Linguistics 726 Mathematical Linguistics (really: mathematics for and in linguistics)


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A sampling of papers on trees or including definitions of trees.


From BHP: miscellaneous.


1. Blackburn, Patrick, Gardent, Claire , and Meyer-Viol, Wilfried. 1993. Talking about trees. In Proceedings of the 6th Conference of the European Chapter of the Association for Computational Linguistics (EACL- 93), 21 - 29. Utrecht, the Netherlands. 



2.  Rogers, James, and Vijay-Shanker, K. 1992. Reasoning with descriptions of trees. In ACL-92, 72--80.


3. Muskens, Reinhard. 2001. Talking about trees and truth-conditions. Journal of Logic, Language, and Information 10:417-455.


4. Frank, Robert, and Vijay-Shanker, K. 2001. Primitive C-Command. Syntax 4:164-204.


5. Frank, Robert, Vijay-Shanker, K., and Chen, John. 1996. Dominance, Precedence and C-Command in Description-based Parsing. Paper presented at XII Congreso de Lenguajes Naturales y Lenguajes Formales, Barcelona, Spain. Reprint.




From Chris Potts


I've attached in PDF a small compilation of tree definitions in linguistics and logic.  [See separate PDF file potts-tree-defs.pdf ]

No collection of trees in linguistics would be complete without a mention of McCawley 1968:

  McCawley, James D. 1968.  Concerning the base component of a transformational grammar.  Foundations of Language 4(1):55-88.  Reprinted in McCawley (1976), 35-58.
  McCawley, James D. 1976.  Meaning and Grammar. New York: Academic Press.

This paper is probably the first in linguistics to axiomatize trees.  I provide his definition in the attached compilation.

Geoffrey Sampson argues for multiple mothers here:

  Sampson, Geoffrey. 1975.  The single mother condition.  Journal of Linguistics 11(1):1-11.

***During my guest lectures, we'll be discussing some work that Patrick Blackburn and his colleagues have done on the logics for trees and the tree-like foundation for AVM logics.  Here are some especially relevant papers:

  Blackburn, Patrick. 1993.  Modal logic and attribute value structures.  In Maarten de Rijke, ed., Diamonds and Defaults,  Synthese Language Library, 19-65. Dordrecht: Kluwer.

  Blackburn, Patrick and Claire Gardent. 1995.  A specification language for Lexical Functional Grammars.  In Proceedings of  the Seventh Conference of the European Chapter of the  Association for Computational Linguistics, 39-44. San  Francisco: Morgan Kaufmann.

  Blackburn, Patrick, Claire Gardent, and Wilfried Meyer-Viol.  1993.  Talking about trees.  In Proceedings of the Sixth Conference of the European Chapter of the Association for  Computational Linguistics, 21-29. San Francisco:  Morgan Kaufmann.

  Blackburn, Patrick and Wilfried Meyer-Viol. 1997.  Modal logic and model-theoretic syntax.  In Maarten de Rijke, ed.,  Advances in Intensional Logic, 29-60. Dordrecht: Kluwer.

When last I checked, all of these papers were downloadable from Patrick's website.

 Rogers, James. to appear.  Syntactic structures as multi-dimensional trees.  Journal of Language and Computation Special issue of the journal including papers from the ESSLLI  2000 workshop on trees.

He defines n-dimensional trees for any finite n, and he proves a range of rather surprising complexity results.