Linguistics and Philosophy

, Volume 40, Issue 2, pp 119–163 | Cite as

Grammar logicised: relativisation

  • Glyn MorrillEmail author
Open Access
Original Research


Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.


Islands Parasitic gaps Type logical categorial grammar Relativisation Structural facilitation Structural inhibition 


  1. Ades A.E., Steedman M.J. (1982) On the order of words. Linguistics and Philosophy, 4: 517–558CrossRefGoogle Scholar
  2. Ajdukiewicz, K. (1935). Die syntaktische Konnexität. Studia Philosphica,1, 1–27, 1935. (Translated in Polish logic: 1920–1939, pp. 207–231, by S. McCall, Ed., 1967, Oxford: Oxford University Press.)Google Scholar
  3. Andreoli J.M. (1992) Logic programming with focusing in linear logic. Journal of Logic and Computation 2(3): 297–347CrossRefGoogle Scholar
  4. Barker, C., & Shan, C. (2015). Continuations and natural language. New York: Oxford University Press.Google Scholar
  5. Barry, G., Hepple, M., Leslie, N., & Morrill, G. (1991). Proof figures and structural operators for categorial grammar. In Proceedings of the fifth conference of the European Chapter of the Association for Computational Linguistics (pp. 198–203). Berlin.Google Scholar
  6. Carpenter, B. (1997). Type-logical semantics. Cambridge, MA: MIT.Google Scholar
  7. Chomsky, N. (1973). Conditions on transformations. In S. Anderson & P. Kiparsky (Eds.), A Festschrift for Morris Halle (pp. 232–286). New York: Holt, Rinehart and Winston.Google Scholar
  8. Deane P. (1991) Limits to attention: A cognitive theory of island phenomena. Cognitive Linguistics 2(1): 1–63CrossRefGoogle Scholar
  9. Engdahl E. (1983) Parasitic gaps. Linguistics and Philosophy 6: 5–34CrossRefGoogle Scholar
  10. Gentzen, G. (1934). Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39, 176–210 and 405–431. (Translated in The collected papers of Gerhard Gentzen, pp. 68–131, by M. E. Szabo, Ed., 1969, Amsterdam: North-Holland).Google Scholar
  11. Girard J.-Y. (1987) Linear logic. Theoretical Computer Science 50: 1–102CrossRefGoogle Scholar
  12. Girard, J.-Y. (2011). The blind spot. Zürich: European Mathematical Society.Google Scholar
  13. Hepple, M. (1990). The grammar and processing of order and dependency. Ph.D. Thesis, University of Edinburgh.Google Scholar
  14. Hofmeister, H., Casasanto, L. S., & Sag, I. (2013). Islands in the grammar? Standards of evidence. In D. Forget, P. Hirchbuhler, F. Martineau, & M.-L. Rivero (Eds.), Experimental syntax and island effects (pp. 42–63). Cambridge: CUP.Google Scholar
  15. Hofmeister P., Sag I.A. (2010) Cognitive constraints and island effects. Language 86(2): 366–415CrossRefGoogle Scholar
  16. Jäger, G. (2005). Anaphora and type logical grammar (Vol. 24). Trends in logic—Studia Logica Library. Dordrecht: Springer.Google Scholar
  17. Jansche M., Vasishth S. (2002) Review of Mark Steedman, the syntactic process. Journal of Linguistics 38: 684–690Google Scholar
  18. Kanazawa M. (1992) The Lambek calculus enriched with additional connectives. Journal of Logic, Language and Information 1: 141–171CrossRefGoogle Scholar
  19. Kanovich, M., Kuznetsov, S., & Scedrov, A. (2016). Undecidability of the Lambek calculus with a relevant modality. In A. Foret, G. Morrill, R. Muskens, R. Osswald, & S. Pogodalla (Eds.), Formal grammar 2015: Revised selected papers. Formal grammar 2016: Proceedings. LNCS (Vol. 9804, pp. 240–256) Berlin. Springer.Google Scholar
  20. Kehler, A. (2002). Coherence, reference and the theory of grammar. Stanford, CA: CSLI.Google Scholar
  21. Kluender, R. (1992). Deriving island constraints from principles of predication. In H. Goodluck & M. Rochemont (Eds.), Island constraints: Theory, acquisition, and processing (pp. 223–258). Dordrecht: Kluwer.Google Scholar
  22. Kluender, R. (1998). On the distinction between strong and weak islands: A processing perspective. In P. Culicover & L. McNally (Eds.), The limits of syntax. Syntax and semantics (Vol. 29, pp. 241–279). San Diego: Academic Press.Google Scholar
  23. Kubota Y., Levine R. (2015) Against ellipsis: Arguments for the direct licensing of ‘non-canonical’ coordinations. Linguistics and Philosophy 38(6): 521–576CrossRefGoogle Scholar
  24. Lakoff, G. (1986). Frame semantic control of the coordinate structure constraint. In A. M. Farley, P. T. Farley, & K.-E. McCullough (Eds.), CLS 22 PART 2: Papers from the parasession on pragmatics and grammatical theory (Vol. 152). Chicago: Chicago Linguistics Society.Google Scholar
  25. Lambek J. (1958) The mathematics of sentence structure. American Mathematical Monthly 65: 154–170CrossRefGoogle Scholar
  26. 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 mathematics XII (pp. 166–178). Providence, RI: American Mathematical Society.Google Scholar
  27. Lambek, J. (1988). Categorial and categorical grammars. In R. T. Oehrle, E. Bach, & D. Wheeler (Eds.), Categorial grammars and natural language structures. Studies in linguistics and philosophy (Vol. 32, pp. 297–317). Dordrecht: D. Reidel.Google Scholar
  28. Levine, R. D., & Hukari, T. E. (2006). The unity of unbounded dependency constructions. Stanford, CA: CSLI.Google Scholar
  29. Mihaliček, V., & Pollard, C. (2012). Distinguishing phenogrammar from tectogrammar simplifies the analysis of interrogatives. In P. de Groote & M.-J. Nederhof (Eds.), Formal grammar 2010/2011 (pp. 130–145). Heidelberg: Springer.Google Scholar
  30. Moortgat, M. (1988). Categorial investigations: Logical and linguistic aspects of the Lambek Calculus, Foris, Dordrecht. Ph.D. Thesis, Universiteit van Amsterdam.Google Scholar
  31. Moortgat, M. (1995). Multimodal linguistic inference. Journal of Logic, Language and Information, 5(3,4), 349–385, 1996. (Also in Bulletin of the IGPL,3(2,3), 371–401, 1995.)Google Scholar
  32. Moortgat, M. (1997). Categorial type logics. In J. van Benthem & A. ter Meulen (Eds.), Handbook of logic and language (pp. 93–177). Amsterdam/Cambridge, MA: Elsevier/MIT.Google Scholar
  33. Moot, R., & Retoré, C. (2012). The logic of categorial grammars: A deductive account of natural language syntax and semantics. Heidelberg: Springer.Google Scholar
  34. Morrill, G. (1990a). Grammar and logical types. In M. Stockhof & L. Torenvliet (Eds.), Proceedings of the seventh Amsterdam colloquium (pp. 429–450). Amsterdam: ILLC.Google Scholar
  35. Morrill, G. (1990b). Intensionality and boundedness. Linguistics and Philosophy, 13(6), 699–726Google Scholar
  36. Morrill, G. (1992). Categorial formalisation of relativisation: Pied piping, islands, and extraction sites. Technical Report LSI-92-23-R. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya.Google Scholar
  37. Morrill, G. (1994). Type logical grammar: Categorial logic of signs. Dordrecht: Kluwer.Google Scholar
  38. Morrill G. (2000) Incremental processing and acceptability. Computational Linguistics 26(3): 319–338CrossRefGoogle Scholar
  39. Morrill, G. (2011a). Logic programming of the displacement calculus. In S. Pogodalla & J.-P. Prost (Eds.), Proceedings of logical aspects of computational linguistics 2011, LACL’11, Montpellier. LNAI 6736 in Springer lecture notes in AI (pp. 175–189). Berlin: Springer.Google Scholar
  40. Morrill, G. (2011b). Categorial grammar: Logical syntax, semantics, and processing. New York: Oxford University Press.Google Scholar
  41. Morrill, G. (2012). Logical grammar. In R. Kempson, T. Fernando, & N. Asher (Eds.), The handbook of philosophy of linguistics (pp. 63–92). Oxford: Elsevier.Google Scholar
  42. Morrill G., Merenciano J.-M. (1996) Generalising discontinuity. Traitement automatique des langues 37(2): 119–143Google Scholar
  43. Morrill, G., & Valentín, O. (2010). Displacement calculus. Linguistic Analysis, 36(1–4), 167–192. Special issue Festschrift for Joachim Lambek. arXiv.1004.4181.
  44. Morrill, G., & Valentín, O. (2014a). Displacement logic for anaphora. Journal of Computing and System Science, 80, 390–409. doi: 10.1016/j.jcss.2013.05.006.
  45. Morrill, G., & Valentín, O. (2014b). Semantically inactive multiplicatives and words as types. In N. Asher & S. Soloviev (Eds.), Proceedings of logical aspects of computational linguistics, LACL’14, Toulouse. LNCS, FoLLI Publications on logic, language and information (Vol. 8535, pp. 149–162). Berlin: Springer.Google Scholar
  46. Morrill, G., & Valentín, O. (2015a). Computational coverage of TLG: Nonlinearity. In M. Kanazawa, L. S. Moss, & V. de Paiva (Eds.), Proceedings of NLCS’15. Third workshop on natural language and computer science. EPiC (Vol. 32, pp. 51–63), Kyoto, 2015. Workshop affiliated with Automata, Languages and Programming (ICALP) and Logic in Computer Science (LICS).Google Scholar
  47. Morrill, G., & Valentín, O. (2015b). Multiplicative-additive focusing for parsing as deduction. In I.Cervesato & C. Schürmann (Eds.), First international workshop on focusing, workshop affiliated with LPAR 2015. EPTCS (Vol. 197, pp. 29–54). Fiji: Suva.Google Scholar
  48. Morrill, G., & Valentín, O. (2016). On the logic of expansion in natural language. In M. Amblard, P. de Groote, S. Pogodalla, & C. Retoré (Eds.), Proceedings of logical aspects of computational linguistics, LACL’16, Nancy. LNCS, FoLLI Publications on logic, language and information. Berlin: Springer.Google Scholar
  49. Morrill, G., Valentín, O., & Fadda, M. (2009). Dutch grammar and processing: A case study in TLG. In P. Bosch, D. Gabelaia, & J. Lang (Eds.), Logic, language, and computation: 7th international Tbilisi symposium, revised selected papers. Lecture notes in artificial intelligence (Vol. 5422, pp. 272–286). Berlin: Springer.Google Scholar
  50. Morrill, G., Valentín, O., & Fadda, M. (2011). The displacement calculus. Journal of Logic, Language and Information, 20(1), 1–48. doi: 10.1007/s10849-010-9129-2.
  51. Muskens, R. (2003). Language, lambdas and logic. In G.-J. M. Kruijff & R. T. Oehrle (Eds.), Resource-sensitivity in binding and anaphora. Studies in linguistics and philosophy (Vol. 80, pp. 23–54). Dordrecht: Kluwer.Google Scholar
  52. Newmeyer F.J. (2016) Nonsyntactic explanations of island constraints. Annual Review of Linguistics 2: 187–210CrossRefGoogle Scholar
  53. Postal P.M. (1993) Parasitic gaps and across-the-board phenomenon. Linguistic Inquiry 24(4): 735–754Google Scholar
  54. Sag I.A. (1983) On parasitic gaps. Linguistics and Philosophy 6: 35–45CrossRefGoogle Scholar
  55. Sprouse J., Wagers M., Phillips C. (2012) A test of the relation between working memory capacity and syntactic island effects. Language 88: 82–123CrossRefGoogle Scholar
  56. Steedman M. (1987) Combinatory grammars and parasitic gaps. Natural Language and Linguistic Theory 5: 403–439CrossRefGoogle Scholar
  57. Szabolcsi, A. (1983). ECP in categorial grammar. Manuscript. Nijmegen: Max Planck Institute.Google Scholar
  58. Szabolcsi, A. (2006). Strong versus weak islands. In M. Everaert & H. van Riemsdijk (Eds.), The Blackwell companion to syntax (pp. 479–531). Oxford: Blackwell.Google Scholar
  59. Taraldsen, T. (1979). The theoretical interpretation of a class of marked extractions. In A. Belleti, L. Brandi, & L. Rizzi (Eds.), Theory of markedness in generative grammar. Scuole Normal Superiore de Pisa: Pisa.Google Scholar
  60. Valentín, O. (2012). Theory of discontinuous Lambek calculus. Ph.D. Thesis, Universitat Autònoma de Barcelona, Barcelona.Google Scholar
  61. Valentín, O. (2014). The hidden structural rules of the discontinuous Lambek calculus. In C. Casadio, B. Coeke, M. Moortgat, & P. Scott (Eds.), Categories and types in logic, language and physics: Essays dedicated to Jim Lambek on the occasion of his 90th birthday. LNCS, FoLLI Publications in logic, language and information (Vol. 8222, pp. 402–420). Berlin: Springer.Google Scholar
  62. Valentín, O., Serret, D., & Morrill, G. (2013). A count invariant for Lambek calculus with additives and bracket modalities. In G. Morrill & M.-J. Nederhof (Eds.), Proceedings of formal grammar 2012 and 2013. LNCS, FoLLI Publications in logic, language and information (Vol. 8036, pp. 263–276). Berlin: Springer.Google Scholar
  63. van Benthem, J. (1991). Language in action: Categories, lambdas, and dynamic logic. Studies in logic and the foundations of mathematics (Vol. 130). Amsterdam. Revised student edition printed in 1995 by the MIT.Google Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations