A Logic with Measurable Spaces for Natural Language Semantics

We present a Logic with Measurable Spaces (LMS) and argue that it is suitable to represent the semantics of a number of natural language phenomena. LMS draws inspiration from several sources. It is decidable (like descriptive logics). It features Sigma spaces (like Martin-L¨of type-theory). It internalises the notion of the cardinality (in fact, here, measures) of spaces (see [6]) and ratios thereof, allowing to capture the notion of event probability. In addition to being a powerful system, it is also concise and has a precise semantics in terms of integrals. Thanks to all these qualities, we hope that LMS can play a role in the foundations of natural language semantics.