Probabilistic compositional semantics, purely

Julian Grove, Jean-Philippe Bernardy

Abstract: We provide a general framework for the integration of formal semantics with probabilistic reasoning. This framework is conservative, in the sense that it relies only on typed λ -calculus and is thus compatible with logical systems already in use. The framework is also presented modularly, in that it regards probabilistic effects (i.e., sampling and marginalization) as side effects, using continuations. We show how our framework may be used to build probabilistic programs compositionally within typed λ -calculus and then illustrate its use on two applications: semantic learning and pragmatic inference within the Rational Speech Act framework.