Entailment Relations on Distributions

John van de Wetering
(Radboud University)

In this paper we give an overview of partial orders on the space of probability distributions that carry a notion of information content and serve as a generalisation of the Bayesian order given in (Coecke and Martin, 2011). We investigate what constraints are necessary in order to get a unique notion of information content. These partial orders can be used to give an ordering on words in vector space models of natural language meaning relating to the contexts in which words are used, which is useful for a notion of entailment and word disambiguation. The construction used also points towards a way to create orderings on the space of density operators which allow a more fine-grained study of entailment. The partial orders in this paper are directed complete and form domains in the sense of domain theory.

In Dimitrios Kartsaklis, Martha Lewis and Laura Rimell: Proceedings of the 2016 Workshop on Semantic Spaces at the Intersection of NLP, Physics and Cognitive Science (SLPCS 2016), Glasgow, Scotland, 11th June 2016, Electronic Proceedings in Theoretical Computer Science 221, pp. 58–66.
Published: 2nd August 2016.

ArXived at: http://dx.doi.org/10.4204/EPTCS.221.7 bibtex PDF
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