A Probabilistic Rich Type Theory for Semantic Interpretation

We propose a probabilistic type theory in which a situation s is judged to be of a type T with probability p. In addition to basic and functional types it includes, inter alia, record types and a notion of typing based on them. The type system is intensional in that types of situations are not reduced to sets of situations. We specify the fragment of a compositional semantics in which truth conditions are replaced by probability conditions. The type system is the interface between classifying situations in perception and computing the semantic interpretations of phrases in natural language.