Building a shared world: mapping distributional to model-theoretic semantic spaces

In this paper, we introduce an approach to automatically map a standard distributional semantic space onto a set-theoretic model. We predict that there is a functional relationship between distributional information and vectorial concept representations in which dimensions are predicates and weights are generalised quantifiers. In order to test our prediction, we learn a model of such relationship over a publicly available dataset of feature norms annotated with natural language quantifiers. Our initial experimental results show that, at least for domain-specific data, we can indeed map between formalisms, and generate high-quality vector representations which encapsulate set overlap information. We further investigate the generation of natural language quantifiers from such vectors.