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An Alternate View on Strong Lexicalization in Tag

De Santo, Aniello, Alëna Aksënova, and Thomas Graf

Abstract TAGs were recently shown not to be closed under strong lexicalization but to be strongly lexicalizable by context-free tree grammars of rank 2. This paper presents an alternative lexicalization procedure that builds on an earlier generalization of TAGs to multi-dimensional trees. A previous theorem that every Tree Substitution grammar is strongly lexicalized by a corresponding TAG is lifted to higher dimensions to show that for every $d$-dimensional TAG there exists a $(d+1)$-dimensional TAG that strongly lexicalizes it. A similar lifting reveals that $d$-dimensional TAGs are not closed under strong lexicalization, so for arbitrary TAGs an increase in dimensionality is an unavoidable consequence of strong lexicalization.

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  author    = {De Santo, Aniello and Aks\"{e}nova, Al\"{e}na and Graf, Thomas},
  title     = {An Alternate View on Strong Lexicalization in TAG},
  year      = {2016},
  note      = {Slides of a talk given at the 12th International Workshop on Tree Adjoining Grammars and Related Formalisms, June 29 -- July 1, Düsseldorf, Germany}