Developments in Sheaf-Theoretic Models of Natural Language Ambiguities
Kin Ian Lo Mehrnoosh Sadrzadeh Shane Mansfield
Sheaves are mathematical objects consisting of a base which constitutes a
topological space and the data associated with each open set thereof, e.g.
continuous functions defined on the open sets. Sheaves have originally been
used in algebraic topology and logic. Recently, they have also modelled events
such as physical experiments and natural language disambiguation processes. We
extend the latter models from lexical ambiguities to discourse ambiguities
arising from anaphora. To begin, we calculated a new measure of contextuality
for a dataset of basic anaphoric discourses, resulting in a higher proportion
of contextual models--82.9%--compared to previous work which only yielded 3.17%
contextual models. Then, we show how an extension of the natural language
processing challenge, known as the Winograd Schema, which involves anaphoric
ambiguities can be modelled on the Bell-CHSH scenario with a contextual
fraction of 0.096.