Linguistics and Philosophy

, Volume 31, Issue 2, pp 129–209 | Cite as

Donkey pluralities: plural information states versus non-atomic individuals

  • Adrian BrasoveanuEmail author
Research Article


The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e., reference to a quantificational dependency between sets of objects (e.g., atomic/non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (PhD dissertation, University of Amsterdam, 1996), plural discourse reference is modeled as plural information states (i.e., as sets of variable assignments) in a new dynamic system couched in classical type logic that extends Compositional DRT (Muskens, Linguistics and Philosophy, 19, 143–186, 1996). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The idea that plural info states are semantically necessary (in addition to non-atomic individuals) is motivated by relative-clause donkey sentences with multiple instances of singular donkey anaphora that have mixed (weak and strong) readings. At the same time, allowing for non-atomic individuals in addition to plural info states enables us to capture the intuitive parallels between singular and plural (donkey) anaphora, while deriving the incompatibility between singular (donkey) anaphora and collective predicates. The system also accounts for empirically unrelated phenomena, e.g., the uniqueness effects associated with singular (donkey) anaphora discussed in Kadmon (Linguistics and Philosophy, 13, 273–324, 1990) and Heim (Linguistics and Philosophy, 13, 131–177, 1990) among others.


Plurals Anaphora Weak and strong donkey readings Uniqueness effects Compositional dynamic semantics Type logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abusch D. (1994) The scope of indefinites. Natural Language Semantics 2: 83–135CrossRefGoogle Scholar
  2. Asher N., Wang L. (2003) Ambiguity and anaphora with plurals in discourse. In: Young R., Zhou Y. (eds) Proceedings of SALT XIII. CLC Publications, Ithaca, pp 19–36Google Scholar
  3. Barker C. (1996) Presuppositions for proportional quantifiers. Natural Language Semantics 4: 237–259CrossRefGoogle Scholar
  4. Barwise J. (1987) Noun phrases, generalized quantifiers and anaphora. In: Gärdenfors P. (eds) Generalized quantifiers. Kluwer, Dordrecht, pp 1–29Google Scholar
  5. Barwise J., Cooper R. (1981) Generalized quantifiers in natural languages. Linguistics and Philosophy 4: 159–219CrossRefGoogle Scholar
  6. Bäuerle, R., & Egli, U. (1985). Anapher, Nominalphrase und Eselssätze. Papier 105 des Sonderforschungsbereichs 99, Universität Konstanz.Google Scholar
  7. Beaver D., Zeevat H. (2006) Accommodation. In: Ramchand G., Reiss C. (eds) Oxford handbook of linguistic interfaces. Oxford University Press, OxfordGoogle Scholar
  8. Bittner M. (2007) Online update: Temporal, modal and De Se anaphora in polysynthetic discourse. In: Barker C., Jacobson P. (eds) Direct compositionality. Oxford University Press, Oxford, pp 363–404Google Scholar
  9. Brasoveanu, A. (2007). Structured nominal and modal reference. PhD dissertation, Rutgers University.Google Scholar
  10. Brasoveanu, A., & Farkas, D. F. (2008). Exceptional scope as discourse reference to quantificational dependencies. In Proceedings of the 7th International Tbilisi Symposium on Language, Logic and Computation (to appear).Google Scholar
  11. Chierchia G. (1995) The dynamics of meaning. University of Chicago Press, ChicagoGoogle Scholar
  12. Chierchia G. (2001) A puzzle about indefinites. In: Cecchetto C., Chierchia G., Guasti M.T. (eds) Semantic interfaces: Reference, anaphora and aspect. CSLI, Stanford, pp 51–89Google Scholar
  13. Chierchia G. (2006) Broaden your views: Implicatures of domain widening and the “Logicality” of language. Linguistic Inquiry 37: 535–590CrossRefGoogle Scholar
  14. Chomsky N. (1981) Lectures on government and binding. Foris, DordrechtGoogle Scholar
  15. Cooper R. (1979) The interpretation of pronouns. In: Henry F., Schnelle H. (eds) The nature of syntactic representations, syntax and semantics, volume 10 (Selections from the Third Gröningen Round Table). Academic Press, New York, pp 61–92Google Scholar
  16. Dalrymple M., Kanazawa M., Kim Y., McHombo S., Peters S. (1998) Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy 21: 159–210CrossRefGoogle Scholar
  17. Dekker, P. (1993). Transentential meditations: Ups and downs in dynamic semantics. PhD dissertation, University of Amsterdam.Google Scholar
  18. Elbourne P. (2005) Situations and individuals. MIT Press, CambridgeGoogle Scholar
  19. Elworthy D. (1995) A theory of anaphoric information. Linguistics and Philosophy 18: 297–332CrossRefGoogle Scholar
  20. Evans G. (1977) Pronouns, quantifiers and relative clauses (I). The Journal of Canadian Philosophy 7: 467–536Google Scholar
  21. Evans G. (1980) Pronouns. Linguistic Inquiry 11: 337–362Google Scholar
  22. Evans G. (1985) Collected papers. Oxford University Press, OxfordGoogle Scholar
  23. Farkas D.F. et al (1981) Quantifier scope and syntactic islands. In: Hendrik R. (eds) Proceedings of CLS 7. CLC Publications, Ithaca, pp 59–66Google Scholar
  24. Farkas D.F. (2002) Varieties of indefinites. In: Jackson B. (eds) Proceedings of SALT XII. CLC Publications, Ithaca, pp 59–84Google Scholar
  25. Fodor J.D., Sag I. (1982) Referential and quantificational indefinites. Linguistics and Philosophy 5: 355–398CrossRefGoogle Scholar
  26. Gallin, D. (1975). Intensional and higher-order modal logic with applications to Montague semantics. North-Holland Mathematics Studies.Google Scholar
  27. Geurts B. (2002) Donkey business. Linguistics and Philosophy 25: 129–156CrossRefGoogle Scholar
  28. Groenendijk J., Stokhof M. (1991) Dynamic predicate logic. Linguistics and Philosophy 14: 39–100CrossRefGoogle Scholar
  29. Heim, I. (1982). The semantics of definite and indefinite noun phrases. PhD dissertation, UMass Amherst [published in 1988, New York: Garland].Google Scholar
  30. Heim I. (1983) On the projection problem for presuppositions. In: Barlow M., Flickinger D., Wescoat M. (eds) Proceedings of WCCFL 2. Stanford University, Stanford, pp 114–125Google Scholar
  31. Heim I. (1990) E-type pronouns and donkey anaphora. Linguistics and Philosophy 13: 137–177CrossRefGoogle Scholar
  32. Heim I. (1991) Artikel und Definitheit. In: Stechow A., Wunderlich D. (eds) Semantik: Ein internationales Handbuch der zeitgenössischen Forschung. Walter de Gruyter, BerlinGoogle Scholar
  33. Heim I., Kratzer A. (1998) Semantics in generative grammar. Blackwell, OxfordGoogle Scholar
  34. Kadmon, N. (1987). On unique and non-unique reference and asymmetric quantification. PhD dissertation, UMass Amherst.Google Scholar
  35. Kadmon N. (1990) Uniqueness. Linguistics and Philosophy 13: 273–324CrossRefGoogle Scholar
  36. Kamp H. (1981) A theory of truth and semantic representation. In: Groenendijk J., Janssen T., Stokhof M. (eds) Formal methods in the study of language, Part 1. Mathematical Center, Amsterdam, pp 277–322Google Scholar
  37. Kamp H., Reyle U. (1993) From discourse to logic. Introduction to model-theoretic semantics of natural language, formal logic and discourse representation theory. Kluwer, DordrechtGoogle Scholar
  38. Kanazawa M. (1994) Weak vs. strong readings of donkey sentences and monotonicity inference in a dynamic setting. Linguistics and Philosophy 17: 109–158CrossRefGoogle Scholar
  39. Kanazawa, M. (1994b). Dynamic generalized quantifiers and monotonicity. In M. Kanazawa & C. Pinón (Eds.), Dynamics, polarity and quantification (pp. 213–249). CSLI Lecture Notes 48. Stanford: CSLI.Google Scholar
  40. Kanazawa M. (2001) Singular donkey pronouns are semantically singular. Linguistics and Philosophy 24: 383–403CrossRefGoogle Scholar
  41. Karttunen L. (1976) Discourse referents. In: McCawley J.D. (eds) Syntax and semantics, volume 7: Notes from the linguistic underground. Academic Press, New York, pp 363–385Google Scholar
  42. Karttunen L., Peters S. (1979) Conventional implicature. In: Oh C.-K., Dineen D.A. (eds) Syntax and semantics: Presupposition Vol. 11. Academic Press, London, pp 1–56Google Scholar
  43. Kratzer A. (1998) Scope or pseudo-scope: Are there wide-scope indefinites?. In: Rothstein S. (eds) Events in grammar. Kluwer, Dordrecht, pp 163–196Google Scholar
  44. Krifka M. (1996) Pragmatic strengthening in plural predications and donkey sentences. In: Galloway T., Spence J. (eds) Proceedings from SALT VI. CLC Publications, Ithaca, pp 136–153Google Scholar
  45. Krifka M. (1996) Parametric sum individuals for plural anaphora. Linguistics and Philosophy 19: 555–598CrossRefGoogle Scholar
  46. Lappin S., Francez N. (1994) E-type pronouns, i-sums and donkey anaphora. Linguistics and Philosophy 17: 391–428CrossRefGoogle Scholar
  47. Lewis D. (1975) Adverbs of quantification. In: Keenan E. (eds) Formal semantics of natural language. Cambridge University Press, Cambridge, pp 3–15Google Scholar
  48. Link G. (1983) The logical analysis of plurals and mass terms: A lattice-theoretical approach. In: Bäuerle R., Schwarze C., Stechow A. (eds) Meaning, use and interpretation of language. Walter de Gruyter, Berlin, pp 302–323Google Scholar
  49. May, R. (1977). The grammar of quantification. PhD dissertation, MIT.Google Scholar
  50. Moltmann F. (2006) Unbound anaphoric pronouns: E-type, dynamic and structured-propositions approaches. Synthese 153(2): 199–260CrossRefGoogle Scholar
  51. Montague R. (1974) The proper treatment of quantification in ordinary English. In: Thomason R. (eds) Formal philosophy. Selected papers of Richard Montague. Yale University Press, New Haven, pp 247–270Google Scholar
  52. Muskens R. (1995) Tense and the logic of change. In: Egli U., Pause P., Schwarze C., Stechow A., Wienold G. (eds) Lexical knowledge in the organisation of language. Benjamins, Amsterdam, Philadelphia, pp 147–183Google Scholar
  53. Muskens R. (1996) Combining Montague semantics and discourse representation. Linguistics and Philosophy 19: 143–186CrossRefGoogle Scholar
  54. Muskens, R. (2005). Natural language semantics, ESSLLI 17th course notes, Edinburgh. Available at http://let.uvt.hl/general/people/rmuskas/courses.htm.
  55. Neale S. (1990) Descriptions. MIT Press, CambridgeGoogle Scholar
  56. Nouwen, R. (2003). Plural pronominal anaphora in context. PhD dissertation, Utrecht University, LOT Dissertation Series 84.Google Scholar
  57. Parsons, T. (1978). Pronouns as paraphrases, UMass Amherst, ms.Google Scholar
  58. Partee B., Rooth M. (1983) Generalized conjunction and type ambiguity. In: Bauerle R., Schwartze C., Stechow A. (eds) Meaning, use and interpretation of language. Walter de Gruyter, Berlin, pp 361–383Google Scholar
  59. Pelletier F.J., Schubert L.K. (1989) Generically speaking or using Discourse Representation Theory to interpret generics. In: Chierchia G., Partee B.H., Turner R. (eds) Properties, types and meanings, Vol. 2. Kluwer, Dordrecht, pp 193–268Google Scholar
  60. Peters S., Westerståhl D. (2006) Quantifiers in language and logic. Oxford University Press, Oxford & New YorkGoogle Scholar
  61. Reinhart T. (1997) Quantifier scope: How labor is divided between QR and choice functions. Linguistics and Philosophy 20: 335–397CrossRefGoogle Scholar
  62. Roberts C. (2003) Uniqueness in definite noun phrases. Linguistics and Philosophy 26: 287–350CrossRefGoogle Scholar
  63. Rooth M. (1987) Noun phrase interpretation in Montague grammar, file change semantics and situation semantics. In: Gärdenfors P. (eds) Generalized quantifiers. Kluwer, Dordrecht, pp 237–268Google Scholar
  64. Sauerland U. (2003) A new semantics for number. In: Young R., Zhou Y. (eds) Proceedings of SALT XIII. CLC Publications, Ithaca, pp 258–275Google Scholar
  65. Scha, R. (1981). Distributive, collective and cumulative quantification. In J. Groenendijk, T. Janssen & M. Stokhof (Eds.), Formal methods in the study of language, Part 2 (pp. 483–512). Mathematical Centre Tracts 136, University of Amsterdam.Google Scholar
  66. Schein, B. (2003). Adverbial, descriptive reciprocals. In J. Hawthorne (Ed.), Language & philosophical linguistics, philosophical perspectives 17.1 (pp. 333–367).Google Scholar
  67. Schwarzschild R. (1992) Types of plural individuals. Linguistics and Philosophy 15: 641–675CrossRefGoogle Scholar
  68. Schwarzschild R. (1996) Pluralities. Springer, Dordrecht/Boston/LondonGoogle Scholar
  69. Schwarzschild R. (2002) Singleton indefinites. Journal of Semantics 19: 289–314CrossRefGoogle Scholar
  70. Steedman, M. (2007). Surface-compositional scope-alternation without existential quantifiers. University of Edinburgh ms.Google Scholar
  71. Stone M. (1992) Or and anaphora. In: Barker C., Dowty D. (eds) Proceeding of SALT II (OSU Working papers in linguistics 40). OSU, Columbus, pp 367–385Google Scholar
  72. van den Berg, M. (1994). A direct definition of generalized dynamic quantifiers. In P. Dekker & M. Stokhof (Eds.), Proceedings of the 9th Amsterdam Colloquium. ILLC/Department of Philosophy, University of Amsterdam.Google Scholar
  73. van den Berg, M. (1996). Some aspects of the internal structure of discourse. The dynamics of nominal anaphora. PhD dissertation, University of Amsterdam.Google Scholar
  74. van der Does, J. (1993). The dynamics of sophisticated laziness. ILLC, University of Amsterdam, ms.Google Scholar
  75. van der Sandt R. (1992) Presupposition projection as anaphora resolution. Journal of Semantics 9: 333–377CrossRefGoogle Scholar
  76. van Eijck J., de Vries F.-J. (1992) Dynamic interpretation and Hoare deduction. Journal of Logic, Language and Information 1: 1–44CrossRefGoogle Scholar
  77. von Fintel, K. (1994). Restrictions on quantifier domains. PhD dissertation, UMass Amherst.Google Scholar
  78. Winter Y. (1997) Choice functions and the scopal semantics of indefinites. Linguistics and Philosophy 20: 399–467CrossRefGoogle Scholar
  79. Winter Y. (2000) Distributivity and dependency. Natural Language Semantics 8: 27–69CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.University of California, Santa CruzSanta CruzUSA

Personalised recommendations