Skip to main content
SpringerLink
Log in

Discontinuity in categorial grammar

  • Published:
Linguistics and Philosophy Aims and scope Submit manuscript

Abstract

Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.

Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bach, Emmon: 1979, ‘Control in Montague Grammar’,Linguistic Inquiry 10, 515–531.

    Google Scholar 

  • Bach, Emmon: 1980, ‘In Defense of Passive’,Linguistics and Philosophy 3, 297–341.

    Google Scholar 

  • Bach, Emmon: 1981, ‘Discontinuous Constituents in Generalized Categorial Grammars’,Proceedings of the 11th Annual Meeting of the North Eastern Linguistics Society, New York, pp. 1–12.

  • Bach, Emmon: 1984, ‘Some Generalizations of Categorial Grammars’, in Fred Landman and Frank Veltman (eds.),Varieties of Formal Semantics, Foris, Dordrecht, pp. 1–23.

    Google Scholar 

  • Barry, Guy, Mark Hepple, Neil Leslie, and Glyn Morrill: 1991, ‘Proof Figures and Structural Operators for Categorial Grammar’, inProceedings of the Fifth Conference of the European Chapter of the Association for Computational Linguistics, Berlin.

  • van Benthem, Johan: 1990 ‘Categorial Grammar Meets Unification’, Report No. CSLI-90-142, Center for the Study of Language and Information, Stanford University.

  • van Benthem, Johan: 1991,Language in Action: Categories, Lambdas and Dynamic Logic, Studies in Logic and the Foundations of Mathematics Volume 130, North-Holland, Amsterdam.

  • Buszkowski, Wojciech: 1986, ‘Completeness Results for Lambek Syntactic Calculus’,Zeitschrift für mathematische Logik und Grundlagen der Mathematik,32, 13–28.

    Google Scholar 

  • Carpenter, Bob: 1992, ‘Categorial Grammars, Lexical Rules and the English Predicative’, in Robert Levine (ed.)Formal Grammar: Theory and Implementation, Oxford University Press, Oxford, pp. 168–242.

    Google Scholar 

  • Dowty, David R.: 1979, ‘Dative ‘Movement’ and Thomason's Extensions of Montague Grammar’, in S. Davis and M. Methun (eds.),Linguistics, Philosophy and Montague Grammar, University of Texas Press, pp. 153–222.

  • Dowty, David R.: 1982, ‘Grammatical Relations and Montague Grammar’, in P. Jacobson anf G. K. Pullum (eds.),The Nature of Syntactic Representation, D. Reidel, Dordrecht, pp. 79–130.

    Google Scholar 

  • Dunn, Michael J.: 1991, ‘Gaggle Theory: An Abstraction of Galois Connections and Residuation, with Applications to Negation, Implication, and Various Logical Operators’, in J. van Eijck (ed.),Logics in AI, Proceedings of JELIA '90, Lecture Notes in Artificial Intelligence478, Springer-Verlag, pp. 31–51.

  • Emms, Martin: 1990 ‘Polymorphic Quantifiers’, in Martin Stokhof and Leen Torenvliet (eds.),Proceedings of the Seventh Amsterdam Colloquium, Institute for Language, Logic and Information, Universiteit van Amsterdam, pp. 139–163, also in Guy Barry and Glyn Morrill (eds.),Studies in Categorial Grammar, Edinburgh Working Papers in Cognitive Science, Volume 5, Centre for Cognitive Science, University of Edinburgh, pp. 65–111.

  • Fitch, Frederic Brenton: 1952,Symbolic Logic, An Introduction, The Ronald Press Company, New York.

    Google Scholar 

  • Gabbay, D.: 1991,Labelled Deductive Systems, to appear, Oxford University Press, Oxford.

    Google Scholar 

  • Gazdar, Gerald, Ewan Klein, Geoffrey Pullum, and Ivan Sag: 1985,Generalised Phrase Structure Grammar, Basil Blackwell, Oxford.

    Google Scholar 

  • Girard, Jean-Yves: 1989, ‘Towards a Geometry of Interaction’,Contemporary Mathematics Volume 92, American Mathematical Society, pp. 69–108.

  • Hindley, J. Roger and Jonathan P. Seldin: 1986,Introduction to Combinators and λ-Calculus, London Mathematical Society Student Texts 1, Cambridge University Press, Cambridge.

    Google Scholar 

  • Jacobson, Pauline: 1987, ‘Phrase Structure, Grammatical Relations, and Discontinuous Constituents’, in G. Huck and A. Ojeda (eds.),Syntax and Semantics 20: Discontinuous Constituency, Academic Press, New York, pp. 27–69.

    Google Scholar 

  • Jacobson, Pauline: 1992, ‘Flexible Categorial Grammars: Questions and Prospects’, in Robert Levine (ed.),Formal Grammar: Theory and Implementation, Oxford University Press, Oxford, pp. 168–242.

    Google Scholar 

  • Kandulski, Maciej: 1988, ‘The Non-Associative Lambek Calculus’, in W. Buszkowski, W. Marciszewski and J. van Benthem (eds.),Categorial Grammar, Linguistic and Literary Studies in Eastern Europe 25, John Benjamins, Amsterdam, pp. 141–151.

    Google Scholar 

  • Lambek, J.: 1958, ‘The Mathematics of Sentence Structure’,American Mathematical Monthly 65, 154–170.

    Google Scholar 

  • Lambek, J.: 1961, ‘On the Calculus of Syntactic Types’, in R. Jakobson (ed.),Structure of Language and its Mathematical Aspects, Proceedings of the Symposia in Applied MathematicsXII, American Mathematical Society, pp. 166–178.

  • Lambek, J.: 1988, ‘Categorial and Categorical Grammars’, in Richard T. Oehrle, Emmon Bach and Deidre Wheeler (eds.),Categorial Grammars and Natural Language Structures, Studies in Linguistics and Philosophy Volume 32, D. Reidel, Dordrecht, pp. 297–317.

    Google Scholar 

  • Montague, Richard: 1973, ‘The Proper Treatment of Quantification in Ordinary English’, in J. Hintikka, J. M. E. Moravcsik and P. Suppes (eds.),Approaches to Natural Language, D. Reidel, Dordrecht, reprinted in R. H. Thomason (ed.): 1974,Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven, pp. 247–270.

    Google Scholar 

  • Moortgat, Michael: 1988,Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus, Foris, Dordrecht.

    Google Scholar 

  • Moortgat, Michael: 1990, ‘The Quantification Calculus: Questions of Axiomatisation’, in Deliverable R1.2.A of DYANA Dynamic Interpretation of Natural Language, ESPRIT Basic Research Action BR3175.

  • Moortgat, Michael: 1991, ‘Generalised Quantification and Discontinuous Type Constructors’, to appear in Sijtsma and Van Horck (eds.),Proceedings of the Tilburg Symposium on Discontinuous Constituency, Walter de Gruyter, Berlin.

  • Moortgat, Michael: 1992, ‘Labelled Deductive Systems for Categorial Theorem Proving’, Working Paper OTS-WP-CL-92-002, Onderzoeksinstituut voor Taal en Spraak, Rijksuniversiteit Utrecht, also inProceedings of the Eighth Amsterdam Colloquium, Institute for Language, Logic and Information, Universiteit van Amsterdam.

  • Moortgat, Michael and Glyn Morrill: 1991, ‘Heads and Phrases: Type Calculus for Dependency and Constituency’, to appear inJournal of Language, Logic and Information.

  • Morrill, Glyn: 1990a, ‘Intensionality and Boundedness’,Linguistics and Philosophy 13, 699–726.

    Google Scholar 

  • Morrill, Glyn: 1990b, ‘Grammar and Logical Types’, in Martin Stokhof and Leen Torenvliet (eds.),Proceedings of the Seventh Amsterdam Colloquium, Institute for Language, Logic and Information, Universiteit van Amsterdam, pp. 429–450, also in Guy Barry and Glyn Morrill (eds.),Studies in Categorial Grammar, Edinburgh Working Papers in Cognitive Science Volume 5, Centre for Cognitive Science, University of Edinburgh, pp. 127–148.

  • Morrill, Glyn: 1990c, ‘Rules and Derivations: Binding Phenomena and Coordination in Categorial Logic’, Deliverable R1.2.D of DYANA Dynamic Interpretation of Natural Language, ESPRIT Basic Research Action BR3175.

  • Morrill, Glyn: 1992a,Type Logical Grammar, Report de Recerca LSI-92-5-R, Department de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, and Working Paper OTS-WP-CL-92-002, Onderzoeksinstituut voor Taal en Spraak, Rijksuniversiteit Utrecht, monograph to appear, Kluwer, Dordrecht.

  • Morrill, Glyn: 1992b, ‘Categorial Formalisation of Relativisation: Pied Piping, Islands and Extraction Sites’, Report de recerca LSI-92-23-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya.

  • Morrill, Glyn: 1994a, ‘Clausal Proofs and Discontinuity’, to appear in theBulletin of the Interest Group in Propositional and Predicate Logic.

  • Morrill, Glyn: 1994b, ‘Structural Facilitation and Structural Inhibition’, Report de recerca LSI-94-26-R, Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya.

  • Morrill, Glyn, Neil Leslie, Mark Hepple, and Guy Barry: 1990, ‘Categorial Deductions and Structural Operations’, in Guy Barry and Glyn Morrill (eds.),Studies in Categorial Grammar, Edinburgh Working Papers in Cognitive Science, Volume 5, Centre for Cognitive Science, University of Edinburgh, 1–21.

  • Morrill, Glyn and Teresa Solias: 1993, ‘Tuples, Discontinuity and Gapping’, inProceedings of European Chapter of the Association for Computational Linguistics, Utrecht, pp. 287–297.

  • Oehrle, Richard T. and Shi Zhang: 1989, ‘Lambek Calculus and Preposing of Embedded Subjects’,Chicago Linguistic Society 25, Chicago.

  • Pollard, Carl J.: 1984,Generalized Phrase Structure Grammar, Head Grammars and Natural Languages, Stanford University, Stanford.

    Google Scholar 

  • Pollard, Carl J.: 1988, ‘Categorial Grammar and Phrase Structure Grammar: An Excursion on the Syntax-Semantics Frontier’, in Richard T. Oehrle, Emmon Bach and Deidre Wheeler (eds.),Categorial Grammars and Natural Language Structures, Studies in Linguistics and Philosophy, Volume 32, D. Reidel, Dordrecht, pp. 391–415.

    Google Scholar 

  • Pollard, Carl and Ivan A. Sag: 1987,Information-Based Approach to Syntax and Semantics, CSLI Lecture Notes 13, Center for the Study of Language and Information, Stanford.

    Google Scholar 

  • Pollard, Carl and Ivan A. Sag: 1994,Head-Driven Phrase Structure Grammar, Studies in Contemporary Linguistics, University of Chicago Press, Chicago.

    Google Scholar 

  • Prawitz, D.: 1965,Natural Deduction: A Proof-Theoretical Study, Almqvist and Wiksell, Uppsala.

    Google Scholar 

  • Reinhart, Tanya: 1983, ‘Coreference and Bound Anaphora: A Restatement of the Anaphora Questions’,Linguistics and Philosophy 6, 47–88.

    Google Scholar 

  • Ross, J. R.: 1967,Constraints on Variables in Syntax, Ph.D. dissertation, Massachusetts Institute of Technology, Indiana University Linguistics Club.

  • Solias, Teresa: 1992,Gramáticas Categoriales, Coordinación Generalizada y Elisión, doctorate thesis, Departamento de Lingüística, Lógica, Lenguas Modernas y Fílosofia de la Ciencia, Universidad Autónoma de Madrid.

  • Steedman, Mark: 1985, ‘Dependency and Coordination in the Grammar of Dutch and English’,Language 61(3), 523–568.

    Google Scholar 

  • Szabolcsi, Anna: 1987, ‘Bound Variables in Syntax (Are There Any?)’, in Jeroen Groenendijk, Dick de Jongh and Martin J.B. Stokhof (eds.),Proceedings of the Sixth Amsterdam Colloquium, Institute for Language, Logic and Information, University of Amsterdam, pp. 331–351, revised version in Renate Bartsch et al. (eds): 1989, Foris, Dordrecht.

  • Szabolcsi, Anna: 1992, ‘Combinatory Grammar and Projection from the Lexicon’, in Ivan A. Sag and Anna Szabolcsi (eds.),Lexical Matters, CSLI Lecture Notes No. 24, Center for the Study of Language and Information, Stanford, pp. 241–268.

    Google Scholar 

  • Venema, Yde: 1993, ‘Tree Models and (Labelled) Categorial Grammar’,Proceedings of the Ninth Amsterdam Colloquium.

  • Versmissen, Koen: 1991, ‘Discontinuous Type Constructors in Categorial Grammar’, ms. Onderzoeksinstituut voor Taal en Spraak, Rijksuniversiteit Utrecht.

  • Wasow, Thomas, Ivan A. Sag and Geoffrey Nunberg: 1983, ‘Idioms: An Interim Report’, in Shiro Hattori and Kazuko Inoue (eds.),Proceedings of the XIIIth International Congress of Linguists, Tokyo: CIPL, pp. 102–115.

    Google Scholar 

  • Weir, D. J., K. Vijay-Shanker and A. K. Joshi: 1986, ‘The Relationship between Tree Adjoining Grammars and Head Grammars’, inProceedings of the 24th Meeting of the Association for Computational Linguistics.

  • Zielonka, Wojciech: 1981, ‘Axiomatizability of Ajdukiewicz—Lambek Calculus by Means of Cancellation Schemes’,Zeitschrift für mathematische Logik und Grundlagen der Mathematik 27, 215–224.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028, Barcelona, Spain

    Glyn Morrill

Authors
  1. Glyn Morrill
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper in its current form has benefitted from extensive reviewing forLinguistics and Philosophy. I thank the reviewers and the editor for their attention.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morrill, G. Discontinuity in categorial grammar. Linguist Philos 18, 175–219 (1995). https://doi.org/10.1007/BF00985216

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00985216

Keywords

Search

Navigation