CLASP
The Centre for Linguistic Theory and Studies in Probability

A Logic with Measurable Spaces for Natural Language Semantics

Joint work withRasmus BlanckAleksandre Maskharashvili

The ability of humans to reason under uncertainty has reflectionswithin natural language where we find various lexico-syntacticconstructions which allow us to express uncertain information.Moreover, we are able draw conclusions - make inferences underuncertainty. To give an adequate account to this crucial aspect of natural language, it has been long argued for employing probabilistic tools in defining semantics of natural language. In this abstract we address this issue by proposing a Logic with Measurable Spaces (LMS). We argue that LMS is suitable to represent the semantics of a number of important natural language phenomena. LMS draws inspiration from several sources. It is aims at being decidable (like descriptive logics). It features Sigma spaces (like Martin-Löf type-theory). It internalises the notion of the cardinality (in fact, here, measures) of spaces and ratiosthereof, allowing to capture the notion of event probability.