Summary: Coordination in Categorial Grammar

[Ash Asudeh]

Dear All,

A couple of weeks ago I posted a question about how Categorial Grammar
does n-ary coordination as in "Kim slept, dreamt and laughed." and "Kim,
Sandy and Robin saw an ostrich.", etc.

There was sufficient interest for a brief summary.

John Beavers and Roger Levy both made suggestions that turned out to
have basically been made in the CG literature, but in an a
perhaps understated manner. The CG literature discusses binary
coordination for the most part.

John suggested a generalization of the binary coordination in Steedman
1985. This is done in Steedman 1989 and 1990. These papers break up the
conjunction rule into a forward rule and a backward rule. The forward rule
basically looks for a coordinator and a following category and adorns the
category with a feature. The backword rule takes this coordination-marked
category and combines it with other categories that are like the
coordination-marked category save for the coordination mark. Steedman
doesn't really discuss using these rules for n-ary coordination, but it's
possible to work out how it might go. Steedman 2000 moves back to the "X
conj X" style rule.

Roger suggested some kind of category adornment in the standard
coordinator type. I think his specific proposal was (X$\X/X) (I may be
mistaken). The use of the $-convention from Steedman's recent work won't
work however, because it abbreviates a functor into the category it
adorns. But, in his book on Type Logical Grammar, Morrill 1994 uses a kind
of Kleene plus notation like (X+\X/X). I unfortunately don't have the book
here, but Glyn said in personal communication that he handles the
semantics of the coordinator in terms of multisets. Steedman handles the
semantics in terms of the phi function, but I am unsure about how the
specifics of the function would work in n-ary coordination.

Thanks to John Beavers, Roger Levy, Glyn Morrill, and Mark Steedman for
their replies to my message and further discussion.

What was behind the question was a paper written by Dick Crouch and me for
the LFG02 proceedings on coordination in Glue Semantics (available at
www.stanford.edu/~asudeh). What we came up with is related to the CG
approaches. However, it solves the n-ary coordination problem by using
non-linear lambda expressions in the meaning language. A non-linear lamba
expression is one that has more than one occurrence of the lambda bound
variable in it (e.g. \x.P(x,x)). Such lambda expressions are allowed
freely in the meaning language of Glue, but not in the proof terms, since
we assume linear logic as our proof logic. If the last three sentences
made no sense, I apologize; I just wanted to put them in for people who
might be interested.

Anyway, the *linguistic* point of using the non-linear lambdas for
coordination is that we end up with a recursive treatment of coordination
that can handle any number of conjuncts in an n-ary fashion and use one
actual overtly-realized coordinator that has the normal boolean semantics.
This will distribute through the resulting non-linear function in the
required manner.

References follow below.

Best,
Ash

@InProceedings{asudeh;crouch02,
  author = 	 {Ash Asudeh and Richard Crouch},
  title = 	 {Coordination and parallelism in {Glue Semantics}:
Integrating discourse cohesion and the {Element Constraint}},
  booktitle = 	 {Proceedings of the {LFG02} Conference},
  crossref =	 {butt;king02}
}

@Proceedings{butt;king02,
  title = 	 {Proceedings of the {LFG02} conference},
  year = 	 2002,
  editor =	 {Miriam Butt and Tracy Holloway King},
  address =	 {Stanford, CA},
  publisher =	 {CSLI Publications},
}

@Book{morrill94,
  author =	 {Glyn Morrill},
  title = 	 {{Type Logical Grammar}},
  publisher = 	 {Kluwer},
  year = 	 1994,
  address =	 {Dordrecht},
}

@InCollection{steedman89,
  author = 	 {Mark Steedman},
  title = 	 {Constituency and coordination in a combinatory grammar},
  booktitle = 	 {Alternative Conceptions of Phrase Structure},
  crossref =	 {baltin;kroch89},
  pages =	 {201--231},
}

@Book{baltin;kroch89,
  editor =	 {Mark Baltin and Anthony Kroch},
  title = 	 {Alternative Conceptions of Phrase Structure},
  publisher = 	 {University of Chicago Press},
  year = 	 1989,
  address =	 {Chicago},
}

@Article{steedman90,
  author = 	 {Mark Steedman},
  title = 	 {Gapping as constituent coordination},
  journal = 	 {Linguistics and Philosophy},
  year = 	 1990,
  volume =	 13,
  number =	 2,
  pages =	 {207--263},
}

@Book{steedman00,
  author =	 {Mark Steedman},
  title = 	 {The Syntactic Process},
  address =      {Cambridge, MA},
  publisher = 	 {MIT Press},
  year = 	 2000
}