Skip to main content
SpringerLink
Log in

Generative Grammars in Resource Logics

  • Published:
Research on Language and Computation

Abstract

This paper reviews recent research which aims tosituate proposals in mainstream linguistic theory in the broadlandscape of resource logics. Particular attention is given hereto recent work in the transformational tradition pioneered byChomsky and many others, where attention has been given to grammars that are ``minimalist'' in the sense of having a restrictedrange of grammatical mechanisms. These grammars are relatively recent, and although they are based on a long tradition,they are largely informal. The study ofresource logics, on the other hand, is formal and stems naturally froma long logical tradition. Resource logics may provide a valuable common ground upon which proposals in generative grammar can beformulated clearly, redundancies and notationalvariants can be identified, and compatibility with the data canhave the deciding role it deserves.

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

  • Aarts E., Trautwein K. (1995) Non-associative Lambek Categorial Grammar in Polynomial Time. Mathematical Logic Quarterly, 41, pp. 476-484.

    Google Scholar 

  • Abrusci V. M. (1991) Phase Semantics and Sequent Calculus for Pure Non-commutative Classical Linear Logic. Journal of Symbolic Logic, 56/4, pp. 1403-1451.

    Google Scholar 

  • Abrusci V. M. (1994) Exchange Connectives for Non-commutative Intuitionistic Propositional Calculus. In Abrusci M., Casadio C., Moortgat M. (eds.), Linear Logic and Lambek Calculus, DYANA, Roma.

    Google Scholar 

  • Abrusci V. M., Casadio C. (eds.) (1996) Third Roma Workshop: Proofs and Linguistics Categories — Applications of Logic to the Analysis and Implementation of Natural Language, CLUEB, Bologna.

    Google Scholar 

  • Abrusci V. M., Maringelli E. (1998) A New Correctness Criterion for Cyclic Multiplicative Proofnets. In Retoré (1998), pp. 449-459.

  • Abrusci V. M. and Ruet P. (1999) Non-commutative Logic I: The Multiplicative Fragment. Annals of Pure and Applied Logic, 101/1, pp. 29-64.

    Google Scholar 

  • Brody M. (1995) Lexico-Logical Form: A Radically Minimalist Theory. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Buszkowski W. (1997) Mathematical Linguistics and Proof Theory. In ter Meulen A. (eds.) (1997) Handbook of Logic and Language. North-Holland Elsevier, Amsterdam. van Benthem and ter Meulen (1997), chapter 12, pp. 683-736.

    Google Scholar 

  • Buszkowski W., Penn G. (1990) Categorial Grammars Determined from Linguistic Data by Unification. Studia Logica, 49, pp. 431-454.

    Google Scholar 

  • Carpenter B. (1996) The Turing-completeness of Multimodal Categorial Grammars. Carnegie-Mellon University.

  • Chomsky N. (1956) Three Models for the Description of Language. IRE Transactions on Information Theory, IT-2, pp. 113-124.

    Google Scholar 

  • Chomsky N. (1995) The Minimalist Program. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Chomsky N. (1998) Minimalist Inquiries: The Framework. MIT, forthcoming.

  • Collins C. (1997) Local Economy. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Cornell T. L. (1996) A Minimalist Grammar for the Copy Language. Technical report, SFB 340 Technical Report #79, University of Tübingen.

  • Cornell T. L. (1997) Representational Minimalism. SFB 340 Technical Report #83, University of Tübingen. Revised version forthcoming in Mönnich U., Kolb H.-P. (eds.).

  • Cornell T. L. (1997) A Type Logical Perspective on Minimalist Derivations. Proceedings, Formal Grammar'97, Aix-en-Provence.

  • Cornell T. L. (1999) Derivational and Representational Views of Minimalist Transformational Grammar. In Lamarche F., Perrier G. (eds.), Logical Aspects of Computational Linguistics, LACL'97, volume 1582 of LNCS/LNAI, Springer-Verlag. Lecomte, Lamarche, Perria (1999), pp. 92-111.

  • Cornell T. L. (1998) Island Effects in Type Logical Approaches to the Minimalist Program. Proceedings of the Joint Conference on Formal Grammar, Head-Driven Phrase Structure Grammar, and Categorial Grammar, FHCG-98, pp. 279-288, Saarbrücken, 1998.

  • Cornell T. L. (2004) Lambek Calculus for Transformational Grammar. Research on Language and Computation, 2/1. pp. 105-126.

    Google Scholar 

  • Cremers C. (2001) Dislocation, Clustering and Disharmony. Research on Language and Computation, 2/1, pp. 87-103.

    Google Scholar 

  • Demaille A. (1999) Logiques linéaires hybrides et leurs modalités. Thèse de doctorat, spécialité informatique, Ecole Nationale Supérieure des Télécommunications de Paris, juin 1999.

  • de Groote P. (1996) Partially Commutative Linear Logic: Sequent calculus and Phase Semantics. In Casadio C. (eds.) (1996) Third Roma Workshop: Proofs and Linguistics Categories — Applications of Logic to the Analysis and Implementation of Natural Language, Abrusci and Casadio (1996), pp. 199-208. CLUEB, Bologna.

    Google Scholar 

  • de Groote P. (1999) Non-associative Lambek Calculus in Polynomial Time. In Murray N. V. (ed.), 8th Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX'99, number 1617 in Lecture Notes in Artificial Intelligence, Springer-Verlag, June 1999, pp. 128-139.

  • de Groote P., Retoré C. (1996) Semantic Readings of Proof Nets. In Kruijff G-J., Morrill G., Oehrle D. (eds.), Formal Grammar, Prague, August 1996, FoLLI, pp. 57-70.

    Google Scholar 

  • Fulop S. (1999) On the Logic and Learning of Language. PhD thesis, University of California, Los Angeles.

    Google Scholar 

  • Girard J-Y. (1987) Linear Logic. Theoretical Computer Science, 50/1, pp. 1-102.

    Google Scholar 

  • Girard J-Y. (1987) Towards a Geometry of Interaction. Categories in Logic and Computer Science — Boulder, June 1987, volume 92 of Contemporary Mathematics, AMS, pp. 68-109.

  • Girard J-Y. (1995) Linear Logic: Its Syntax and Semantics. In Girard J-Y., Lafont, Y, Regnier, L. (eds.), Advances in Linear Logic, volume 222 of London Mathematical Society Lecture Notes, Cambridge University Press, pp. 1-42.

  • Girard J-Y., Lafont Y., Taylor P. (1998) Proofs and Types. Number 7 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press.

  • Gleitman L. R., Liberman M. (eds.) (1995) An Invitation to Cognitive Sciences, Vol. 1: Language. MIT Press.

  • Gleitman, L. R., Newport E. L. (1995) The Invention of language by Children: Environmental and Biological Influences on the Acquisition of Language. In Liberman M. (eds.) (1995) An Invitation to Cognitive Sciences, Vol. 1: Language. MIT Press. Gleitman and Liberman (1995), chapter 1, pp. 1-24.

  • Gold E. M. (1967) Language Identification in the Limit. Information and Control, 10, pp. 447-474.

    Google Scholar 

  • Harkema H. (2000) A Recognizer for Minimalist Grammars. Proceedings, Sixth International Workshop on Parsing Technologies, IWPT'2000.

  • Harkema H. (2001) A Characterization of Minimalist Languages. In Morrill G. V., Retoré C. (eds.) (2001) Logical Aspects of Computational Linguistics, LACL'01, vol. 2099 of LNCS/LNAI, Springer-Verlag, 2001. de Groote, Morrill, Retoré (2001), pp. 193-211.

  • Heim I., Kratzer A. (1988) Semantics in Generative Grammar. Blackwell, Oxford.

    Google Scholar 

  • Jackendoff R. (1995) The Architecture of the Language Faculty. Number 28 in Linguistic Inquiry Monographs, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Jäger G. (1987) On the Generative Capacity of Multi-modal Categorial Logics. IRCS technical report 98-26, University of Pennsylvania.

  • Johnson M. E. (1998) Proof Nets and the Complexity of Processing Center-embedded Constructions. In Retoré (1998), pp. 433-447.

  • Joshi A., Kulick S. (1997) Partial Proof Trees, Resource Sensitive Logics and Syntactic Constraints. In Retoré (1997), pp. 21-42.

  • Joshi A., Kulick S., Kurtonina N. (2001) An LTAG Perspective on Categorial Inference. In Moortgat (2001), pp. 90-105.

  • Joshi A., Kulick S., Kurtonina N. (2004) Partial Proof Trees, Hybrid Logic, and Quantifier Scope. Research on Language and Computation, 2/1, pp. 57-68.

    Google Scholar 

  • Joshi A. K., Schabes Y. (1997) Tree-adjoining Grammars. In Rozenberg G., Salomaa A. (eds.), Handbook of Formal Languages, Volume 3: Beyond Words, Springer, NY, pp. 69-124.

    Google Scholar 

  • Kanazawa M. (1998) Lambek Calculus: Recognizing Power and Complexity. Chiba University.

  • Kanazawa M. (1994) Learnable Classes of Categorial Grammmars. CSLI Publications/FOLLI, Stanford, California. (Revised 1994 Ph.D. thesis, Stanford University).

    Google Scholar 

  • Kayne R. (1983) Connectedness. Linguistic Inquiry, 14, pp. 223-249.

    Google Scholar 

  • Kayne R. (1994) The Antisymmetry of Syntax. Number 25 in Linguistic Inquiry Monographs, MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Kurtonina N., Moortgat M. (1997) Structural Control. In Blackburn P., de Rijke M. (eds.), Specifying Syntactic Structures, CSLI, pp. 75-113. Distributed by Cambridge University Press.

  • Lamarche F., Retoré C. (1996) Proof Nets for the Lambek Calculus — an Overview. In Casadio C. (eds.) (1996) Third Roma Workshop: Proofs and Linguistics Categories — Applications of Logic to the Analysis and Implementation of Natural Language, CLUEB, Bologna. Abrusci and Casadio (1996), pp. 241-262.

    Google Scholar 

  • Lambek J. (1958) The Mathematics of Sentence Structure. American Mathematical Monthly, 65, pp. 154-170.

    Google Scholar 

  • Lambek J. (1961) On the Calculus of Syntactic Types. In Jakobson R. (ed.), Structure of Language and Its Mathematical Aspects, American Mathematical Society, pp. 166-178.

  • Lang B. (1994) Recognition Can Be Harder than Parsing. Computational Intelligence, 10.

  • Larson R. K. (1995) Knowledge of Meaning. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Lecomte, A., Lamarche F., Perrier G. (eds.), Logical Aspects of Computational Linguistics, LACL'97, volume 1582 of LNCS/LNAI, Springer-Verlag.

  • Lecomte A. (1999) Proof-nets, Hybrid Logics and minimalist Representations. Mathematics of Languages, 6.

  • Lecomte A. (2004) Rebuilding MP on a Logical Ground. Research on Language and Computation, 2/1, pp. 27-55.

    Google Scholar 

  • Lecomte A., Retoré C. (1995) Pomset Logic as an Alternative Categorial Grammar. In Morrill G., Oehrle R. (eds.), Formal Grammar, Barcelona, pp. 181-196, August 1995, FoLLI.

    Google Scholar 

  • Lecomte A., Retoré C. (1998) Words as Modules: A Lexicalised Grammar in the Framework of Linear Logic Proof Nets. In Martin-Vide C. (ed.), Mathematical and Computational Analysis of Natural Language — Selected Papers from ICML'96, volume 45 of Studies in Functional and Structural Linguistics, John Benjamins Publishing Company, pp. 129-144.

  • Lecomte A., Retoré C. (1999) Towards a Minimal Logic for Minimalist Grammars: Another Use of Lambek Calculus. Formal Grammar, FG'99, FoLLI.

  • Lecomte A., Retoré C. (2001) Extending Lambek Grammars: A Logical Account of Minimalist Grammars. Proceedings of the 39th Annual Meeting of the Association for Computational Linguistics, ACL 2001, Toulouse, pp. 179-198.

  • Michaelis J. (2001) Derivational Minimalism is Mildly Context-sensitive. In Moortgat (2001).

  • Michaelis J. (2001) Transforming Linear Context Free Rewrite Systems into Minimalist Grammars. In Morrill G. V., Retoré C. (eds.) (2001), Logical Aspects of Computational Linguistics, LACL'01, vol. 2099 of LNCS/LNAI, Springer-Verlag, 2001. de Groote, Morrill, Retoré (2001), pp. 228-244.

  • Michaelis J., Kracht M. (1997) Semilinearity as a Syntactic Invariant. In Retoré (1997), pp. 37-40.

  • Moortgat M. (1988) Categorial Investigations. Foris, Dordrecht.

    Google Scholar 

  • Moortgat M. (1997) Categorial Type Logic. In ter Meulen A. (eds.) (1997) Handbook of Logic and Language. North-Holland Elsevier, Amsterdam. van Benthem and ter Meulen (1997), chapter 2, pp. 93-177.

    Google Scholar 

  • Moortgat M. (ed.) (2001) Logical Aspects of Computational Linguistics, LACL'98, selected papers, vol. 2014 of LNCS/LNAI, Springer-Verlag, 2001.

  • Morrill G. V. (1994) Type-logical Grammar: Categorial Logic of Signs. Kluwer, Dordrecht.

    Google Scholar 

  • Morrill G. V. (1998) Incremental Processing and Acceptability. Research Report LSI-98-48-R, Universitat Politècnica di Catalunya.

  • de Groote P., Morrill G. V., Retoré C. (eds.) (2001) Logical Aspects of Computational Linguistics, LACL'01, vol. 2099 of LNCS/LNAI, Springer-Verlag, 2001.

  • Nakanishi R., Takada K., Seki H. (1997) An Efficient Recognition Algorithm for Multiple Context Free Languages. Proceedings of the Fifth Meeting on Mathematics of Language, MOL5.

  • Nicolas J. (1999) Grammatical Inference as Unification. Rapport de Recherche RR-3632, INRIA. http://www.inria.fr/RRRT/publications-eng.html.

  • Pentus M. (1997) Product-free Lambek Calculus and Context-free Grammars. Journal of Symbolic Logic, 62/2, pp. 648-660.

    Google Scholar 

  • Pinker S. (1995) Language Acquisition. In Liberman M. (eds.) (1995) An Invitation to Cognitive Sciences, Vol. 1: Language. MIT Press. Gleitman and Liberman (1995), chapter 6, pp. 135-182.

  • Pogodalla S. (2001) Lexicalized Proof-nets in Pomset Logic and TAG. In Moortgat (2001), pp. 230-250.

  • Pollard C., Sag I. (1994) Head-driven Phrase Structure Grammar. The University of Chicago Press, Chicago.

    Google Scholar 

  • Prince A., Smolensky P. (1993) Optimality Theory: Constraint Interaction in Generative Grammar. Forthcoming.

  • Retoré C. (1993) Réseaux et Séquents Ordonnés. Thèse de Doctorat, spécialité Mathématiques, Université Paris 7, février 1993.

  • Retoré C. (1996) Calcul de Lambek et logique linéaire. Traitement Automatique des Langues, 37/2, pp. 39-70.

    Google Scholar 

  • Retoré C. (1997) Pomset Logic: A Non-commutative Extension of Classical Linear Logic. In de Groote Ph., Hindley J. R. (eds.), Typed Lambda Calculus and Applications, TLCA'97, volume 1210 of LNCS, pp. 300-318.

  • Retoré C. (ed.) (1997) Logical Aspects of Computational Linguistics, LACL'96, volume 1328 of LNCS/LNAI, Springer-Verlag.

  • Retoré C. (guest ed.) (1998) Recent Advances in Logical and Algebraic Approaches to Grammar. Special issue of the Journal of Logic Language and Information, 7/4.

  • Retoré C. (2003) Handsome Proof-nets: Perfect Matchings and Cographs. Theoretical Computer Science, 294/3, 2003, pp. 473-388. Preliminary report: Handsome proof-nets: R&B-graphs, perfect matchings and series-parallel graphs. Rapport de Recherche RR-3652, INRIA, March 1999. http://www. inria.fr/RRRT/publications-eng.html.

    Google Scholar 

  • Richards N. (1998) The Principle of Minimal Compliance. Linguistic Inquiry, 29, pp. 599-629.

    Google Scholar 

  • Roorda D. (1991) Resource Logic: Proof Theoretical Investigations. PhD thesis, FWI, Universiteit van Amsterdam.

  • Ruet P. (1997) Logique non-commutative et programmation concurrente. Thèse de doctorat, spécialité logique et fondements de l'informatique, Université Paris 7.

  • Seki H., Matsumura T., Fujii M., Kasami T. (1991) On Multiple Context-free Grammars. Theoretical Computer Science, 88, pp. 191-229.

    Google Scholar 

  • Stabler E. P. (1996) Acquiring and Parsing Languages with Movement. UCLA manuscript. Revised version forthcoming.

  • Stabler E. P. (1997) Derivational Minimalism. In Retoré (1997), pp. 68-95.

  • Stabler E. P. (1998) Acquiring Grammars with Movement. Syntax, 1, pp. 72-97. Draft available at http://phonetics.ling.ucla.edu/.

    Google Scholar 

  • Stabler E. P. (1999) Remnant Movement and Complexity. In Bouma G., Hinnichs E., Kruijff G-J., Oehrle R. (eds.), Constraints and Resources in Natural Language Syntax and Semantics, CSLI, 1999, pp. 299-326.

  • Stabler E. P. (1999) Minimalist Grammars and Recognition. Linguistic Form and Its Computation, (Final Workshop of SFB340), Bad Teinach, October 1999, publication forthcoming.

  • Szabolcsi A. (ed.) (1996) Ways of Scope Taking. Kluwer, Boston.

    Google Scholar 

  • Tellier I. (1998) Meaning Helps Learning Syntax. Fourth International Colloquium on Grammatical Inference, ICG'98.

  • Tiede H-J. (1999) Deductive Systems and Grammars: Proofs as Grammatical Structures. PhD thesis, Illinois Wesleyan University.

  • Tiede H-J. (2001) Lambek Calculus Proofs and Tree Automata. In Moortgat (2001), pp. 251-265.

  • Troelstra A. S. (1992) Lectures on Linear Logic, volume 29 of CSLI Lecture Notes, CSLI. (distributed by Cambridge University Press).

  • van Benthem J. (1986) Essays in Logical Semantics. Reidel, Dordrecht.

    Google Scholar 

  • van Benthem J., ter Meulen A. (eds.) (1997) Handbook of Logic and Language. North-Holland Elsevier, Amsterdam.

    Google Scholar 

  • van Benthem J. (1991) Language in Action: Categories, Lambdas and Dynamic Logic, volume 130 of Studies in logic and the foundation of mathematics, North-Holland, Amsterdam.

    Google Scholar 

  • Vasishth S. (2004) Surface Structure Constraints on Negative Polarity and Word Order in English and Hindi. Research on Language and Computation, 2/1, pp. 127-146.

    Google Scholar 

  • Vermaat W. (1999) Controlling Movement: Minimalism in a Deductive Perspective. Masters Thesis, Universiteit Utrecht.

  • Vermaat W. (2003) The Minimalist Move Operation in a deductive Perspective. Research on Language and Computation, 2/1, pp. 69-85.

    Google Scholar 

  • Vijayashanker K. (1987) A Study of Tree Adjoining Languages. PhD thesis, University of Pennsylvania.

  • Weir D. (1988) Characterizing Mildly Context-sensitive Grammar Formalisms. PhD thesis, University of Pennsylvania, Philadelphia.

    Google Scholar 

  • Yetter D. N. (1990) Quantales and (Non-commutative) Linear Logic. Journal of Symbolic Logic, 55, pp. 41-64.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA-Futurs & LaBRI, Domaine Universitaire, 351, cours de la Libération, 33405, Talence cedex, France (E-mail

    Christian Retoré

  2. Department of Linguistics, University of California, Los Angeles, 3125 Campbell Hall, Los Angeles, CA, 90095-1543, USA (E-mail

    Edward Stabler

Authors
  1. Christian Retoré
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward Stabler
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Retoré, C., Stabler, E. Generative Grammars in Resource Logics. Research on Language and Computation 2, 3–25 (2004). https://doi.org/10.1023/A:1025455403876

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025455403876

Search

Navigation