Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ades A.E., Steedman M.J. (1982) On the order of words. Linguistics and Philosophy, 4: 517–558
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.)
Andreoli J.M. (1992) Logic programming with focusing in linear logic. Journal of Logic and Computation 2(3): 297–347
Barker, C., & Shan, C. (2015). Continuations and natural language. New York: Oxford University Press.
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.
Carpenter, B. (1997). Type-logical semantics. Cambridge, MA: MIT.
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.
Deane P. (1991) Limits to attention: A cognitive theory of island phenomena. Cognitive Linguistics 2(1): 1–63
Engdahl E. (1983) Parasitic gaps. Linguistics and Philosophy 6: 5–34
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).
Girard J.-Y. (1987) Linear logic. Theoretical Computer Science 50: 1–102
Girard, J.-Y. (2011). The blind spot. Zürich: European Mathematical Society.
Hepple, M. (1990). The grammar and processing of order and dependency. Ph.D. Thesis, University of Edinburgh.
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.
Hofmeister P., Sag I.A. (2010) Cognitive constraints and island effects. Language 86(2): 366–415
Jäger, G. (2005). Anaphora and type logical grammar (Vol. 24). Trends in logic—Studia Logica Library. Dordrecht: Springer.
Jansche M., Vasishth S. (2002) Review of Mark Steedman, the syntactic process. Journal of Linguistics 38: 684–690
Kanazawa M. (1992) The Lambek calculus enriched with additional connectives. Journal of Logic, Language and Information 1: 141–171
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.
Kehler, A. (2002). Coherence, reference and the theory of grammar. Stanford, CA: CSLI.
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.
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.
Kubota Y., Levine R. (2015) Against ellipsis: Arguments for the direct licensing of ‘non-canonical’ coordinations. Linguistics and Philosophy 38(6): 521–576
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.
Lambek J. (1958) The mathematics of sentence structure. American Mathematical Monthly 65: 154–170
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.
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.
Levine, R. D., & Hukari, T. E. (2006). The unity of unbounded dependency constructions. Stanford, CA: CSLI.
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.
Moortgat, M. (1988). Categorial investigations: Logical and linguistic aspects of the Lambek Calculus, Foris, Dordrecht. Ph.D. Thesis, Universiteit van Amsterdam.
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.)
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.
Moot, R., & Retoré, C. (2012). The logic of categorial grammars: A deductive account of natural language syntax and semantics. Heidelberg: Springer.
Morrill, G. (1990a). Grammar and logical types. In M. Stockhof & L. Torenvliet (Eds.), Proceedings of the seventh Amsterdam colloquium (pp. 429–450). Amsterdam: ILLC.
Morrill, G. (1990b). Intensionality and boundedness. Linguistics and Philosophy, 13(6), 699–726
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.
Morrill, G. (1994). Type logical grammar: Categorial logic of signs. Dordrecht: Kluwer.
Morrill G. (2000) Incremental processing and acceptability. Computational Linguistics 26(3): 319–338
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.
Morrill, G. (2011b). Categorial grammar: Logical syntax, semantics, and processing. New York: Oxford University Press.
Morrill, G. (2012). Logical grammar. In R. Kempson, T. Fernando, & N. Asher (Eds.), The handbook of philosophy of linguistics (pp. 63–92). Oxford: Elsevier.
Morrill G., Merenciano J.-M. (1996) Generalising discontinuity. Traitement automatique des langues 37(2): 119–143
Morrill, G., & Valentín, O. (2010). Displacement calculus. Linguistic Analysis, 36(1–4), 167–192. Special issue Festschrift for Joachim Lambek. arXiv.1004.4181.
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.
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.
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).
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.
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.
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.
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.
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.
Newmeyer F.J. (2016) Nonsyntactic explanations of island constraints. Annual Review of Linguistics 2: 187–210
Postal P.M. (1993) Parasitic gaps and across-the-board phenomenon. Linguistic Inquiry 24(4): 735–754
Sag I.A. (1983) On parasitic gaps. Linguistics and Philosophy 6: 35–45
Sprouse J., Wagers M., Phillips C. (2012) A test of the relation between working memory capacity and syntactic island effects. Language 88: 82–123
Steedman M. (1987) Combinatory grammars and parasitic gaps. Natural Language and Linguistic Theory 5: 403–439
Szabolcsi, A. (1983). ECP in categorial grammar. Manuscript. Nijmegen: Max Planck Institute.
Szabolcsi, A. (2006). Strong versus weak islands. In M. Everaert & H. van Riemsdijk (Eds.), The Blackwell companion to syntax (pp. 479–531). Oxford: Blackwell.
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.
Valentín, O. (2012). Theory of discontinuous Lambek calculus. Ph.D. Thesis, Universitat Autònoma de Barcelona, Barcelona.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.
About this article
Cite this article
Morrill, G. Grammar logicised: relativisation. Linguist and Philos 40, 119–163 (2017). https://doi.org/10.1007/s10988-016-9197-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10988-016-9197-0