Abstract
We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bargelli D., Lambek J. (2001). An algebraic approach to French sentence structure. In: de Groote P. et al. (eds). Logical aspects of computational linguistics. Springer LNAI 2099, Berlin Heidelberg New york, pp. 62–78
Buszkowski W. (2001). Lambek grammars based on pregroups. In: de Groote P. et al. (eds). Logical aspects of computational linguistics. Springer LNAI 2099, Berlin Heidelberg New york, pp. 95–109
Buszkowski W. (2002). Cut elimination for Lambek calculus of adjoints. In: Abrusci V.M. et al. (eds). New perspectives in logic and formal linguistics, proceedings of the 5th Roma Workshop. Bulzoni Editore, Rome, pp. 85–93
Casadio C. (2001). Non-commutative linear logic in linguistics. Grammars 4/3, 1–19
Casadio C. (2002) Logic for grammar. Bulzoni Editore, Rome
Casadio C., Lambek J. (2002). A tale of four grammars. Studia Logica 71, 315–329
Chomsky N. (1957). Syntactic structures. Mouton, The Hague
Chomsky N. (1981). Lectures on government and binding. Foris Publications, Dordrecht
Chomsky N. (1986). Barriers. MIT, Cambridge MA
Chomsky N. (1995). The minimalist program. MIT, Cambridge, MA
Dexter C. (1994). The second Inspector Morse omnibus. Pan Books, London
Gazdar G. (1981). Unbounded dependencies and coordinate structure. Linguistic Inquiry 12, 155–184
Gazdar G., Klein E., Pullam G., Sag I. (1985). Generalized phrase structure grammar. Harvard University Press, Cambridge, MA
Harris Z. (1966). A cyclic cancellation-automaton for sentence well-formedness. International Computation Centre Bulletin 5, 69–94
Harris Z. (1968). Mathematical structure of language. Interscience Publishers, New York
Kleene S.C. (1952). Introduction to metamathematics. Van Nostrand, New York
Lambek J. (1958). The mathematics of sentence structure. American Mathematical Monthly 65, 154–169
Lambek J. (1999). Type grammar revisited. In: Lamarche F. et al. (eds). Logical aspects of computational linguistics. Springer LNAI 1582, Berlin Heidelberg New york, pp. 1–27
Lambek, J. (2000). Pregroups: A new algebraic approach to sentence structure. In C. Martin-Vide, & G. Pǎun (Eds.), Recent topics in mathematical and computational linguistics. Bucharest: Editura Academici Române.
Lambek J. (2001). Type grammars as pregroups. Grammars 4, 21–39
Lambek J. (2004). A computational algebraic approach to English grammar. Syntax 7(2): 128–147
Lambek, J. Invisible endings of English adjectives and nouns. Linguistic Analysis, to appear in 2007.
Lambek, J. (2004). Should pregroup grammars be adorned with additional operations? LIRMM, Rapport de recherche 12949.
McCawley J.D. (1988). The syntactic phenomena of English. The University of Chicago Press, Chicago
Moortgat M. (1977). Categorial type logics. In: van Benthem J., ter Meulen A. (eds). Handbook of logic and language. Elsevier, Amsterdam, pp. 93–177
Peirce C.S. (1897). The logic of relatives. The Monist 7, 161–217
Pinker S. (1994). The language instinct. William Morrow and Company, New York
Preller, A. (2004). Pregroups meet constraints on transformations. Manuscript IRMM Montpellier.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lambek, J. From word to sentence: a pregroup analysis of the object pronoun who(m). J Log Lang Inf 16, 303–323 (2007). https://doi.org/10.1007/s10849-006-9035-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-006-9035-9