Skip to main content
SpringerLink
Log in

Contextual Grammars and Natural Languages

  • Chapter
  • First Online:
Handbook of Formal Languages

Abstract

The systematic investigation of natural languages by means of algebraic, combinatorial and set-theoretic models begun in the 1950s concomitantly in Europe and the U.S.A. An important year in this respect seems to be 1957, when Chomsky published his pioneering book [6] concerning the new generative approach to syntactic structures and some Russian mathematicians proposed a conceptual framework for the study of general morphological categories [10], of the category of grammatical case (A. N. Kolmogorov; see [74]), and of the category of part of speech [75], giving the start in the development of analytical mathematical models of languages.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover 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

  1. A. V. Aho, Indexed grammars — an extension of context-free grammars, Journal of the ACM, 15 (1968), 647–671.

    Article  MathSciNet  Google Scholar 

  2. C. Calude, On metrizability of a free monoid, Discrete Mathematics, 15 (1976), 307–310.

    Article  MathSciNet  Google Scholar 

  3. B. Cazimir, Analyse contextuelle par rapport à deux langages, Revue Roum. Math. Pures Appl., 20, 2 (1975), 201–211.

    MathSciNet  MATH  Google Scholar 

  4. B. Cazimir, Opérateurs contextuels et catégories morphologiques par rapport à deux langages, Bull. Math. Soc. Sci. Math. Roumanie, 17(65), 3 (1975), 247–269.

    MathSciNet  MATH  Google Scholar 

  5. E. Celan, S. Marcus, Le diagnostic comme langage, Cahiers Ling. Théorique et Appl., 10, 2 (1973), 163–173.

    MATH  Google Scholar 

  6. N. A. Chomsky, Syntactic Structures, Mouton, The Hague, 1957.

    MATH  Google Scholar 

  7. V. Coardo§, Formal languages and Galois connections, Revue Roum. Ling. — Cahiers Ling. Théor. Appl., 13, 2 (1976), 665–668.

    Google Scholar 

  8. E. Csuhaj-Varju, J. Dassow, J. Kelemen, Gh. Pâun, Grammar Systems. A Grammatical Approach to Distribution and Cooperation, Gordon and Breach, London, 1994.

    MATH  Google Scholar 

  9. A. Dincà, The metric properties of the semigroups and the languages, Lecture Notes in Computer Science, 45, Springer-Verlag, Berlin, 1976, 260–264.

    Google Scholar 

  10. R. L. Dobrushin, The elementary grammatical category (in Russian), Byulleten Objedinenija po Problemam Mashinogo Perevoda, 5 (1957), 19–21.

    Google Scholar 

  11. R. L. Dobrushin, Mathematical methods in linguistics. Applications (in Russian), Matematicheskie Prosveshchenie, 6 (1961), 52–59.

    Google Scholar 

  12. V. Du Feu, S. Marcus, English grammatical homonymy and grammatical categories from the view point of algebraic linguistics, Revue Roum. de Ling., 18, 3 (1973), 215–241.

    Google Scholar 

  13. G. Gazdar, G. K. Pullum, Computationally relevant properties of natural languages and their grammars, New Generation Computing, 3 (1985), 273–306.

    Article  Google Scholar 

  14. A. V. Gladkij, Configuration characteristics of languages (in Russian), Problemy Kibernetiki, 10 (1963), 251–260.

    Google Scholar 

  15. Z. S. Harris, Methods in Structural Linguistics, Chicago Univ. Press, 1951.

    Google Scholar 

  16. T. Head, Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors, Bull. Math. Biology, 49 (1987), 737–759.

    Article  MathSciNet  Google Scholar 

  17. T. Head, Splicing schemes and DNA, In Lindenmayer Systems: Impacts on Theoretical Computer Science and Developmental Biology ( G. Rozenberg, A. Salomaa, eds.), Springer-Verlag, Berlin, 1992, 371–383.

    Chapter  Google Scholar 

  18. T. Head, Gh. Pàun, D. Pixton, Language theory and molecular genetics: generative mechanisms suggested by DNA recombination, in this Handbook.

    Google Scholar 

  19. W. A. van Helden, Case and Gender-Concept Formation Between Morphology and Syntax (2 volumes), Rodopi, Amsterdam-Atlanta, Georgia, 1993.

    Google Scholar 

  20. M. Ito, Quelques remarques sur l’espace contextuel, Mathematical Linguistics, 57 (1971), 18–28.

    Google Scholar 

  21. M. Ito, Sur l’extension et la restriction d’un langage associé à l’espace contextuel, Proc. Japan Academy, 48 (1972), 94–97.

    Article  MathSciNet  Google Scholar 

  22. A. K. Joshi, Tree adjoining grammars: How much context-sensitivity is required to provide reasonable structural descriptions? In Natural Language Processing: Psycholinguistic, Computational and Theoretic Perspectives ( D. R. Dowty et al., eds.), Cambridge Univ. Press, New York, 1985, 206–250.

    Chapter  Google Scholar 

  23. A. K. Joshi, L. Levy, M. Takahashi, Tree adjunct grammars, Journal of the Computer and System Sciences, 10, 1 (1975), 136–163.

    Article  MathSciNet  Google Scholar 

  24. O. S. Kulagina, On a way to define the grammatical concepts by means of set-theory (in Russian), Problemy Kibernetiki, 1 (1958), 203–214.

    Google Scholar 

  25. J. Kunze, Versuch eines objektivierten Grammatikmodells II, Zeitschrift für Phonetik, Sprach. und. Komm., 20, 56 (1967), 415–448.

    Google Scholar 

  26. J. Lambek, On the calculus of syntactic types, In Structure of Language and its Mathematical Aspects (R. Jakobson, ed.), Proc. of the 12th Symp. Appl. Math., Providence, R.I., 1961, 166–178.

    Chapter  Google Scholar 

  27. A. Manaster Ramer, Uses and misuses of mathematics in linguistics, Proc. of the Xth Congress of Natural and Formal Languages, Sevilla, 1994.

    Google Scholar 

  28. S. Marcus, On a logical model of the part of speech (in Romanian), Studii Cercetâri Matematice, 13, 1 (1962), 137–162.

    Google Scholar 

  29. S. Marcus, Sur un modèle logique de la catégorie grammaticale élémentaire, I, Revue Roum. Math. Pures Appl., 7, 1 (1962), 91–107.

    MATH  Google Scholar 

  30. S. Marcus, Mathematical Linguistics (in Romanian), Ed. Didactica, Pedagogic., Bucure§ti, 1963.

    Google Scholar 

  31. S. Marcus, Modèles mathématiques pour la catégorie grammaticale du cas, Revue Roum. Math. Pures Appl., 8, 4 (1963), 585–610.

    MathSciNet  MATH  Google Scholar 

  32. S. Marcus, Typologie des langues et modèles logiques, Acta Math. Acad. Sci. Hungaricae, 14, 3–4 (1963), 269–281.

    Article  Google Scholar 

  33. S. Marcus, Algebraic Linguistics; Analytical Models, Academic Press, New York, 1967.

    MATH  Google Scholar 

  34. S. Marcus, Introduction mathématique à la linguistique structurale, Dunod, Paris, 1967.

    MATH  Google Scholar 

  35. S. Marcus, Catégories de Dobrushin, fermetures de Sestier, voisinages de Sakai, Glossa, 1, 1 (1967), 59–67.

    Google Scholar 

  36. S. Marcus, Catégories morphologiques, Hème Conférence Internationale sur le Traitement Automatique des Langues, Grenoble, 1967, communication 39, 1–8.

    Google Scholar 

  37. S. Marcus, Opérateurs contextuels et catégories morphologiques, Bull. Math. Soc. Sci. Math. Roumanie, 10, 3 (1968), 65–72.

    MATH  Google Scholar 

  38. S. Marcus, Sur la domination au sens de Kunze dans la linguistique algébrique, Revue Roum. Math. Pures Appl., 14, 3 (1969), 378–396.

    MATH  Google Scholar 

  39. S. Marcus, Contextual grammars, Revue Roum. Math. Pures Appl., 14, 10 (1969), 1473–1482.

    MathSciNet  MATH  Google Scholar 

  40. S. Marcus, Les modèles mathématiques et l’opposition romane-slave dans la typologie du genre grammatical, Actes du XIIème Congress Intern. de Linguistique et de Philologie Romane, vol. 1, Ed. Academiei, Bucuresti, 1970, 247–252.

    Google Scholar 

  41. S. Marcus (ed.), Contextual Ambiguities in Natural and in Artificial Languages, I, Ghent (Belgium), Communication and Cognition, 1981.

    Google Scholar 

  42. S. Marcus (ed.), Contextual Ambiguities in Natural and in Artificial Languages, II, Ghent (Belgium), Communication and Cognition, 1983.

    Google Scholar 

  43. S. Marcus, C. Martin-Vide, Gh. Pâun, Contextual grammars and natural languages, Intern. Conf. Math. of Natural Languages, Philadelphia, Penn., 1995.

    Google Scholar 

  44. S. Marcus, C. Martin-Vide, Gh. Pâun, On the internal contextual grammars with maximal use of selectors, Automata and Formal Languages Conf., Salgotarjan, 1996.

    Google Scholar 

  45. S. Marcus, C. Martin-Vide, Gh. Pâun, Contextual grammars versus natural languages, submitted, 1996.

    Google Scholar 

  46. C. Martin-Vide, A. Mateescu, J. Miquel-Verges, Gh. Pâun, Internal contextual grammars: minimal, maximal and scattered use of selectors, BISFAI 95 Conf. (M. Kappel, E. Shamir, eds. ), Jerusalem, 1995, 132–142.

    Google Scholar 

  47. B. Mayoh, Grammatical categories, Revue Roum. Math. Pures Appl, 12, 6 (1967), 843–848.

    MathSciNet  MATH  Google Scholar 

  48. L. Nebeskÿ, Conditional replacement of words, Prague Bull. Math. Linguistics, 3 (1965), 3–12.

    Google Scholar 

  49. L. Nebeskÿ, Language systems, Revue Roum. Math. Pures Appl., 13, 3 (1968), 371–375.

    MathSciNet  MATH  Google Scholar 

  50. M. Novotnÿ, Complete characterizations of classes of Chomsky by means of configurations, Acta Facultatis Rerum Naturalium Univ. Cornenianae. Math-ematica, special issue, 1971, 63–71.

    Google Scholar 

  51. M. Novotnÿ, On some relations defined by languages, Prague Studies in Math. Linguistics, 4 (1972), 157–170.

    MathSciNet  Google Scholar 

  52. O. Ore, Galois connections, Trans. Amer. Math. Soc., 55 (1944), 493–513.

    Article  MathSciNet  Google Scholar 

  53. D. Panà, Closure operators and the relation of domination in algebraic linguistics (in Romanian), Studii Cercetâri Matematice, 27, 4 (1975), 461–470.

    MathSciNet  MATH  Google Scholar 

  54. B. H. Partee, A. T. Meulen, R. A. Wall, Mathematical Methods in Linguistics, Kluwer, Dordrecht, 1990.

    MATH  Google Scholar 

  55. Gh. Pâun, Contextual Grammars (in Romanian), Ed. Academiei, Bucuresti, 1982.

    Google Scholar 

  56. Gh. Pâun, Marcus contextual grammars. After 25 years, Bulletin EATCS, 52 (1994), 263–273.

    Google Scholar 

  57. Z. Pawlak, Rough sets, Intern. J. Computer and Information Sciences, 11 (1982), 341–356.

    Article  Google Scholar 

  58. C. J. Pollard, Generalized Structure Grammars, Head Grammars, and Natural Languages, PhD Thesis, Stanford University, California, 1984.

    Google Scholar 

  59. M. Popescu, Sur un modèle linguistico-mathématique du changement du diagnostic, Bull. Math. Soc. Sci. Math. Roumanie, 21, 12 (1977), 113–122.

    MathSciNet  MATH  Google Scholar 

  60. I. I. Revzin, Models of Language (in Russian), Izdatelstvo Akademii Nauk, Moskow, 1962.

    Google Scholar 

  61. I. I. Revzin, The Modeling Method and the Typology of Slavic Languages (in Russian), Nauka, Moskow, 1967.

    Google Scholar 

  62. J. Riguet, Relations binaires, fermetures, correspondences de Galois, Bull. Soc. Math. France, 76 (1948), 114–155.

    Article  MathSciNet  Google Scholar 

  63. W. J. Savitch, Why it might pay to assume that languages are infinite, Annals of Math. and Artificial Intelligence, 8 (1993), 17–25.

    Article  MathSciNet  Google Scholar 

  64. L. Schwartz, On Trybulec domination in algebraic linguistics, Revue Roum. Math. Pures Appl., 17, 3 (1972), 425–433.

    MATH  Google Scholar 

  65. L. Schwartz, Binary relations, Galois connections and topological closure operators (in Romanian), Studii §i Cercetari Matematice, 34, 1 (1982), 73–83.

    MATH  Google Scholar 

  66. D. Schwarz, A general notion of domination relation in algebraic linguistics, Revue Roum. Ling. — Cahiers Ling. Théor. Appl., 13, 1 (1976), 305–313.

    Google Scholar 

  67. M. Semeniuk-Polkowska, Syntactic pseudo-configurations based on Trybulec domination, Revue Roum. Math. Pures Appl., 27, 6 (1982), 709–717.

    MathSciNet  MATH  Google Scholar 

  68. A. Sestier, Contributions à une théorie ensembliste des classifications linguistiques, Actes du Ier Congrès de l’AFCAL, Grenoble, 1960, 293–305.

    Google Scholar 

  69. Ju. A. Shreider, The algebra of binary relations (in Russian). Annex to S. Marcus, Set-Theoretic Models of Languages (in Russian), Nauka, Moskow, 1970.

    Google Scholar 

  70. Ju. A. Shreider, On the O. S. Kulagina concept of derived relation, Computational Linguistics, 9 (1973), 241–253.

    MathSciNet  Google Scholar 

  71. S. Y. Solomon, The n-derivative of a partition, Recueil Linguistique de Bratislava, 4 (1973), 237–243.

    Google Scholar 

  72. L. Tesnière, Elélements de syntaxe structurale, Klincksieck, Paris, 1959.

    Google Scholar 

  73. A. Trybulec, The decomposition of the vocabulary in languages with given paradigms (in Russian), Nauchno Technicheskaja Informacija, 12 (1967), 40–44.

    Google Scholar 

  74. V. A. Uspenskij, On the definition of case by A. N. Kolmogorov, Byulleten Obyedinenija po Problemam Mashinogo Perevoda, 5 (1957), 11–18.

    Google Scholar 

  75. V. A. Uspenskij, On the definition of parts of speech in the set-theoretic system of language (in Russian), ibidem,22–26.

    Google Scholar 

  76. L. Vasilescu, Analyse distributionelle algébrique des substantifs français, Cahiers Ling. Théor. Appl., 10, 2 (1973), 251–259.

    Google Scholar 

  77. L. Vasilescu, Analyse distributionelle algébrique des formes verbales du français, Cahiers Ling. Théor. Appl., 11, 1 (1974), 137–169.

    Google Scholar 

  78. L. Vasilescu, Analyse distributionelle algébrique des formes adjectivales du français, Revue Roum. Ling., 20, 3 (1975), 233–248.

    Google Scholar 

  79. M. Ward, The closure operators of a lattice, Annals of Math., 43, 2 (1942), 191–196.

    Article  MathSciNet  Google Scholar 

  80. L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Solomon Marcus
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Department of Computer Science, University of Colorado at Boulder, Campus 430, 80309, Boulder, CO, USA

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science Data City, FIN-20520, Turku, Finland

    Arto Salomaa

  4. Academy of Finland and Turku Centre for Computer Science (TUCS), Lemninkäisenkatu 14 A, FIN-20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Marcus, S. (1997). Contextual Grammars and Natural Languages. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07675-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-07675-0_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08230-6

  • Online ISBN: 978-3-662-07675-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation