Tuples, Discontinuity, and Gapping in Categorial Grammar

Tuples, Discontinuity, and Gapping in Categorial Grammar* Glyn Morrill t & Teresa Solias t tDepartament de Llenguatges i Sistemes Informgtics Universitat Polit~cnica de Catalunya Edifici F I B, Pau Gargallo, 5 08028 Barcelona e-maih morrill@lsi.upc.es tDepartamento de Filologfa Espafiola (Lingfiistica) Universidad de Valladolid Facultad de Filosoffa y Letras, Plaza de la Universidad, s/n 47001 Valladolid e-mail: solias@cpd.uva.es Abstract This paper solves some puzzles in the for- malisation of logic for discontinuity in cat- egorial grammar. A 'tuple' operation intro- duced in [Solias, 1992] is defined as a mode of prosodic combination which has associ- ated projection functions, and consequently can support a property of unique prosodic decomposability. Discontinuity operators are defined model-theoretically by a resid- uation scheme which is particularly arn- menable proof-theoretically. This enables a formulation which both improves on the logic for wrapping and infixing of [Moort- gat, 1988] which is only partial, and resolves some problems of determinacy of insertion point in the application of these proposals to in-sits binding phenomena. A discontin- uons product is also defined by the residu- ation scheme, enabling formulation of rules of both use and proof for a 'substring' prod- uct that would have been similarly doomed to partial logic. We show how the apparatus enables char- acterisation of discontinous functors such as particle verbs and phrasal idioms, and binding phenomena such as quantifier rais- ing and pied piping. We conclude by show- ing how the apparatus enables a simple cat- egorial analysis of (SVO) gapping using the discontinuity product and the wrapping op- erator. *The work by Glyn Morrill was for the most part car- ried out under the support of the Ministerio de Edu. caciJn V Ciencia, Madrid, in the form of visting scholar- ship grant SB90 P413308C. 1 Introduction In [Lambek, 1958] the suggestive recursive fractional categorial notations of [Ajdukiewicz, 1935] and [Bar- Hillel, 1953] were provided with a foundational set- ting in mathematical logic. This takes the form of a model theory interpreting category formulas in alge- braic structures. A Gentzen style sequent proof the- ory for which there is a Cut-elimination result means that a decision procedure is provided on the basis of sequent calculus. The category formulas are freely generated from atomic category formulas (e.g. N for referring nom- inals, S for sentences, CN for common nouns, ...) by binary operators \ ('under'), / ('over') and • ('product'). The interpretation is in semigroups, i.e. algebras (L, +) where + is a binary operation satisfying the associativity axiom sl + (s~ + s3) = (sl + s2) + s3. (In the non-associative formulation of [Lambek, 1961], this condition is withdrawn.) We may in particular consider the algebra obtained by taking the set V* of strings over a vocabulary V; then L is V* - {t} where t is the empty string. Each category formula A is interpreted as a subset D(A) of L. Given such a mapping for atomic category formu- las it is extended to the compound category formulas thus: D(A\B) = {sirs' ~ D(A),s' …

Content truncated to 500 words