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Algebraic Governance and Symmetry in Dependency Grammars

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Formal Grammar (FG 2015, FG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9804))

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Abstract

We propose a purely algebraic approach to governance structure in dependency grammars aiming to capture all linguistic dependencies (such as morphological, lexico-semantic, etc.) in monoidal patterns. This provides a clear perspective and allows us to define grammars declaratively through classical projective structures. Using algebraic concepts the model is going to suggest some symmetries among languages.

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Notes

  1. 1.

    There are other definitions of dependency structures, such as those encoding structure as a graph or through Robinson’s axioms, [2], but the above is more concise.

  2. 2.

    An ellipsis occurs when a locus is null but there is underneath a non-null locus; otherwise the locus is definitively null. A class of elliptic syntagmata is also useful, but in order to simplify things we are not using them except in the last example.

  3. 3.

    For the purposes of this article it may be assumed that there are no repeated syntactic functions at the same level. In work in progress we relax this condition but there is not space to present the details here, and they are not relevant to the contribution of the present article.

  4. 4.

    Agreements (dashed lines) are not dependencies (arrows), but loci can be used to describe them.

  5. 5.

    Recall that some of the \(\varphi _i\) and \(\varGamma _i\) can be trivial.

  6. 6.

    This also occurs in Swiss-German, [7].

  7. 7.

    Our analysis of Dutch dependencies uses a parallel arrangement of the functions \(\beta \) which shares distant similarities with [1], but there the framework was constituency grammars.

  8. 8.

    Using the Tesnèrian denomination, this constitutes defining the valence of each word.

  9. 9.

    A similar strategy can be found in Topological Dependency Grammar, [5].

References

  1. Bresnan, J., Kaplan, R.M., Peters, S., Zaenen, A.: Cross-serial dependencies in Dutch. In: Savitch, W.J., Bach, E., Marsh, W., Safran-Naveh, G. (eds.) The Formal Complexity of Natural Language, pp. 286–319. Springer, Netherlands (1987)

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  2. Debusmann, R.: An introduction to dependency grammar. Hausarbeit fur das Hauptseminar Dependenzgrammatik SoSe, pp. 1–16 (2000)

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  3. Debusmann, R., Duchier, D., Kruijff, G.J.M : Extensible dependency grammar: a new methodology. In: Proceedings of the COLING 2004 Workshop on Recent Advances in Dependency Grammar, pp. 70–76 (2004)

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  4. Debusmann, R., Kuhlmann, M.: Dependency grammar: classification and exploration. In: Crocker, M.W., Siekmann, J. (eds.) Resource-Adaptive Cognitive Processes, pp. 365–388. Springer, Heidelberg (2010)

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  5. Duchier, D., Debusmann, R.: Topological dependency trees: a constraint-based account of linear precedence. In: Proceedings of the 39th Annual Meeting on Association for Computational Linguistics, Association for Computational Linguistics, pp. 180–187 (2001)

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  6. Kuhlmann, M.: Mildly non-projective dependency grammar. Comput. Linguist. 39(2), 355–387 (2013)

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  7. Shieber, S.M.: Evidence against the context-freeness of natural language. In: Kulas, J., Fetzer, J.H., Rankin, T.L. (eds.) Philosophy, Language, and Artificial Intelligence. tudies in Cognitive Systems, vol. 2, pp. 79–89. Springer, Heidelberg (1987)

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Acknowledgements

Thanks to Formal Grammar reviewing for many suggestions to improve this paper, and to Glyn Morill and Oriol Valentín for encouragement, advice and support. All errors are my own.

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Carles Cardó

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  1. Carles Cardó
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Correspondence to Carles Cardó .

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Editors and Affiliations

  1. IRISA, University of Rennes 1 , Rennes, France

    Annie Foret

  2. Department of Computer Science, Universitat Politècnica de Catalunya , Barcelona, Spain

    Glyn Morrill

  3. Tilburg University , Tilburg, The Netherlands

    Reinhard Muskens

  4. Department of General Linguistics, Heinrich-Heine-University Düsseldorf , Düsseldorf, Germany

    Rainer Osswald

  5. INRIA Nancy, Villers-lès-Nancy, France

    Sylvain Pogodalla

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Cardó, C. (2016). Algebraic Governance and Symmetry in Dependency Grammars. In: Foret, A., Morrill, G., Muskens, R., Osswald, R., Pogodalla, S. (eds) Formal Grammar. FG FG 2015 2016. Lecture Notes in Computer Science(), vol 9804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53042-9_4

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  • DOI: https://doi.org/10.1007/978-3-662-53042-9_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53041-2

  • Online ISBN: 978-3-662-53042-9

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