Advertisement
Published in:
2010 | OriginalPaper | Chapter
Sortal Equivalence of Bare Grammars
Author : Thomas Holder
Published in: The Mathematics of Language
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.