Abstract
Pregroup grammars are a context-free grammar formalism introduced as a simplification of Lambek calculus. This formalism is interesting for several reasons: the syntactical properties of words are specified by a set of types like the other type-based grammar formalisms ; as a logical model, compositionality is easy ; a polytime parsing algorithm exists.
However, this formalism is not completely lexicalized because each pregroup grammar is based on the free pregroup built from a set of primitive types together with a partial order, and this order is not lexical information. In fact, only the pregroup grammars that are based on primitive types with an order that is equality can be seen as fully lexicalized.
We show here how we can transform, using a morphism on types, a particular pregroup grammar into another pregroup grammar that uses the equality as the order on primitive types. This transformation is at most quadratic in size (linear for a fixed set of primitive types), it preserves the parse structures of sentences and the number of types assigned to a word.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lambek, J.: Type grammars revisited. In: Lecomte, A., Perrier, G., Lamarche, F. (eds.) LACL 1997. LNCS (LNAI), vol. 1582, pp. 22–24. Springer, Heidelberg (1999)
Lambek, J.: The mathematics of sentence structure. American Mathematical Monthly 65, 154–170 (1958)
Casadio, C., Lambek, J.: An algebraic analysis of clitic pronouns in italian. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)
Bargelli, D., Lambek, J.: An algebraic approach to french sentence structure. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)
Lambek, J.: Type grammar meets german word order. Theoretical Linguistics 26, 19–30 (2000)
Lambek, J., Preller, A.: An algebraic approach to the german noun phrase. Linguistic Analysis 31, 3–4 (2003)
Cardinal, K.: An algebraic study of Japanese grammar. McGill University, Montreal (2002)
Lambek, J.: Mathematics and the mind. In: Abrusci, V., Casadio, C. (eds.) New Perspectives in Logic and Formal Linguisitics. In: Proceedings Vth ROMA Workshop, Bulzoni Editore (2001)
Buszkowski, W.: Lambek grammars based on pregroups. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Béchet, D., Foret, A. (2007). Fully Lexicalized Pregroup Grammars . In: Leivant, D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2007. Lecture Notes in Computer Science, vol 4576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73445-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-73445-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73443-7
Online ISBN: 978-3-540-73445-1
eBook Packages: Computer ScienceComputer Science (R0)