A framework for Distributional Formal Semantics

Formal semantics and distributional semantics offer complementary strengths in capturing the meaning of natural language. As such, a considerable amount of research has sought to unify them, either by augmenting formal semantic systems with a distributional component, or by defining a formal system on top of distributed representations. Arriving at such a unified framework has, however, proven extremely challenging. One reason for this is that formal and distributional semantics operate on a fundamentally different `representational currency': formal semantics defines meaning in terms of models of the world, whereas distributional semantics defines meaning in terms of linguistic co-occurrence. Here, we pursue an alternative approach by deriving a vector space model that defines meaning in a distributed manner relative to formal models of the world. We will show that the resulting Distributional Formal Semantics offers probabilistic distributed representations that are also inherently compositional, and that naturally capture quantification and entailment. We moreover show that, when used as part of a neural network model, these representations allow for capturing incremental meaning construction and probabilistic inferencing. This framework thus lays the groundwork for an integrated distributional and formal approach to meaning.