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A Logic with Measurable Spaces for Natural Language Semantics

Conference contribution
Authors Jean-Philippe Bernardy
Rasmus Blanck
Aleksandre Maskharashvili
Published in TbiLLC 2019: Thirteenth International Tbilisi Symposium on Language, Logic and Computation,16-20 September 2019.
Publication year 2019
Published at Department of Philosophy, Linguistics and Theory of Science
Language en
Links events.illc.uva.nl/Tbilisi/Tbilisi2...
Keywords Logic, Language, Computation, Probability, Measure, Types, Spaces, Decidability, Semantics, Inference
Subject categories Linguistics, Computational linguistics, Language Technology (Computational Linguistics), Mathematical logic, Logic

Abstract

We present a Logic with Measurable Spaces (LMS) and argue that it is suitable to represent the semantics of many natural language phenomena. LMS draws inspiration from several sources. It is decidable (like description logics). It features Sigma spaces (like Martin-Löf type-theory). It internalises the notion of the cardinality (in fact, here, measures) of spaces and ratios thereof, allowing to capture the notion of event probability. In addition, LMS is arguably a concise system. Thanks to all these qualities, we hope that LMS can play a role in the foundations of natural language semantics.

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