Abstract
Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore, a semantical interpretation is independent of the order of the associated logic. Lexical entries are read as expressions in a two sorted predicate logic with ∈ and functional symbols. The parsing of a sentence defines a substitution that combines the expressions associated to the individual words. The resulting variable free formula is the translation of the sentence. It can be computed in time proportional to the parsing structure. Non-logical axioms are associated to certain words (relative pronouns, indefinite article, comparative determiners). Sample sentences are used to derive the characterizing formula of the DRS corresponding to the translation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Béchet, D., Forêt, A., & Tellier, I. (2004). Learnability of pregroup grammars. In proc. international conference on grammatical inference (pp. 65–76). Berlin Heidelberg New York: Springer, LNAI 3262.
Buszkowski, W. (2001). L. grammars based on pregroups. In P. de Groote et al. (Eds.), Logical aspects of computational linguistics. Berlin Heidelberg New York: Springer, LNAI 2099.
Degeilh S., Preller A. (2005). Efficiency of pregroups and the French noun phrase. Journal of Language, Logic and Information 14(4): 423–444
Earley, J. (1970). An efficient context-free parsing algorithm. Communications of the AMC, 13(2), 94–102.
Fenstad, J. E., Halvorsen, P.-K., Langholm, T., & van Benthem, J. (1978). Situations, language and logic, studies in linguistics and philisophy. Dordrecht: Reidel.
Kamp, H., & Reyle U. (1993). From discourse to logic, introduction to modeltheoretic semantics of natural language. Dordrecht: Kluwer Academic Publishers.
Lambek J. (1958). The mathematics of sentence structure. American Mathematical Monthly 65: 154–170
Lambek J., Scott P. (1986). Introduction to higher order categorical logic. Cambridge, Cambridge University Press
Lambek, J. (1999). Type grammar revisited. In A. Lecomte et al. (Eds.), Logical aspects of computational linguistics(pp. 1–27.) Berlin Heidelberg New York: Springer, LNAI 1582.
Lambek J. (2004). A computational algebraic approach to English grammar. Syntax 7(2): 128–147
Moortgat, M., & Oehrle, R. (2004). Pregroups and type-logical grammar: Searching for convergence. In P. Scott, C. Casadio, & R. A. Seeley (Eds.), Language and grammar studies in mathematical linguistics and natural language. Stanford: CSLI Publications.
Pollard, C. (2004). Higher-Order categorical grammars. In Proc. of categorial grammars 04, Montpellier, France.
Preller, A., & Lambek, J. (2005). Free compact 2-categories, mathematical structures for computer sciences. Cambridge: Cambridge University Press.
Preller, A. (2005). Category theoretical semantics for pregroup grammars. In Blache, & Stabler (Eds.), LACL 2005, LNAI 3492 (pp. 254–270).
van Benthem J. (2005). Guards, bounds and generalized semantics. journal of Language, Logic and Information 14: 263–279
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Preller, A. Toward discourse representation via pregroup grammars. JoLLI 16, 173–194 (2007). https://doi.org/10.1007/s10849-006-9033-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-006-9033-y