Sortal equivalence of bare grammars

  • Authors:

  • Thomas Holder

  • Affiliations:

  • -

  • Venue:
  • MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
  • Year:
  • 2007

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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 Autπ(L). The automorphism group Aut(L) of L is found to be a group extension by Autπ(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.