Generalized Quantifier Theory Meets Cognition

[ Course description | Lectures | Schedule | Literature | Additional Materials | Related Courses ]

European Summer School in Logic, Language, and Information

Ljubljana, Slovenia

August 8-12, 2011 (second week)

Time: 17-18.30

Instructor:Jakub Szymanik

Course description:

Animals are able to count and represent quantities, but reasoning with linguistic expressions of (relative) quantities (known as quantifiers) seems a uniquely human ability. We can understand, for example, sentences such as “Most linguists are logicians”, “Less than half of the cognitive neuroscientists are computer scientists”, and “At least 3 of the applicants are psychologists.” We can also assess the conditions that make such sentences true or false. While the cognitive bases of counting and quantity representations have been extensively studied (see, e.g., Dehaene 1999), the cognitive processing of linguistically expressed quantities is far from being understood. Quantifier expressions occur whenever we describe the world, and communicate about it. Generalized quantifier theory studies the possible meanings and the inferential power of quantifier expressions by logical means. The classical version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Until now, advances in "classical" generalized quantifier theory mainly focused on definability questions and their applications to linguistics (see Peters and Westerståhl 2006 for an overview). However, generalized quantifiers have been also studied from psychological perspective (see, e.g., Moxey and Sanford 1993; Clark 1976). The lectures will survey some of the recently established links between generalized quantifier theory and cognitive science. In particular, we will be concerned with extending generalized quantifier theory with computational aspects in order to draw and empirically test psycholinguistic predictions. One major focus will be computational complexity and its interplay with "difficulty" as experienced by subjects asked to verify quantifier sentences.


There will be 5 lectures covering topics on the intersection of generalized quantifier theory and psycholinguistics. We will discuss various cognitive strategies triggered by quantifiers (e.g., precise counting and approximation), computational complexity of various quantifier constructions, cognitive difficulty of quantifier processing, and reasoning with quantifiers.

  1. Quantifiers and cognitive strategies Slides
  2. Quantifiers and approximation Slides
  3. Quantifiers and counting Slides
  4. Quantifiers and monotonicity Slides
  5. Polyadic quantifiers and computational complexity Slides
The participants can in advance consult the slides from a similar course I taught in Stockholm.

It is an advanced course assuming some familiarity with formal semantics, basics of automata (finite and puh-down machines) and computational complexity theory (P vs. NP). If you are not familiar with those topics the following will be especially helpful:
The following papers will be discussed in the course:


  1. Van Benthem, Towards a Computational Semantics, in: Gärdenfors (ed.) `Generalized Quantifiers', pp. 31-37. PDF
  2. Feigenson et al., Core systems of number, TRENDS in Cognitive Sciences Vol.8 No.7 July 2004.  PDF
  3. Geurts, Reasoning with quantifiers, Cognition, 86, 2003, pp. 223-251. PDF
  4. Geurts and Van der Slik, Monotonicity and Processing Load, Journal of Semantics, 22, 2005, pp. 97-117. PDF
  5. Gierasimczuk and Szymanik, Branching Quantification vs. Two-way Quantification, Journal of Semantics, 26(4), 2009, pp. 329-366. PDF
  6. Hackl, On the Grammar and Processing of Proportional Quantifiers: Most versus More Than Half, Natural Language Semantics, 17, 2009, pp. 63-98. PDF
  7. Halberda et al., Multiple spatially-overlapping sets can be enumerated in parallel, Psychological Science, 17, 2006, pp. 572-576. PDF Demo
  8. Halberda et al., The Development of `Most' Comprehension and Its Potential Dependence on Counting Ability in Preschoolers, Language Learning and Development, 4(2), 2008, pp. 99-121. PDF Demo
  9. Just and Carpenter, Comprehension of negation with quantification, Journal of Verbal Learning and Verbal Behavior, 10(3), 1971, pp. 244-253. PDF
  10. Koster-Moeller et al., Verification Procedures for Modified Numeral Quantifiers, Proceedings of the 27th West Coast Conference on Formal Linguistics, ed. Natasha Abner and Jason Bishop, pp. 310-317. PDF
  11. Kotek et al., A Superlative Reading of Most, presented at PUQL.
  12. Lidz et al., Interface Transparency and the Psychosemantics of most, Natural Language Semantics, DOI: 10.1007/s11050-010-9062-6. PDF
  13. McMillan et al., Neural Basis for Generalized Quantifier Comprehension, Neuropsychologia, 43, 2005, pp. 1729-1737. PDF
  14. Mostowski, Computational Semantics for Monadic Quantifiers, Journal of Applied Non-Classical Logics, 8, 1998, pp. 107-121. PDF
  15. Pietroski et al., The Meaning of `Most': semantics, numerosity, and psychology, Mind and Language, 24(5), 2009, pp. 554-585. PDF
  16. Solt, On measurement and quantification: The case of most and more than half, manuscript. PDF
  17. Szymanik, Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language,  Linguistics and Philosophy, Vol. 33, Iss. 3, 2010, pp. 215-250. PDF
  18. Szymanik and Zajenkowski, Comprehension of Simple Quantifiers. Empirical Evaluation of a Computational Model, Cognitive Science, 34(3), 2010, pp. 521-532. PDF
  19. Szymanik and Zajenkowski, Quantifiers and Working Memory, Lecture Notes in Artificial Intelligence 6042, M. Aloni and K. Schulz (Eds.), Springer, 2010, pp. 456-464. PDF
  20. Tanenhaus et al., Sentence-Picture Verification Models as Theories of Sentence Comprehension: A Critique of Carpenter and Just, Psychological Review 1976, Vol. 83. No. 4, pp. 310-317. PDF
  21. Tomaszewicz, Verification Strategies for Two Majority Quantifiers in Polish, In Reich, Ingo et al. (eds.), Proceedings of Sinn & Bedeutung 15, Saarland Unversity Press: Saarbrücken, Germany, 2011. PDF
  22. Zajenkowski, Styla, and Szymanik. A Computational Approach to Quantifiers as an Explanation for Some Language Impairments in Schizophrenia, Journal of Communication Disorder, accepted. PDF. Presented at PUQL

Additional Materials:

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