Towards Compositional Distributional Discourse Analysis

In the last couple of decades, the traditional symbolic approach to AI and cognitive science -- which aims at characterising human intelligence in terms of abstract logical processes -- has been challenged by so-called connectionist AI: the study of the human brain as a complex network of basic processing units [18]. When it comes to human language, the same divide manifests itself as the opposition between two principles, which in turn induce two distinct approaches to Natural Language Processing (NLP). On one hand Frege's principle of compositionality asserts that the meaning of a complex expression is a function of its sub-expressions, and the way in which they are composed -- distributionality on the other hand can be summed up in Firth's maxim "You shall know a word by the company it keeps". Once implemented in terms of concrete algorithms we have expert systems driven by formal logical rules on one end, artificial neural networks and machine learning on the other. Categorical Compositional Distributional (DisCoCat) models, first introduced in [4], aim at getting the best of both worlds: the string diagrams notation borrowed from category theory allows to manipulate the grammatical reductions as linear maps, and compute graphically the semantics of a sentence as the composition of the vectors which we obtain from the distributional semantics of its constituent words. In this paper, we introduce basic anaphoric discourses as mid-level representations between natural language discourse on one end -- formalised in terms of basic discourse representation structures (DRS) [2]; and knowledge queries over the Semantic Web on the other -- given by basic graph patterns in the Resource Description Framework (RDF) [19]. We construct discourses as formal diagrams of real-valued matrices and we then use these diagrams to give abstract reformulations of NLP problems: probabilistic anaphora resolution and question answering.