David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 7 (4):461-497 (1998)
There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable.
|Keywords||Group theory parsing generation diagrams|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Rui P. Chaves (2008). Linearization-Based Word-Part Ellipsis. Linguistics and Philosophy 31 (3):261-307.
Patrick Simonetta (1998). Equivalence Elementaire Et Decidabilite Pour Des Structures du Type Groupe Agissant Sur Un Groupe Abelien. Journal of Symbolic Logic 63 (4):1255-1285.
Richard Moot & Mario Piazza (2001). Linguistic Applications of First Order Intuitionistic Linear Logic. Journal of Logic, Language and Information 10 (2):211-232.
Wojciech Zielonka (1990). Linear Axiomatics of Commutative Product-Free Lambek Calculus. Studia Logica 49 (4):515 - 522.
Anders Søgaard & Martin Lange (2009). Polyadic Dynamic Logics for Hpsg Parsing. Journal of Logic, Language and Information 18 (2):159-198.
Added to index2009-01-28
Total downloads25 ( #65,711 of 1,096,504 )
Recent downloads (6 months)1 ( #238,630 of 1,096,504 )
How can I increase my downloads?