David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Linguistics and Philosophy 33 (3):215-250 (2010)
We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science.
|Keywords||generalized quantifiers computational complexity theory polyadic quantification multi quantifier sentences Stron Meaning Hypothesis|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Kent Bach (1982). Semantic Nonspecificity and Mixed Quantifiers. Linguistics and Philosophy 4 (4):593 - 605.
Jon Barwise & Robin Cooper (1981). Generalized Quantifiers and Natural Language. Linguistics and Philosophy 4 (2):159--219.
Sigrid Beck (2000). The Semantics of Different: Comparison Operator and Relational Adjective. [REVIEW] Linguistics and Philosophy 23 (2):101-139.
Gilad Ben-Avi & Yoad Winter (2003). Monotonicity and Collective Quantification. Journal of Logic, Language and Information 12 (2):127-151.
A. Blass & Y. Gurevich (1986). Henkin Quantifiers and Complete Problems. Annals of Pure and Applied Logic 32:1--16.
Citations of this work BETA
Sivan Sabato & Yoad Winter (2012). Relational Domains and the Interpretation of Reciprocals. Linguistics and Philosophy 35 (3):191-241.
Cédric Dégremont, Lena Kurzen & Jakub Szymanik (2012). Exploring the Tractability Border in Epistemic Tasks. Synthese (3):1-38.
Similar books and articles
Jakub Szymanik & Marcin Zajenkowski (2009). Comprehension of Simple Quantifiers. Empirical Evaluation of a Computational Model. Cognitive Science: A Multidisciplinary Journal 34 (3):521-532.
Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Oliver Bott, Fabian Schlotterbeck & Jakub Szymanik (forthcoming). Interpreting Tractable Versus Intractable Reciprocal Sentences. In Proceedings of the International Conference on Computational Semantics.
Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
Marcin Mostowski & Jakub Szymanik (2007). Computational Complexity of Some Ramsey Quantifiers in Finite Models. Bulletin of Symbolic Logic 13:281--282.
Jakub Szymanik (2010). Almost All Complex Quantifiers Are Simple. In C. Ebert, G. Jäger, M. Kracht & J. Michaelis (eds.), Mathematics of Language 10/11, Lecture Notes in Computer Science 6149. Springer.
Jakub Szymanik & Marcin Zajenkowski (2009). Improving Methodology of Quantifier Comprehension Experiments. Neuropsychologia 47 (12):2682--2683.
Jakub Szymanik (2009). The Computational Complexity of Quantified Reciprocals. In Peter Bosch, David Gabelaia & Jérôme Lang (eds.), Lecture Notes on Artificial Intelligence 5422, Logic, Language, and Computation 7th International Tbilisi Symposium on Logic, Language, and Computation. Springer.
Jakub Szymanik (2009). Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. Dissertation, University of Amsterdam
Added to index2010-04-03
Total downloads24 ( #71,597 of 1,100,944 )
Recent downloads (6 months)3 ( #115,721 of 1,100,944 )
How can I increase my downloads?