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

**Instructor:**Jakub Szymanik

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.

- Quantifiers and cognitive strategies Slides

- Quantifiers and approximation Slides

- Quantifiers and counting Slides
- Quantifiers and monotonicity Slides
- Polyadic quantifiers and computational complexity Slides

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:

- Dag Westerståhl Generalized Quantifiers, Stanford Encyclopedia of Philosophy
- Hopcroft et al. Introduction to Automata Theory, Languages, and Computation

- Van Benthem, Towards a Computational Semantics, in: Gärdenfors (ed.) `Generalized Quantifiers', pp. 31-37. PDF
- Feigenson et al., Core systems of number, TRENDS in Cognitive
Sciences Vol.8 No.7 July 2004. PDF

- Geurts, Reasoning with quantifiers, Cognition, 86, 2003, pp. 223-251. PDF
- Geurts and Van der Slik, Monotonicity and Processing Load, Journal of Semantics, 22, 2005, pp. 97-117. PDF
- Gierasimczuk and Szymanik, Branching Quantification vs. Two-way Quantification, Journal of Semantics, 26(4), 2009, pp. 329-366. PDF
- Hackl, On the Grammar and Processing of Proportional Quantifiers: Most versus More Than Half, Natural Language Semantics, 17, 2009, pp. 63-98. PDF
- Halberda et al., Multiple spatially-overlapping sets can be
enumerated in parallel, Psychological Science, 17, 2006, pp. 572-576. PDF Demo

- 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

- Just and Carpenter, Comprehension of negation with quantification, Journal of Verbal Learning and Verbal Behavior, 10(3), 1971, pp. 244-253. PDF
- 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

- Kotek et al., A Superlative Reading of Most, presented at PUQL.
- Lidz et al., Interface Transparency and the Psychosemantics of most, Natural Language Semantics, DOI: 10.1007/s11050-010-9062-6. PDF
- McMillan et al., Neural Basis for Generalized Quantifier Comprehension, Neuropsychologia, 43, 2005, pp. 1729-1737. PDF
- Mostowski, Computational Semantics for Monadic Quantifiers, Journal of Applied Non-Classical Logics, 8, 1998, pp. 107-121. PDF
- Pietroski et al., The Meaning of `Most': semantics, numerosity, and psychology, Mind and Language, 24(5), 2009, pp. 554-585. PDF
- Solt, On measurement and quantiﬁcation: The case of most and more than half, manuscript. PDF

- Szymanik, Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language, Linguistics and Philosophy, Vol. 33, Iss. 3, 2010, pp. 215-250. PDF
- Szymanik and Zajenkowski, Comprehension of Simple Quantifiers. Empirical Evaluation of a Computational Model, Cognitive Science, 34(3), 2010, pp. 521-532. PDF
- 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
- 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

- 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

- 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

- Jaap van der Does Lectures on Quantifiers.
- Kevin Paterson's ESSLLI'10 slides on Quantifier Processing.
- Test your Approximate Number Sense
- Stanislas Dehaene's lecture Cerebral Bases of the Number Sense in the Parietal Lobe.
- Larry Moss' ESSLLI'10 lecture slides on Monotonicity Calculus.
- Many related papers can be found on my website, including mydissertation.