explicitly categorical use of pregroups in Compositional Distributional Semantics and Natural Language Processing. These categorical interpretations make certain assumptions about the nature of natural languages that, when stated formally, may be seen to impose strong restrictions on pregroup grammars for natural languages. We formalize this as a hypothesis about the form that pregroup models of natural languages must take, and demonstrate by an artificial language example that these restrictions are not imposed by the pregroup axioms themselves. We compare and contrast the artificial language examples with natural languages (using Welsh, a language where the 'noun' type cannot be taken as primitive, as an illustrative example). The hypothesis is simply that there must exist a causal connection, or information flow, between the words of a sentence in a language whose purpose is to communicate information. This is not necessarily the case with formal languages that are simply generated by a series of 'meaning-free' rules. This imposes restrictions on the types of pregroup grammars that we expect to find in natural languages; we formalize this in algebraic, categorical, and graphical terms. We take some preliminary steps in providing conditions that ensure pregroup models satisfy these conjectured properties, and discuss the more general forms this hypothesis may take.