Abstract
In the framework of labelled proof nets the task of parsing in categorial grammar can be reduced to the problem of first-order matching under theory. Here we shall show how to use the same method of labelled proof nets to reduce the task of generating to the problem of higher-order matching.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
V. Danos and L. Regnier. The structure of multiplicatives. Archive for mathematical logic, (28):181–203, 1989.
Gilles Dowek. Third order matching is decidable. In 7th Annual IEEE Symposium of Logic in Computer Science, pages 2–10, 1992.
Dov Gabbay. Labelled Deductive Systems. Oxford University Press, 1996.
Jean Gallier and Wayne Snyder. Designing unification procedures using transformations: a survey. In Workshop Logic For Computer Science. MSRI Berkeley, 1989.
Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50(1):1–102, 1987.
W. Goldfard. The undecibility of the second-order unification problem. Theoretical Computer Science, 13(2):225–230, 1981.
G. Huet. Constrained Resolution: A Complete Method for Higher-Order Logic. PhD thesis, Case Western Reserve University, 1972.
G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1(1):27–57, 1975.
J. Lambek. The mathematics of sentence structure. American Mathematical Monthly, (65): 154–170, 1958.
Jordi Levy. Linear second-order unification. Rewriting Techniques and Applications, 1996.
Xavier Lloré and Glyn Morrill. Difference lists and difference bags for logic programming of categorial deduction. In Proceedings of the Sociedad Espanola para el Procesamiento del Lenguaje Natural, pages 115–129, 1995.
Michael Moortgat. Labelled deductive systems for categorial theorem proving. In Proceedings Eight Amsterdam Colloquium, pages 403–424, Amsterdam, 1992. Institute of Language, Logic and Information, Universiteit van Amsterdam.
Glyn Morrill. Type Logical Grammar: Categorial Logic of Signs. Kluwer Academic Publishers, 1994.
Glyn Morrill. Clausal proofs and discontinuity. Bulletin of the Interest Group in Pure and Applied Logics, 3(2–3):403–427, 1995.
Glyn Morrill. Higher-order linear logic programming of categorial deduction. In Proceedings ACL, pages 133–140, 1995.
Glyn Morrill. Memoisation of categorial proof nets: parallelism in categorial processing. In Michele Abrusci and Claudia Casadio, editors, Proof and Linguistic Categories: Proceedings 1996 Roma Workshop, pages 157–169. Università di Bologna, 1996. To appear in S. Manandhar, W. Nutt and G. Lopez (eds.), Springer-Verlag.
F. Pereira and D. Warren. Parsing as deduction. In Proceedings ACL, pages 132–144, 1983.
Dirk Roorda. Resource Logics: Proof-theoretical Investigations. PhD thesis, Universiteit van Amsterdam, 1991.
Wayne Snyder and Jean Gallier. Higher-order unification revisited: Complete sets of transformations. Journal of Symbolic Computation, (8): 101–140, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Merenciano, J.M., Morrill, G. (1997). Generation as deduction on labelled proof nets. In: Retoré, C. (eds) Logical Aspects of Computational Linguistics. LACL 1996. Lecture Notes in Computer Science, vol 1328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052164
Download citation
DOI: https://doi.org/10.1007/BFb0052164
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63700-4
Online ISBN: 978-3-540-69631-5
eBook Packages: Springer Book Archive