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On the Mild Context-Sensitivity of k-Tree Wrapping Grammar

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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

Tree Wrapping Grammar (TWG) has been proposed in the context of formalizing the syntactic inventory of Role and Reference Grammar (RRG). It is close to Tree Adjoining Grammar (TAG) while capturing predicate-argument dependencies in a more appropriate way and being able to deal with discontinuous constituents in a more general way. This paper is concerned with the formal properties of TWG. More particularly, it considers k-TWG, a constrained form of TWG. We show that for every k-TWG, a simple Context-Free Tree Grammar (CFTG) of rank k can be constructed, which is in turn equivalent to a well-nested Linear Context-Free Rewriting System (LCFRS) of fan-out \(k+1\). This shows that, when formalizing a grammar theory such as RRG, which is based on thorough and broad empirical research, we obtain a grammar formalism that is mildly context-sensitive.

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Notes

  1. 1.

    We assume that fresh variables are used each time a new variable is needed.

  2. 2.

    Note that the fact that we can construct an equivalent well-nested LCFRS for a k-TWG does not mean that k-TWG (for some fixed k) cannot deal with ill-nested dependencies. The structures described by the LCFRS do not correspond to the dependency structures obtained from TWG derivations. The latter are determined only by the fillings of substitution slots.

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Author information

Authors and Affiliations

  1. Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

    Laura Kallmeyer

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  1. Laura Kallmeyer
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Correspondence to Laura Kallmeyer .

Editor information

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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Kallmeyer, L. (2016). On the Mild Context-Sensitivity of k-Tree Wrapping Grammar. 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_5

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  • DOI: https://doi.org/10.1007/978-3-662-53042-9_5

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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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