If we are to take lexical semantics seriously – that is, to have a theory that can model the meanings of words, including all their subtle connotations – then we cannot hope to write down all the details by hand. In fact, Mollica and Piantadosi (2019) estimate that the vast majority of the information required to learn a language is lexical semantics (around 96%). Data-driven techniques are necessary to move from an abstract semantic theory to a fleshed-out model of a real language. Furthermore, an explicit computational model does more than just allow us to test the theory – as we will see, using probabilistic techniques can provide new insights on old problems.

I will begin this chapter with a discussion of what we need from a theory of lexical semantics, both in terms of how meaning can be formally represented, and also in terms of how those representations can be learnt. In §3.2, I will then discuss several challenging phenomena (vagueness, polysemy, and context dependence), which probabilistic models have been developed to deal with. Tying together this discussion, in §3.3 I will spell out a view of lexical semantics in terms of probabilistic truth-conditional functions. I will then expand on this view in two ways. In §3.4, I will introduce Bernoulli Fields, which deal with some subtleties in how probabilities can be introduced toa truth-conditional model, and which give a more accurate account of vagueness. Then, in §3.5, I will discuss pragmatic reasoning with a probabilistic truth-conditional model, giving a refinement on previous work.