Skip to main content
SpringerLink
Log in

The Multimodal Lambek Calculus

  • Chapter
The Logic of Categorial Grammars

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6850))

  • 1452 Accesses

Summary

The multimodal Lambek calculus extends the (non-associative) Lambek calculus in two ways. First, it provides a way of mixing different resource management possibilities — for example associative and non-associative or commutative and non-commutative — without collapse, that is to say that associativity can be valid for certain formulae but not for others. Second, it introduces unary connectives, which introduce new derivability patterns and which provide us with another way to lexically anchor the structural rules of associativity and commutativity.

Since the multimodal extensions of the Lambek calculus have been motivated by the desire to give a better linguistic treatment of some grammatical phenomena, some of these linguistic analyses will be discussed as examples illustrating the use of the multimodal extensions.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barry, G., Hepple, M., Leslie, N., Morrill, G.: Proof figures and structural operators for categorial grammar. In: Proceedings of EACL 1995, Berlin, pp. 198–203 (1991)

    Google Scholar 

  • Bernardi, R.: Reasoning with polarity in categorial type logic. PhD thesis, Utrecht Institute of Linguistics OTS, Utrecht University (2002)

    Google Scholar 

  • Bernardi, R., Moot, R.: Generalized quantifiers in declarative and interrogative sentences. Logic Journal of the IGPL 11(4), 419–434 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Chomsky, N.: The minimalist program. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  • Danos, V., Regnier, L.: The structure of multiplicatives. Archive for Mathematical Logic 28, 181–203 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  • Dowty, D.: Non constituent coordination, wrapping and multimodal categorial grammars: Syntactic form as logical form. Tech. rep., Ohio State University (1997); expanded draft of an August 1996 paper from the International Congress of Logic, Methodology and Philosophy of Science, downloaded from the author’s website (March 17, 2011)

    Google Scholar 

  • Girard, J.Y.: Linear logic. Theoretical Computer Science 50(1), 1–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  • de Groote, P.: Partially commutative linear logic: sequent calculus and phase semantics. In: Abrusci, V.M., Casadio, C. (eds.) Third Roma Workshop: Proofs and Linguistics Categories – Applications of Logic to the Analysis and Implementation of Natural Language, pp. 199–208. CLUEB, Bologna (1996)

    Google Scholar 

  • Hepple, M.: A general framework for hybrid substructural categorial logics. Tech. rep., Institute for Research in Cognitive Science, University of Pennsylvania (1993)

    Google Scholar 

  • Heylen, D.: Types and sorts – resource logic for feature checking. PhD thesis, Universiteit Utrecht (1999)

    Google Scholar 

  • Jäger, G.: Anaphora and Quantification in Categorial Grammar. In: Moortgat, M. (ed.) LACL 1998. LNCS (LNAI), vol. 2014, pp. 70–90. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  • Jäger, G.: Anaphora and Type Logical Grammar, Trends in Logic – Studia Logic Library, vol. 24. Springer (2005)

    Google Scholar 

  • Kurtonina, N.: Frames and labels. A modal analysis of categorial inference. PhD thesis, OTS Utrecht, ILLC Amsterdam (1995)

    Google Scholar 

  • Kurtonina, N.: Categorial inference and modal logic. Journal of Logic, Language and Information 7(4), 399–411 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Kurtonina, N., Moortgat, M.: Structural control. In: Blackburn, P., de Rijke, M. (eds.) Specifying Syntactic Structures, pp. 75–113. CSLI, Stanford (1997)

    Google Scholar 

  • Moortgat, M.: Multimodal linguistic inference. Bulletin of the IPGL Special Issue (1995) Kempson, R. (ed.)

    Google Scholar 

  • Moortgat, M.: In situ binding: A modal analysis. In: Dekker, P., Stokhof, M. (eds.) Proceedings 10th Amsterdam Colloquium, pp. 539–549. ILLC, Amsterdam (1996a)

    Google Scholar 

  • Moortgat, M.: Multimodal linguistic inference. Journal of Logic, Language and Information 5(3-4), 349–385 (1996b)

    Article  MathSciNet  MATH  Google Scholar 

  • Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, ch. 2, pp. 93–177. North-Holland Elsevier, Amsterdam (1997)

    Chapter  Google Scholar 

  • Moortgat, M.: Constants of grammatical reasoning. In: Bouma, G., Hinrichs, E., Kruijff, G.J., Oehrle, R.T. (eds.) Constraints and Resources in Natural Language Syntax and Semantics, pp. 195–219. CSLI, Stanford (1999)

    Google Scholar 

  • Moortgat, M.: Categorial type logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, 2nd edn., ch. 2, pp. 95–179. North-Holland Elsevier, Amsterdam (2011)

    Chapter  Google Scholar 

  • Moortgat, M., Morrill, G.: Heads and phrases: Type calculus for dependency and constituent structure. Tech. rep., Research Institute for Language and Speech (OTS), Utrecht (1991)

    Google Scholar 

  • Moortgat, M., Oehrle, R.T.: Logical parameters and linguistic variation. In: Fifth European Summer School in Logic, Language and Information, Lisbon. Lecture notes on categorial grammar (1993)

    Google Scholar 

  • Moortgat, M., Oehrle, R.T.: Adjacency, dependency and order. In: Proceedings 9th Amsterdam Colloquium, pp. 447–466 (1994)

    Google Scholar 

  • Moot, R.: Proof nets for linguistic analysis. PhD thesis, Utrecht Institute of Linguistics OTS, Utrecht University (2002)

    Google Scholar 

  • Moot, R.: Lambek grammars and hyperedge replacement grammars. Tech. rep., LaBRI, CNRS (2008a)

    Google Scholar 

  • Moot, R.: Lambek grammars, tree adjoining grammars and hyperedge replacement grammars. In: Gardent, C., Sarkar, A. (eds.) Proceedings of TAG+9, The Ninth International Workshop on Tree Adjoining Grammars and Related Formalisms, pp. 65–72 (2008)

    Google Scholar 

  • Moot, R., Retoré, C.: Les indices pronominaux du français dans les grammaires catégorielles. Lingvisticae Investigationes 29(1), 137–146 (2006)

    Article  Google Scholar 

  • Morrill, G.: Type Logical Grammar. Kluwer Academic Publishers, Dordrecht (1994)

    Book  MATH  Google Scholar 

  • Morrill, G.: Discontinuity in categorial grammar. Linguistics and Philosophy 18(2), 175–219 (1995)

    Article  MathSciNet  Google Scholar 

  • Morrill, G., Leslie, N., Hepple, M., Barry, G.: Categorial deductions and structural operations. In: Barry, G., Morrill, G. (eds.) Studies in Categorial Grammar, Edinburgh Working Papers in Cognitive Science, vol. 5, pp. 1–21. Centre for Cognitive Science (1990)

    Google Scholar 

  • Oehrle, R., Zhang, S.: Lambek calculus and preposing of embedded subjects. Chicago Linguistics Society 25 (1989)

    Google Scholar 

  • Prior, A.: Past, Present and Future. Oxford University Press (1967)

    Google Scholar 

  • Ross, J.R.: Constraints on variables in syntax. PhD thesis, Massachusets Institute of Technology (1967)

    Google Scholar 

  • Shieber, S.: Evidence against the context-freeness of natural language. Linguistics & Philosophy 8, 333–343 (1985)

    Article  Google Scholar 

  • Steedman, M.: Surface structure and interpretation. Linguistic Inquiry Monographs, vol. 30. MIT Press, Cambridge (1997)

    Google Scholar 

  • Vermaat, W.: The minimalist move operation in a deductive perspective. Journal of Language and Computation 2(1), 69–85 (2004); Special Issue on Resource Logics and Minimalist Grammars

    Article  MathSciNet  MATH  Google Scholar 

  • Vermaat, W.: The logic of variation. A cross-linguistic account of wh-question formation. PhD thesis, Utrecht Institute of Linguistics OTS, Utrecht University (2005)

    Google Scholar 

Download references

Authors
  1. Richard Moot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Retoré
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Moot, R., Retoré, C. (2012). The Multimodal Lambek Calculus. In: The Logic of Categorial Grammars. Lecture Notes in Computer Science, vol 6850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31555-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31555-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31554-1

  • Online ISBN: 978-3-642-31555-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation