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From quantum foundations via natural language meaning via string diagrams.
by
Bob Coecke
Oxford University
Earlier work on an entirely diagrammatic formulation of quantum theory, which is soon to appear in the form of a textbook [CK], has somewhat surprisingly guided us towards providing an answer for the following question: how do we produce the meaning of a sentence given that we understand the meaning of its words? The correspondence between these seemingly far apart areas was established in terms of string diagrams [CSC, C], and more recently, also internal Frobenius algebras and completely positive maps have started to play a key role in both areas. This work has practical applications in the area of Natural Language Processing. The fact that meaning in natural language, depending on the subject domain, encompasses discussions within any scientific discipline, we obtain a template for theories such as animal behaviour, social interaction, and many others.
[CK] B. Coecke and A. Kissinger (2014) Picturing Quantum Processes. Cambridge UP.
[CSC] B. Coecke, M. Sadrzadeh and S. Clark (2010) Mathematical foundations for a compositional distributional model of meaning. Linguistic Analysis - Lambek festschrift. arXiv:1003.4394
[C] B. Coecke (2012) The logic of quantum mechanics - Take II. arXiv:1204.3458
Date received: December 9, 2014
Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-48.