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.

We present BIS, a Bayesian Inference Semantics, for probabilistic reasoning in natural language. The current system is based on the framework of Bernardy et al. (2018), but departs from it in important respects. BIS makes use of Bayesian learning for inferring a hypothesis from premises. This involves estimating the probability of the hypothesis, given the data supplied by the premises of an argument. It uses a syntactic parser to generate typed syntactic structures that serve as input to a model generation system. Sentences are interpreted compositionally to probabilistic programs, and the corresponding truth values are estimated using sampling methods. BIS successfully deals with various probabilistic semantic phenomena, including frequency adverbs, generalised quantifiers, generics, and vague predicates. It performs well on a number of interesting probabilistic reasoning tasks. It also sustains most classically valid inferences (instantiation, de Morgan’s laws, etc.). To test BIS we have built an experimental test suite with examples of a range of probabilistic and classical inference patterns.

We propose a compositional Bayesian semantics that interprets declarative sentences in a natural language by assigning them probability conditions. These are conditional probabilities that estimate the likelihood that a competent speaker would endorse an assertion, given certain hypotheses. Our semantics is implemented in a functional programming language. It estimates the marginal probability of a sentence through Markov Chain Monte Carlo (MCMC) sampling of objects in vector space models satisfying specified hypotheses. We apply our semantics to examples with several predicates and generalised quantifiers, including higher-order quantifiers. It captures the vagueness of predication (both gradable and non-gradable), without positing a precise boundary for classifier application. We present a basic account of semantic learning based on our semantic system. We compare our proposal to other current theories of probabilistic semantics, and we show that it offers several important advantages over these accounts.