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Sortal Equivalence of Bare Grammars

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The Mathematics of Language (MOL 2009, MOL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6149))

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Abstract

We discuss a concept of structural equivalence between grammars in the framework of Keenan and Stabler’s bare grammars. The definition of syntactic sorts for a grammar L permits the introduction of a sort structure group Aut π (L). The automorphism group Aut(L) of L is found to be a group extension by Aut π (L). We develop then a concept of equivalence of grammars based on isomorphisms between the syntactic sort algebras. We study the implications of this equivalence with techniques from category theory: we invert the class of grammar homomorphisms that induce isomorphisms of sort algebras. The resulting category of fractions is found to be equivalent to a category of sortally reduced grammars.

The author would like to thank Hans-Martin Gärtner, Andreas Haida, Ed Keenan, Greg Kobele, Marcus Kracht, Jens Michaelis and Ed Stabler for discussions and support in various forms.

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Authors
  1. Thomas Holder
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Editors and Affiliations

  1. Department of Linguistics, University of Tuebingen, Wilhelmstrasse 19, 72074, Tuebingen, Germany

    Christian Ebert  & Gerhard Jäger  & 

  2. Faculty of Linguistics and Literary Studies, University of Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Jens Michaelis

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Holder, T. (2010). Sortal Equivalence of Bare Grammars. In: Ebert, C., Jäger, G., Michaelis, J. (eds) The Mathematics of Language. MOL MOL 2009 2007. Lecture Notes in Computer Science(), vol 6149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14322-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-14322-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14321-2

  • Online ISBN: 978-3-642-14322-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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