Probabilistic Type Theory and Natural Language Semantics

Type theory has played an important role in specifying the formal con- nection between syntactic structure and semantic interpretation within the history of formal semantics. In recent years rich type theories de- veloped for the semantics of programming languages have become in- fluential in the semantics of natural language. The use of probabilistic reasoning to model human learning and cognition has become an in- creasingly important part of cognitive science. In this paper we o ff er a probabilistic formulation of a rich type theory, Type Theory with Records (TTR), and we illustrate how this framework can be used to approach the problem of semantic learning. Our probabilistic version of TTR is intended to provide an interface between the cognitive process of classifying situations according to the types that they instantiate, and the compositional semantics of natural language.

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