Skip to main content

Semantics with Dependent Types for Indefinites Cover

.blurhash-client-img { display: none !important; }

Semantics with Dependent Types for Indefinites

Studies in Logic, Grammar and Rhetoric

Volume 46 (2016): Issue 1 (September 2016)

By: Justyna Grudzińska

Open Access

|Nov 2016

Abstract

The paper proposes a new semantics with dependent types for indefinites, encompassing both the data related to their exceptional scopal behavior and the data related to their anaphoric (dynamic) properties. The proposal builds on the formal system combining generalized quantifiers ([Mostowski 1957], [Lindström 1966]) with dependent types ([Martin-Löf 1972], [Makkai 1995]) in [Grudzińska & Zawadowski 2014] and [Grudzińska & Zawadowski 2016].

References

Abusch, Dorit (1994), The Scope of Indefinites. Natural Language Semantics 2. 83–135.10.1007/BF01250400
Search in Google Scholar Back to article
Barwise, Jon & Robin Cooper (1981), Generalized Quantifiers and Natural Language. Linguistics & Philosophy 4. 159-219.10.1007/BF00350139
Search in Google Scholar Back to article
Bekki, Daisuke (2014). Representing anaphora with dependent types. In Asher, N., Soloviev, S. (eds.) Logical Aspects of Computational Linguistics, Lecture Notes in Computer Science, vol. 8535, Springer. 14–29.10.1007/978-3-662-43742-1_2
Search in Google Scholar Back to article
Brasoveanu, Adrian (2008), Donkey Pluralities: Plural Information States Versus Non-Atomic Individuals. Linguistics & Philosophy 31(2). 129–209.10.1007/s10988-008-9035-0
Search in Google Scholar Back to article
Brasoveanu, Adrian & Donka F. Farkas (2011), How indefinites choose their scope. Linguistics & Philosophy 34. 1–5510.1007/s10988-011-9092-7
Search in Google Scholar Back to article
Chierchia, Gennaro (1992), Anaphora and dynamic binding. Linguistics & Philosophy 15(2). 111–83.10.1007/BF00635805
Search in Google Scholar Back to article
Chierchia, Gennaro, (2001), a Puzzle about Indefinites. In Carlo Cecchetto, Gennaro Chierchia, and Maria Teresa Guasti (eds.), Semantic Interfaces: Reference, Anaphora, and Aspect. CSLI, Stanford. 51–89.
Search in Google Scholar Back to article
Church, Alonzo (1940), a formulation of the simple theory of types. Journal of Symbolic Logic 5(1). 56–68.10.2307/2266170
Search in Google Scholar Back to article
Cooper, Robin (1979), The interpretation of pronouns. In Heny F., Schnelle H. (eds.), Syntax and Semantics 10, New York, Academic Press. 61–92.
Search in Google Scholar Back to article
Cooper, Robin (2004), Dynamic generalised quantifiers and hypothetical contexts. In Ursus Philosophicus, a festschrift for Björn Haglund, Department of Philosophy, Göteborg University.
Search in Google Scholar Back to article
Dekker, Paul (1994), Predicate logic with anaphora. In Lynn Santelmann and Mandy Harvey (eds.), Proceedings SALT IX. Ithaca, NY: DMLL Publications, Cornell University. 79–95.10.3765/salt.v4i0.2459
Search in Google Scholar Back to article
Dekker, Paul (2008), A multi-dimensional treatment of quantification in extraordinary English. Linguistics & Philosophy (1). 101–127.10.1007/s10988-008-9034-1
Search in Google Scholar Back to article
Dobrovie-Sorin, C. & C. Beyssade 2012, Redefining Indefinites. Berlin, Springer.10.1007/978-94-007-3002-1
Search in Google Scholar Back to article
Endriss, Cornelia (2009), Quantificational Topics a Scopal Treatment of Exceptional Wide Scope Phenomena. Studies in Linguistics & Philosophy, Berlin, Springer.10.1007/978-90-481-2303-2_4
Search in Google Scholar Back to article
Farkas, Donka (1981), Quantifier Scope and Syntactic Islands. CLS 17. 59–66.
Search in Google Scholar Back to article
Fernando, Tim (2001). Conservative generalized quantifiers and presupposition. Proceedings SALT XI. Ithaca, NY: DMLL Publications, Cornell University. 172–191.
Search in Google Scholar Back to article
Fodor, Janet & Ivan Sag (1982) Referential and Quantificational Indefinites. Linguistics & Philosophy 5. 355–398.10.1007/BF00351459
Search in Google Scholar Back to article
Geurts, Bart & Rob van der Sandt (1999), Domain Restriction. In P. Bosch & R. A. van der Sandt (eds.), Focus: Linguistic, Cognitive, and Computational Perspectives, Cambridge UP, Cambridge. 268–292.
Search in Google Scholar Back to article
Groenendijk, Jeroen & Martin Stokhof (1984), Studies on the Semantics of Questions and the Pragmatics of Answers, PhD thesis, Amsterdam, University of Amsterdam.
Search in Google Scholar Back to article
Groenendijk, Jeroen & Martin Stokhof (1991), Dynamic Predicate Logic. Linguistics & Philosophy 14. 39-100.10.1007/BF00628304
Search in Google Scholar Back to article
Grudzińska, Justyna (2015), Deskrypcje nieokreślone, Wydawnictwo Naukowe Semper, Warszawa.
Search in Google Scholar Back to article
Grudzińska, Justyna & Marek Zawadowski (2014), System with Generalized Quantifiers on Dependent Types for Anaphora. In R. Cooper, S. Dobnik, S. Lappin, S. Larsson (eds.), Proceedings of the EACL 2014 Workshop on Type Theory and Natural Language Semantics. 10-18.10.3115/v1/W14-1402
Search in Google Scholar Back to article
Grudzińska, Justyna & Marek Zawadowski (2016), Generalized Quantifiers on Dependent Types: a System for Anaphora, to appear. In S. Chatzikyriakidis and Z. Luo (eds.), Type-Theoretical Semantics: Current Perspectives, Studies in Linguistics and Philosophy, Springer.10.1007/978-3-319-50422-3_5
Search in Google Scholar Back to article
Hintikka, Jaakko (1986), The Semantics of a certain. Linguistic Inquiry 17 (2). 331–336.
Search in Google Scholar Back to article
Ionin, Tania (2010), The scope of indefinites: an experimental investigation. Nat Lang Semantics 18. 295–350.10.1007/s11050-010-9057-3
Search in Google Scholar Back to article
Kadmon, Nirit (1987), On unique and Non-unique reference and Asymmetric Quantification. Ph.D. diss, University of Massachusetts, Amherst.
Search in Google Scholar Back to article
Kamp, Hans (1981), a theory of truth and semantic representation. In J. Groenendijk, T. Janssen & M. Stokhof (eds.), Truth, Interpretation and Information, Foris Dordrecht. 1-41.
Search in Google Scholar Back to article
Kamp, Hans & Uwe Reyle (1993), From Discourse to Logic. Kluwer Academic Publishers, Dordrecht.10.1007/978-94-017-1616-1
Search in Google Scholar Back to article
Kratzer, Angelika (1998), Scope or Pseudoscope? Are there Wide-Scope Indefinites? In S. Rothstein (ed), Events and Grammar. Kluwer Academic Publishers, Dordrecht. 163–196.10.1007/978-94-011-3969-4_8
Search in Google Scholar Back to article
Lindström, Per (1966), First-order predicate logic with generalized quantifiers, Theoria 32. 186-95.
Search in Google Scholar Back to article
Makkai, Michael (1995), First Order Logic with Dependent Sorts, with Applications to Category Theory, preprtint McGill University.
Search in Google Scholar Back to article
Lappin Shalom & Francez, Nissim (1994), E-type pronouns, I-sums, and Donkey anaphora. Linguistics & Philosophy 17. 391–428.10.1007/BF00985574
Search in Google Scholar Back to article
Luo, Zhaohui (2012), Formal Semantics in Modern Type Theories with Coercive Subtyping. Linguistics & Philosophy 35. 491–513.10.1007/s10988-013-9126-4
Search in Google Scholar Back to article
Luo, Zhaohui (2012), Common nouns as types. LACL’12, LNCS 7351. 173–185.10.1007/978-3-642-31262-5_12
Search in Google Scholar Back to article
Martin-Löf, Per (1972), An intuitionstic theory of types, Technical Report, University of Stockholm.
Search in Google Scholar Back to article
Martin-Löf, Per (1984), Intuitionistic Type Theory, Bibliopolis.
Search in Google Scholar Back to article
Matthewson, Lisa (1999), On the Interpretation of Wide-scope Indefinites, Natural Language Semantics 7. 79-134.
Search in Google Scholar Back to article
Montague, Richard (1974), Formal Philosophy. Yale University Press.
Search in Google Scholar Back to article
Mostowski, Andrzej (1957), On a generalization of quantifiers, Fundamenta Mathematicae 44. 12-36.
Search in Google Scholar Back to article
Ranta, Aarne (1994), Type-Theoretical Grammar, Oxford University Press, Oxford.10.1093/oso/9780198538578.001.0001
Search in Google Scholar Back to article
Reinhart, Tanya (1997), Quantifier Scope: How Labour is divided between QR and Choice Functions. Linguistics & Philosophy 20. 335-397.10.1023/A:1005349801431
Search in Google Scholar Back to article
Ruys, Eddy (1992), The Scope of Indefinites, PhD thesis, Utrecht University.
Search in Google Scholar Back to article
Schwarzschild, Roger (2002), Singleton Indefinites. Journal of Semantics 19. 289–314.10.1093/jos/19.3.289
Search in Google Scholar Back to article
Steedman, Mark (2012), Taking Scope. The Natural Semantics of Quantifiers, The MIT Press, Cambridge.10.7551/mitpress/9780262017077.001.0001
Search in Google Scholar Back to article
Szabolcsi, Anna (1997), Background notions in lattice theory and generalized quantifiers. In Anna Szabolcsi (ed.), Ways of scope taking. Kluwer Academic Publishers, Dordrecht. 1–27.10.1007/978-94-011-5814-5_1
Search in Google Scholar Back to article
Szabolcsi, Anna (2010), Quantification. Cambridge University Press, Cambridge.10.1017/CBO9780511781681
Search in Google Scholar Back to article
Van den Berg, Martin H. (1996), The Internal Structure of Discourse, Ph.D. thesis, Universiteit van Amsterdam, Amsterdam.
Search in Google Scholar Back to article
Wang, Linton, Eric McCready & Nicholas Asher (2006), Information dependency in quantificational subordination. In K. von Heusinger & K. Turner (eds.), Where semantics meets pragmatics. Elsevier, Amsterdam. 268–304.10.1163/9780080462608_016
Search in Google Scholar Back to article
Winter, Yoad (1997), Choice Functions and the Scopal Semantics of Indefinites. Linguistics & Philosophy 20. 399-467.10.1023/A:1005354323136
Search in Google Scholar Back to article
Zawadowski, Marek (1989), Formalization of the feature system in terms of preorders. In I. Bellert, Feature System for Quantification Structures in Natural Language. Dordrecht, Foris. 155-175.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/slgr-2016-0039 | Journal eISSN: 2199-6059 | Journal ISSN: 0860-150X

Journal RSS Feed

Language: English

Page range: 173 - 192

Published on: Nov 23, 2016

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

exceptional scopes,

unbound anaphora,

Related subjects:

Philosophy, other

© 2016 Justyna Grudzińska, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 46 (2016): Issue 1 (September 2016)

Previous article