In this paper, we present a Bayesian approach to natural language semantics. Our main focus is on the inference task in an environment where judgments require probabilistic reasoning. We treat nouns, verbs, adjectives, etc. as unary predicates, and we model them as boxes in a bounded domain. We apply Bayesian learning to satisfy constraints expressed as premises. In this way we construct a model, by specifying boxes for the predicates. The probability of the hypothesis (the conclusion) is evaluated against the model that incorporates the premises as constraints.