Scope-related cumulativity asymmetries and cumulative composition

Nina Haslinger, Viola Schmitt


Some elements in German and English, e.g. every DPs, give rise to cumulativity asymmetries: They allow for cumulative readings only if they occur in the scope of another semantically plural expression. We present a surface-compositional and event-less analysis of this pattern, expanding Schmitt's (2017) 'plural projection' framework. In this system, any constituent containing a semantically plural subexpression denotes a set of (possibly higher-type) pluralities. Cumulativity is built into the rules implementing this 'projection' of semantic plurality.

Full Text:



Beck, Sigrid & Uli Sauerland. 2000. Cumulation is needed: a reply to Winter (2000). Natural Language Semantics 8(4). 349–371. doi:10.1023/A:1011240827230.

Beck, Sigrid & Yael Sharvit. 2002. Pluralities of questions. Journal of Semantics 19. 105–157. doi:10.1093/jos/19.2.105.

Champollion, Lucas. 2010. Cumulative readings of every do not provide evidence for events and thematic roles. In Maria Aloni, Harald Bastiaanse, Tikitu de Jager & Katrin Schulz (eds.), Logic, language and meaning. 17th Amsterdam Colloquium, Amsterdam, The Netherlands, December 16-18, 2009, Revised Selected Papers, 213–222. Heidelberg: Springer. doi:10.1007/978-3-642-14287-1_22.

Elliott, Patrick D. 2017. Explaining DPs vs. CPs without syntax. In Chicago Linguistic Society, vol. 52, 171–185. Chicago: Chicago Linguistic Society.

Ferreira, Marcelo. 2005. Event quantification and plurality: MIT PhD dissertation.

Flor, Enrico. 2017. The Italian determiner ogni and its cumulative readings: University of Vienna MA thesis.

Gazdar, Gerald. 1980. A cross-categorial semantics for coordination. Linguistics and Philosophy 3. 407–409. doi:10.1007/BF00401693.

Hamblin, Charles. 1973. Questions in Montague English. Foundations of Language 10(1). 41–53. doi:10.1016/b978-0-12-545850-4.50014-5.

Haslinger, Nina & Viola Schmitt. 2018. Asymmetrically distributive items and plural projection. Ms., University of Vienna.

Heim, Irene & Angelika Kratzer. 1998. Semantics in Generative Grammar. Malden, MA: Blackwell.

Heycock, Caroline & Roberto Zamparelli. 2005. Friends and colleagues: Plurality, coordination, and the structure of DP. Natural Language Semantics 13(3). 201–270. doi:10.1007/s11050-004-2442-z.

Kratzer, Angelika. 2000. The event argument and the semantics of verbs. Ms.,

University of Massachusetts at Amherst.

Kratzer, Angelika. 2006. Decomposing attitude verbs. Handout for a talk given

at the Hebrew University of Jerusalem.


Krifka, Manfred. 1990. Boolean and non-Boolean ‘and’. In László Kálmán &

László Pólos (eds.), Papers from the Second Symposium on Logic and Language, 161–188. Budapest: Akadémiai Kiadó.

Link, Godehard. 1984. Hydras. On the logic of relative clause constructions with multiple heads. In Fred Landman & Frank Veltman (eds.), Varieties of Formal Semantics. Proceedings of the Fourth Amsterdam Colloquium, September 1982 (Groningen-Amsterdam Studies in Semantics 3), 245–257. Dordrecht: Foris.

Moulton, Keir. 2015. CPs: Copies and compositionality. Linguistic Inquiry 46(2). 305–342. doi:10.1162/LING_a_00183.

Partee, Barbara Hall & Mats Rooth. 1983. Generalized conjunction and type ambiguity. In Rainer Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, Use and Interpretation of Language, 362–383. de Gruyter.

Rooth, Mats Edward. 1985. Association with focus: University of Massachusetts, Amherst dissertation.

Schein, Barry. 1993. Plurals and Events. Cambridge, Massachusetts: MIT Press.

Schmitt, Viola. 2013. More pluralities: University of Vienna PhD dissertation.

Schmitt, Viola. 2017. Cross-categorial plurality and plural composition. Ms., University of Vienna.

von Stechow, Arnim. 1974. ε-λ-kontextfreie Sprachen: Ein Beitrag zu einer natürlichen formalen Semantik. Linguistische Berichte 34. 1–33.

von Stechow, Arnim. 1980. Modification of noun phrases. A challenge for compositional semantics. Theoretical Linguistics 7. 57–110. doi:10.1515/thli.1980.7.1-3.57.

Zweig, Eytan. 2008. Dependent plurals and plural meaning: New York University PhD dissertation.



Copyright (c) 2018 Nina Haslinger, Viola Schmitt