Rigid and Flexible Quantification in Plural Predicate Logic

Lucas Champollion, Justin Bledin, Haoze Li

Abstract


Noun phrases with overt determiners, such as some apples or a quantity of milk, differ from bare noun phrases like apples or milk in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal for-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial for-adverbials, habituals, and the quantifier all.

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References


van den Berg, Martin H. 1996. Some aspects of the internal structure of discourse: University of Amsterdam dissertation.

Brasoveanu, Adrian. 2008. Donkey pluralities: Plural information states versus non-atomic individuals. Linguistics and Philosophy 31(2). 129–209. doi:10.1007/s10988-008-9035-0.

Brasoveanu, Adrian. 2013. Modified numerals as post-suppositions. Journal of Semantics 30(2). 155–209. doi:10.1093/jos/ffs003.

Champollion, Lucas. 2015. Refining stratified reference. Theoretical Linguistics 41(3-4). 223–240. doi:10.1515/tl-2015-0015.

Champollion, Lucas. 2016a. Covert distributivity in algebraic event semantics. Semantics and Pragmatics 9(15). 1–65. doi:10.3765/sp.9.15.

Champollion, Lucas. 2016b. Linking the collective-distributive opposition and the telic-atelic opposition. In Christopher Hammerly & Brandon Prickett (eds.), 46th Annual Meeting of the North East Linguistic Society (NELS 46), vol. 1, 171–184. Amherst, MA: University of Massachusetts GLSA Publications. http://ling.auf.net/lingbuzz/002985/current.pdf.

Champollion, Lucas. 2017. Parts of a whole: Distributivity as a bridge between aspect and measurement, vol. 66 Oxford studies in theoretical linguistics. Oxford, UK: Oxford University Press.

Champollion, Lucas & Manfred Krifka. 2016. Mereology. In Maria Aloni & Paul Dekker (eds.), Cambridge handbook of formal semantics Cambridge Handbooks in Language and Linguistics, chap. 13, 369–388. Cambridge, UK: Cambridge University Press. doi:10.1017/cbo9781139236157.014.

Dowty, David R. 1979. Word meaning and Montague grammar: The semantics of verbs and times in generative semantics and in Montague’s PTQ. Dordrecht, Netherlands: Reidel. doi:10.1007/978-94-009-9473-7.

Dowty, David R. 1987. Collective predicates, distributive predicates, and all. In Ann Miller & Zheng-sheng Zhang (eds.), 3rd Eastern States Conference on Linguistics (ESCOL), 97–115. Columbus, OH: Ohio State University.

Eberle, Kurt. 1998. The influence of Plural NPs on the Aktionsart in DRT. In Fritz Hamm & Erhard Hinrichs (eds.), Plural quantification, Dordrecht, Netherlands: Kluwer. doi:10.1007/978-94-017-2706-8_3.

Egg, Markus. 1994. Aktionsart und Kompositionalität. Berlin, Germany: Akademie Verlag.

Filip, Hana. 2000. The quantization puzzle. In James Pustejovsky & Carol Tenny (eds.), Events as grammatical objects, from the combined perspectives of lexical semantics, logical semantics and syntax, 3–60. Stanford, CA: CSLI Publications.

Galliani, Pietro. 2017. Dependence logic. In Edward N. Zalta (ed.), The Stanford encyclopedia of philosophy, Metaphysics Research Lab, Stanford University spring 2017 edn.

Garey, Howard B. 1957. Verbal aspect in French. Language 33(2). 91–110. doi:10.2307/410722.

van Geenhoven, Veerle. 2005. Atelicity, pluractionality and adverbial quantification. In Henk J. Verkuyl, Henriëtte de Swart & Angeliek van Hout (eds.), Perspectives on aspect, vol. 32 Studies in theoretical psycholinguistics, 107–124. Berlin, Germany: Springer. doi:10.1007/1-4020-3232-3_6.

Hawke, Peter & Shane Steinert-Threlkeld. 2016. Informational dynamics of epistemic possibility modals. Synthese doi:10.1007/s11229-016-1216-8.

Heim, Irene. 1982. The semantics of definite and indefinite noun phrases. Amherst, MA: University of Massachusetts dissertation. http://semanticsarchive.net/ Archive/jA2YTJmN.

Henderson, Robert M. 2014. Dependent indefinites and their post-suppositions. Semantics and Pragmatics 7(6). 1–58. doi:10.3765/sp.7.6.

Kamp, Hans. 1981. A theory of truth and semantic representation. In Jeroen Groenendijk, Theo Janssen & Martin Stokhof (eds.), Formal methods in the study of language, vol. 135 Mathematical Center Tracts, 277–322. Amsterdam, Netherlands: Mathematisch Centrum. doi:10.1002/9780470758335.ch8.

Krifka, Manfred. 1989. Nominal reference, temporal constitution and quantification in event semantics. In Renate Bartsch, Johan van Benthem & Peter van Emde Boas (eds.), Semantics and contextual expression, 75–115. Dordrecht, Netherlands: Foris. http://amor.cms.hu-berlin.de/~h2816i3x/Publications/ Krifka%201989%20Nominal%20Reference.pdf.

Krifka, Manfred. 1992. Thematic relations as links between nominal reference and temporal constitution. In Ivan A. Sag & Anna Szabolcsi (eds.), Lexical matters, 29–53. Stanford, CA: CSLI Publications. http://amor.cms.hu-berlin.de/~h2816i3x/Publications/Krifka%201992%20Thematic%20Relations.PDF.

Krifka, Manfred. 1998. The origins of telicity. In Susan Rothstein (ed.), Events and grammar, vol. 70 Studies in linguistics and philosophy, 197–235. Dordrecht, Netherlands: Kluwer. doi:10.1007/978-94-011-3969-4_9.

Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Reiner Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, use and interpretation of language, 303–323. Berlin, Germany: de Gruyter. doi:10.1515/9783110852820.302. Reprinted in Link (1998), Chapter 1.

Link, Godehard. 1998. Algebraic semantics in language and philosophy. Stanford, CA: CSLI Publications.

Mittwoch, Anita. 1982. On the difference between eating and eating something: activities versus accomplishments. Linguistic Inquiry 13(1). 113–122. http: //www.jstor.org/stable/4178263.

Moltmann, Friederike. 1991. Measure adverbials. Linguistics and Philosophy 14(6). 629–660. doi:10.1007/bf00631962.

Naumann, Ralf. 1999. A dynamic logic of events and states for the interaction between plural quantification and verb aspect in natural language. Logic Journal of the IGPL 7(5). 591–627. doi:10.1093/jigpal/7.5.591.

Piñón, Christopher. 2015. An illusory common core. Theoretical Linguistics 41(3-4). 185–195. doi:10.1515/tl-2015-0012.

Väänänen, Jouko. 2007. Dependence logic: A new approach to independence friendly logic, vol. 70 London Mathematical Society Student Texts. Cambridge, UK: Cambridge University Press. doi:10.1017/cbo9780511611193.

Verkuyl, Henk J. 1972. On the compositional nature of the aspects. Dordrecht, Netherlands: Reidel. doi:10.1007/978-94-017-2478-4.

White, Michael. 1994. A computational approach to aspectual composition. Philadelphia, PA: University of Pennsylvania dissertation.

Winter, Yoad. 2001. Flexibility principles in Boolean semantics: The interpretation of coordination, plurality, and scope in natural language. Cambridge, MA: MIT Press.

Zucchi, Sandro & Michael White. 2001. Twigs, sequences and the temporal constitution of predicates. Linguistics and Philosophy 24(2). 223–270. doi:10.1023/a:1005690022190.

Zweig, Eytan. 2009. Number-neutral bare plurals and the multiplicity implicature. Linguistics and Philosophy 32(4). 353–407. doi:10.1007/s10988-009-9064-3.




DOI: http://dx.doi.org/10.3765/salt.v27i0.4190