Developing conceptual space semantics for compositional distributional models of meaning
The compositional distributional model of meaning (Coecke et al., 2010) models the meaning of sentences using a category such as pregroups to model the grammar of the sentences and another category with the same compact closed structure to model the meanings of the individual words. In practice, word meanings are often modelled using finite-dimensional vector spaces, built via word co-occurrence in text corpora. The conceptual spaces approach to semantics (Gärdenfors, 2014) views word meanings as inhabiting regions of a conceptual space, with carefully chosen dimensions. This representation has some similarities but also key differences with the compositional distributional model of meaning. The project would examine a few key conceptual spaces such as 'colour', 'taste', or 'shape', for example, and investigate how these can be incorporated within the compositional distributional model of meaning. This might be undertaken by giving a category-theoretic formalisation of these spaces, and identifying a suitable grammatical structure to implement composition, or alternatively, by analysing the behaviour of nouns, adjectives, and verbs within conceptual spaces, and fitting these to the pregroup grammar.
Prerequisites: category theory
Coecke, B., M. Sadrzadeh, and S. Clark. "Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift." Linguistic Analysis 36 (2010): 345-384.
Gärdenfors, Peter. The geometry of meaning: Semantics based on conceptual spaces. MIT Press, 2014.