Towards a semantics for distributional representations

Distributional representations have recently been proposed as a general-purpose representation of natural language meaning, to replace logical form. There is, however, one important difference between logical and distributional representations: Logical languages have a clear semantics, while distributional representations do not. In this paper, we propose a semantics for distributional representations that links points in vector space to mental concepts. We extend this framework to a joint semantics of logic and distributions by linking intensions of logical expressions to mental concepts.