Open System Categorical Quantum Semantics in Natural Language Processing

Authors Robin Piedeleu, Dimitri Kartsaklis, Bob Coecke, Mehrnoosh Sadrzadeh

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Robin Piedeleu
Dimitri Kartsaklis
Bob Coecke
Mehrnoosh Sadrzadeh

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Robin Piedeleu, Dimitri Kartsaklis, Bob Coecke, and Mehrnoosh Sadrzadeh. Open System Categorical Quantum Semantics in Natural Language Processing. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 270-289, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure to compute the meaning of a sentence, given its grammatical structure within a Lambek pregroup and a vectorial representation of the meaning of its parts. Moreover, just like CQM allows for varying the model in which we interpret quantum axioms, one can also vary the model in which we interpret word meaning. In this paper we show that further developments in categorical quantum mechanics are relevant to natural language processing too. Firstly, Selinger's CPM-construction allows for explicitly taking into account lexical ambiguity and distinguishing between the two inherently different notions of homonymy and polysemy. In terms of the model in which we interpret word meaning, this means a passage from the vector space model to density matrices. Despite this change of model, standard empirical methods for comparing meanings can be easily adopted, which we demonstrate by a small-scale experiment on real-world data. Secondly, commutative classical structures as well as their non-commutative counterparts that arise in the image of the CPM-construction allow for encoding relative pronouns, verbs and adjectives, and finally, iteration of the CPM-construction, something that has no counterpart in the quantum realm, enables one to accommodate both entailment and ambiguity.
  • category theory
  • density matrices
  • distributional models
  • semantics


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  1. Samson Abramsky and Bob Coecke. A categorical semantics of quantum protocols. In 19th Annual IEEE Symposium on Logic in Computer Science, pages 415-425, 2004. Google Scholar
  2. Esma Balkır. Using density matrices in a compositional distributional model of meaning. Master’s thesis, University of Oxford, 2014. Google Scholar
  3. William Blacoe, Elham Kashefi, and Mirella Lapata. A quantum-theoretic approach to distributional semantics. In Proceedings of NACL 2013, pages 847-857. Association for Computational Linguistics, June 2013. Google Scholar
  4. A. Carboni and R.F.C. Walters. Cartesian Bicategories I. Journal of Pure and Applied Algebra, 49, 1987. Google Scholar
  5. B. Coecke and K. Martin. A partial order on classical and quantum states. In B. Coecke, editor, New Structures for Physics, Lecture Notes in Physics, pages 593-683. Springer, 2011. Google Scholar
  6. B. Coecke, D. Pavlovic, and J. Vicary. A New Description of Orthogonal Bases. Mathematical Structures in Computer Science, 1, 2008. Google Scholar
  7. B. Coecke, M. Sadrzadeh, and S. Clark. Mathematical Foundations for a Compositional Distributional Model of Meaning. Lambek Festschrift. Linguistic Analysis, 36:345-384, 2010. Google Scholar
  8. Bob Coecke, Chris Heunen, and Aleks Kissinger. Categories of quantum and classical channels. arXiv preprint arXiv:1305.3821, 2013. Google Scholar
  9. Bob Coecke and Robert W Spekkens. Picturing classical and quantum Bayesian inference. Synthese, 186(3):651-696, 2012. Google Scholar
  10. E. Grefenstette and M. Sadrzadeh. Experimental support for a categorical compositional distributional model of meaning. In Proceedings of the EMNLP 2011, 2011. Google Scholar
  11. Z. Harris. Mathematical Structures of Language. Wiley, 1968. Google Scholar
  12. D. Kartsaklis, M. Sadrzadeh, S. Pulman, and B. Coecke. Reasoning about meaning in natural language with compact closed categories and Frobenius algebras. arXiv preprint arXiv:1401.5980, 2014. Google Scholar
  13. Dimitri Kartsaklis and Mehrnoosh Sadrzadeh. Prior disambiguation of word tensors for constructing sentence vectors. In Proceedings of EMNLP 2013, pages 1590-1601, 2013. Google Scholar
  14. G. M. Kelly and M. L. Laplaza. Coherence for compact closed categories. Journal of Pure and Applied Algebra, 19:193-213, 1980. Google Scholar
  15. J. Lambek. From Word to Sentence. Polimetrica, Milan, 2008. Google Scholar
  16. Joachim Lambek. The mathematics of sentence structure. American mathematical monthly, pages 154-170, 1958. Google Scholar
  17. A. Preller and M. Sadrzadeh. Bell states and negative sentences in the distributed model of meaning. In P. Selinger B. Coecke, P. Panangaden, editor, Electronic Notes in Theoretical Computer Science, Proceedings of the 6th QPL Workshop on Quantum Physics and Logic. University of Oxford, 2010. Google Scholar
  18. Anne Preller and Joachim Lambek. Free compact 2-categories. Mathematical Structures in Computer Science, 17(02):309-340, 2007. Google Scholar
  19. M. Sadrzadeh, S. Clark, and B. Coecke. The Frobenius anatomy of word meanings I: subject and object relative pronouns. Journal of Logic and Computation, Advance Access, October 2013. Google Scholar
  20. H. Schütze. Automatic Word Sense Discrimination. Computational Linguistics, 24:97-123, 1998. Google Scholar
  21. Peter Selinger. Dagger compact closed categories and completely positive maps. Electronic Notes in Theoretical Computer Science, 170:139-163, 2007. Google Scholar
  22. Peter Selinger. A survey of graphical languages for monoidal categories. In Bob Coecke, editor, New structures for physics, pages 289-355. Springer, 2011. Google Scholar
  23. Peter D Turney and Patrick Pantel. From frequency to meaning: Vector space models of semantics. Journal of artificial intelligence research, 37(1):141-188, 2010. Google Scholar