Journal of Logic, Language and Information

, Volume 23, Issue 1, pp 53–81 | Cite as

On the Identification of Quantifiers’ Witness Sets: A Study of Multi-quantifier Sentences



Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets involved. Two kinds of maximization have been proposed in the literature: ‘Local’ and ‘Global’ maximization. In this paper, we present an online questionnaire whose results appear to support Local maximization. The latter seems to capture the proper interplay between the semantics and the pragmatics of multi-quantifier sentences, provided that witness sets are selected on pragmatic grounds.


  1. Alshawi, H. (1992). The core language engine. Cambridge, MA: MIT Press.Google Scholar
  2. Beck, S., & Sauerland, U. (2000). Cumulation is needed: A reply to winter (2000). Natural Language Semantics, 4(8), 349–371.CrossRefGoogle Scholar
  3. Brasoveanu, A. (2012). Modified numerals as post-suppositions. Journal of Semantics, 30(1).Google Scholar
  4. Cooper, R. (1983). Quantification and syntactic theory. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  5. Dalrymple, M., Kanazawa, M., Kim, Y., Mchombo, S., & Peters, S. (1998). Reciprocal expressions and the concept of reciprocity. Linguistics and Philosophy, 21, 159–210.CrossRefGoogle Scholar
  6. Diesing, M. (1992). Indefinites. Cambridge, MA: MIT Press.Google Scholar
  7. Geurts, B., & van der Silk, F. (2005). Monotonicity and processing load. The Journal of Semantics, 22(17).Google Scholar
  8. Gierasimczuk, N., & Szymanik, J. (2009). Branching quantification versus two-way quantification. The Journal of Semantics, 4(26), 329–366.Google Scholar
  9. Hackl, M. (2009). On the grammar and processing of proportional quantifiers: Most versus more than half. Natural Language Semantics, 17(1), 63–98.CrossRefGoogle Scholar
  10. Heim, I. (1982). The semantics of definite and indefinite noun phrases. Ph.D. thesis, University of Massachusetts, Amherst.Google Scholar
  11. Kamp, H., & Reyle, U. (1993). From discourse to logic: An introduction to modeltheoretic semantics, formal logic and discourse representation theory. Dordrecht: Kluwer Academic Publishers.Google Scholar
  12. Keller, W. (1988). Nested cooper storage: The proper treatment of quantification in ordinary noun phrases. In U. Reyle & C. Rohrer (Eds.), Natural language parsing and linguistic theories (pp. 432–447). Dordrecht: Reidel.CrossRefGoogle Scholar
  13. Kontinen, J., & Szymanik, J. (2008). A remark on collective quantification. Journal of Logic, Language and Information, 17(2), 131–140.CrossRefGoogle Scholar
  14. Kontinen, J., & Szymanik, J. (2011). Characterizing definability of second-order generalized quantifiers. In: L.D. Beklemishev & R. de Queiroz (Eds.) Proceedings of the 18th workshop on logic, language, information and computation, volume 6642 of lecture notes in computer science (pp 187–200). Berlin. Springer. A journal version will appear in Journal of Computer and System Sciences WoLLIC 2011 special issue.Google Scholar
  15. Krasikova, S. (2011). Definiteness in superlatives. In M. Aloni, V. Kimmelman, F. Roelofsen, G. Sassoon, K. Schulz, & M. Westera (Eds.), Amsterdam colloquium on logic, language and meaning, volume 7218 of lecture notes in computer science (pp. 411–420). Berlin: Springer.Google Scholar
  16. Kratzer, A. (2007). On the plurality of verbs. In J. Dolling & T. Heyde-Zybatow (Eds.), Event Structures in linguistic form and interpretation. Berlin: Mouton de Gruyter.Google Scholar
  17. Landman, F. (1998). Plurals and maximalization. In S. Rothstein (Ed.), Events and grammar (pp. 237–272). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  18. Landman, F. (2000). Events and plurality: The Jerusalem lectures. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  19. Link, G. (1983). The logical analysis of plurals and mass terms. In: R. Bauerle, C. Schwarze, & A. von Stechow (Eds.) CSLI lecture notes, editor, meaning, use, and interpretation in language (pp. 302-323). Berlin: de Gruyter.Google Scholar
  20. May, R. (1985). Logical form: Its structure and derivation. Cambridge: MIT Press.Google Scholar
  21. Montague, R. (1974). The proper treatment of quantification in ordinary English. In R. Thomason (Ed.), Formal philosophy: Selected papers of Richard Montague (pp. 247–270). New Haven: Yale University Press.Google Scholar
  22. Mostowski, M., & Szymanik, J. (2012). Semantic bounds for everyday language. Semiotica, 188(1–4), 363–372.Google Scholar
  23. Neale, S. (1990). Descriptions. Cambridge: MIT Press.Google Scholar
  24. Peters, S., & Westerståhl, D. (2006). Quantifiers in language and logic. Oxford: Oxford University Press.Google Scholar
  25. Reimer, M. (1998). Quantification and context. Linguistics and philosophy, 21(1), 95–115.CrossRefGoogle Scholar
  26. Robaldo, L. (2010a). Independent set readings and generalized quantifiers. The Journal of Philosophical Logic, 39(1), 23–58.CrossRefGoogle Scholar
  27. Robaldo, L. (2010b). Interpretation and inference with maximal referential terms. The Journal of Computer and System Sciences, 76(5), 373–388.CrossRefGoogle Scholar
  28. Robaldo, L. (2011). Distributivity, collectivity, and cumulativity in terms of (in)dependence and maximality. The Journal of Logic, Language, and Information, 20(2), 233–271.CrossRefGoogle Scholar
  29. Sanford, A. J., Moxey, L. M., & Paterson, K. (1994). Psychological studies of quantifiers. The Journal of Semantics, 11(3), 153–170.CrossRefGoogle Scholar
  30. Scha, R. (1981). Distributive, collective and cumulative quantification. In: J. Groenendijk, T. Janssen, & M. Stokhof (Eds.) CSLI Lecture Notes, editor, formal methods in the study of language, part 2 (pp. 483–512). Mathematisch Centrum: Amsterdam.Google Scholar
  31. Schein, B. (1993). Plurals and events. Cambridge, MA: MIT Press.Google Scholar
  32. Schwarzschild, R. (1996). Pluralities. Dordrecht: Kluwer.CrossRefGoogle Scholar
  33. Sher, G. (1990). Ways of branching quantifiers. Linguistics and Philosophy, 13, 393–422.CrossRefGoogle Scholar
  34. Sher, G. (1997). Partially-ordered (branching) generalized quantifiers: A general definition. The Journal of Philosophical Logic, 26, 1–43.CrossRefGoogle Scholar
  35. Spaan, M. (1996). Parallel quantification. Quantifiers, logic, and language (Vol. 54, pp. 281–309). Stanford: CSLI Publications.Google Scholar
  36. Stanley, J., & Szabò, Z. (2000). On quantifier domain restriction. Mind and Language, 15, 219261.Google Scholar
  37. Steedman, M. (2012). Taking scope: The natural semantics of quantifiers. Cambridge, MA: MIT Press.Google Scholar
  38. Szabolcsi, A. (2013). Compositionality without word boundaries: (The) more and (the) most. In: Proceedings of SALT (Vol. 22).Google Scholar
  39. Szymanik, J. (2009). Quantifiers in TIME and SPACE. Computational complexity ofgeneralized quantifiers in natural language. Ph.D. thesis, University of Amsterdam, Amsterdam.Google Scholar
  40. Szymanik, J., & Zajenkowski, M. (2009). Comprehension of simple quantifiers empirical evaluation of a computational model. Cognitive Science: A Multidisciplinary Journal.Google Scholar
  41. Szymanik, J. (2010). Computational complexity of polyadic lifts of generalized quantifiers in natural language. Linguistics and Philosophy, 33, 215–250.CrossRefGoogle Scholar
  42. Szymanik, J., & Zajenkowski, M. (2013). Monotonicity has only a relative effect on the complexity of quantifier verification. In: F. Roelofsen, M. Aloni, & M. Franke (Eds.) Proceedings of the 19th Amsterdam Colloquium (pp. 219–225).Google Scholar
  43. van Benthem, J. (1986). Essays in logical semantics. Dordrecht: Reidel.CrossRefGoogle Scholar
  44. van der Does, J. (1993). Sums and quantifiers. Linguistics and Philosophy, 16, 509–550.CrossRefGoogle Scholar
  45. Winter, Y. (2001). Flexibility principles in boolean semantics: Coordination, plurality, and scope in natural language. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of TurinTurinItaly
  2. 2.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherland
  3. 3.Institute of Artificial IntelligenceUniversity of GroningenGroningenThe Netherland

Personalised recommendations