On the unification of which-interrogatives and alternative-interrogatives

Yael Sharvit

doi:10.1515/ip-2025-0003

Article

On the unification of which-interrogatives and alternative-interrogatives

Yael Sharvit
Yael Sharvit is a professor in the Department of Linguistics at UCLA, Los Angeles, California. Dr. Sharvit’s research focuses on semantics and the syntax-semantics interface. She serves as co-editor-in-chief of the journal Linguistics and Philosophy, and Associate Editor at the Journal of Semantics.

Published/Copyright: April 9, 2025

Published by

Become an author with De Gruyter Brill

Author Information

From the journal Intercultural Pragmatics Volume 22 Issue 1

Abstract

Some similarities between alternative-interrogatives and which-interrogatives seem to support a unifying analysis. The paper discusses two such analyses, and the challenges they face, and some advantages and shortcomings of a non-unifying approach.

Keywords: alternative-interrogatives; which-interrogatives; question presuppositions; fragment replies

Corresponding author: Yael Sharvit, Department of Linguistics, University of California, Los Angeles, Los Angeles, CA, USA, E-mail: ysharvit@gmail.com

About the author

Yael Sharvit

Yael Sharvit is a professor in the Department of Linguistics at UCLA, Los Angeles, California. Dr. Sharvit’s research focuses on semantics and the syntax-semantics interface. She serves as co-editor-in-chief of the journal Linguistics and Philosophy, and Associate Editor at the Journal of Semantics.

Appendix

Some interpretation rules are given in (I)-(VI) below, where W is the set of possible worlds, w ∈ W, g is a variable assignment, and ‘[λ…]’ is read as per Heim and Kratzer (1998), Chapter 2. Discourse rules are assumed but not provided.

– (I)-(III) are used in the unifying flexible or theory.

– (I) and (IV)-(V) are used in the unifying clausal or theory.

– (I), (IV) and (VI), together with either (III) or (V), are used in the non-unifying approach.

⟦greet⟧^w,g(x, y) = True iff x greeted y in w.

⟦ _ _i⟧^w,g = g(i).

⟦student⟧^w,g = {x| x is a student in w}.

⟦French student⟧^w,g = {x| x is a student in w and x is French in w}.

⟦proposition⟧^w,g = {p| p is a proposition in w}.

⟦Sam or Fred⟧^w,g = {⟦Sam⟧^w,g, ⟦Fred⟧^w,g}.
⟦ [which ^♦ γ]_i ϕ⟧^w,g is defined iff {x| x ∈ ⟦γ⟧^w,g and ⟦ϕ⟧^w,g[i→x] = True} is a singleton.

If defined, ⟦ [which ^♦ γ]_i ϕ⟧^w,g = {x| x ∈ ⟦γ⟧^w,g and ⟦ϕ⟧^w,g[i→x] = True}.

⟦ [∃^♦ γ]_i ϕ⟧^w,g = True iff {x| x ∈ ⟦γ⟧^w,g and ⟦ϕ⟧^w,g[i→x] = True} ≠ ∅.

⟦ [[which ^♦ γ]_i [which ^♦ γ′]_k] ϕ⟧^w,g is defined iff for all x ∈ ⟦γ⟧^w,g, {y| y ∈ ⟦γ′⟧^w,g and ⟦ϕ⟧^{w,g[i→x,k→y]} = True} is a singleton.

If defined, ⟦ ⟦which ^♦ γ]_i [which ^♦ γ′]_k] ϕ⟧^w,g = {(x, Y)| x ∈ ⟦γ⟧^w,g and Y = {y| y ∈ ⟦γ′⟧^w,g and ⟦ϕ⟧^{w,g[i→x,k→y]} = True}}.

⟦ϕ or _i φ⟧^w,g = True iff g(i)(w) = True and g(i) ∈ {[λw′ ∈ W. ⟦ϕ⟧^w′,g], [λw′ ∈ W. ⟦φ⟧^w′,g]}.
⟦ [which ^♣ γ]_i ϕ⟧^w,g is defined iff

{p| p(w) = True and {Z| Z ∈ ⟦γ⟧^w,g and p = [λw′ ∈ W. ⟦ϕ⟧^w′,g ^[i→Z]]} ≠ ∅} is a singleton.

If defined, ⟦ [which ^♣ γ]_i ϕ⟧^w,g =

{p| p(w) = True and {Z| Z ∈ ⟦γ⟧^w,g and p = [λw′ ∈ W. ⟦ϕ⟧^w′,g ^[i→Z]]} ≠ ∅}.

⟦ [∃^♣ γ]_i ϕ⟧^w,g = True iff {p| p(w) = True and {Z| Z ∈ ⟦γ⟧^w,g and p = [λw′ ∈ W. ⟦ϕ⟧^w′,g ^[i→Z]]} ≠ ∅} ≠ ∅.

⟦ [[which ^♣ γ]_i [which ^♣ γ′]_k] ϕ⟧^w,g is defined iff for all x ∈ ⟦γ⟧^w,g, {p| p(w) = True and {Z| Z ∈ ⟦γ′⟧^w,g and p = [λw′ ∈ W. ⟦ϕ⟧^w′,g ^{[i→x,k→Z]}]} ≠ ∅} is a singleton.

If defined, ⟦ ⟦which ^♣ γ]_i [which ^♣ γ′]_k] ϕ⟧^w,g = {(x, Y)| x ∈ ⟦γ⟧^w,g and Y = {p| p(w) = True and {Z| Z ∈ ⟦γ′⟧^w,g and p = [λw′ ∈ W. ⟦ϕ⟧^w′,g ^{[i→x,k→Z]}]} ≠ ∅}}.

⟦ALT-Q_i ϕ⟧^w,g is defined iff {p| ⟦ϕ⟧^w,g[i→p] = True} is a singleton.

If defined, ⟦ALT-Q_i ϕ⟧^w,g = {p| ⟦ϕ⟧^w,g[i→p] = True}.

⟦ALT-D_i ϕ⟧^w,g = True iff {p| ⟦ϕ⟧^w,g[i→p] = True} ≠ ∅.

References

Abenina-Adar, Maayan & Yael Sharvit. 2021. On the presuppositional strength of interrogative clauses. Natural Language Semantics 29. 47–90. https://doi.org/10.1007/s11050-020-09169-5.Search in Google Scholar

Atlas, Jay. 1996. Only’ noun phrases, pseudo-negative generalized quantifiers, negative polarity items, and monotonicity. Journal of Semantics 13. 265–328. https://doi.org/10.1093/jos/13.4.265.Search in Google Scholar

Bartels, Christine. 1999. The Intonation of English Statements and questions. New York: Garland.Search in Google Scholar

Bošković, Željko & Steven Franks. 2002. Across-the-board movement and LF. Syntax 3. 107–128. https://doi.org/10.1111/1467-9612.00027.Search in Google Scholar

Chierchia, Gennaro. 1993. Questions with quantifiers. Natural Language Semantics 1(2). 181–234. https://doi.org/10.1007/bf00372562.Search in Google Scholar

Chierchia, Gennaro. 2013. Logic in grammar: Polarity, free choice, and intervention. In Oxford Studies in Semantics and pragmatics. Oxford: Oxford University Press.10.1093/acprof:oso/9780199697977.001.0001Search in Google Scholar

Davidson, Donald. 1967. The logical form of action sentences. In Nicholas Rescher (ed.), The Logic of Decision and action. Pittsburgh: University of Pittsburgh Press.10.2307/jj.13027259.6Search in Google Scholar

Dayal, Veneeta. 2017. Questions. Oxford: Oxford University Press.Search in Google Scholar

Engdahl, Elisabet. 1985. Constituent questions. Dordrecht: Reidel.10.1007/978-94-009-5323-9Search in Google Scholar

Ginzburg, Jonathan & Ivan Sag. 2000. Interrogative investigations: The form. In Meaning and Use of English interrogatives. Stanford: CSLI Publications.Search in Google Scholar

Groenendijk, Jeroen & Martin Stokhof. 1984. Studies on the Semantics of Questions and the Pragmatics of answers. Amsterdam: University of Amsterdam PhD dissertation.Search in Google Scholar

Guerzoni, Elena & Yael Sharvit. 2014. Whether or not anything but not Whether anything or not. In Uli Sauerland & Luka Crnič (eds.), The Art and Craft of semantics: A Festschrift for irene Heim. Mitwpl, Vol. 70, 199–224.Search in Google Scholar

Guerzoni, Elena. 2003. Why even ask? On the Pragmatics of Questions and the Semantics of answers. Doctoral Dissertation. Cambridge, MA: MIT.Search in Google Scholar

Guerzoni, Elena. 2004. Even-NPIs in Yes/No questions. Natural Language Semantics 12. 319–343. https://doi.org/10.1007/s11050-004-8739-0.Search in Google Scholar

Hamblin, Charles L. 1973. Questions in montague English. Foundations of Language 10. 41–53.Search in Google Scholar

Heim, Irene & Angelika Kratzer. 1998. Semantics in generative grammar. Cambrdige, MA and Amherst, MA: Blackwell Publishers.Search in Google Scholar

Higginbotham, James. 1993. Interrogatives. In Ken Hale & Samuel Jay Keyser (eds.), The View from building 20, 195–227. Cambridge, MA: MIT Press.Search in Google Scholar

Hirsch, Aron. 2017. An inflexible Semantics for cross-categorial operators. PhD dissertation. Cambridge, MA: MIT.Search in Google Scholar

Jacobson, Pauline. 2016. The short answer: Implications for direct compositionality (and vice versa). Language 92. 331–375. https://doi.org/10.1353/lan.2016.0038.Search in Google Scholar

Jeong, Sunwoo & Floris Roelofsen. 2023. Focused NPIs in statements and questions. Journal of Semantics 40(1). 1–68. https://doi.org/10.1093/jos/ffac014.Search in Google Scholar

Karttunen, Lauri & Stanley Peters. 1980. Interrogative quantifiers. In Christina Rohrer (ed.), Time, Tense and quantifiers: Proceedings of the stuttgart Conference on the Logic of Tense and quantification, 181–206. Tübingen: Niemeyer.10.1515/9783111346069.181Search in Google Scholar

Karttunen, Lauri. 1977. Syntax and semantics of questions. Linguistics and Philosophy 1(1). 3–44. https://doi.org/10.1007/bf00351935.Search in Google Scholar

Klima, Edward. 1964. Negation in English. The Structure of language. Englewood Cliffs, NJ: Prentice-Hall.Search in Google Scholar

Kratzer, Angelika & Junko Shimoyama. 2002. Indeterminate pronouns: The view from Japanese. In Yukio Otsu (ed.), The Proceedings of the third Tokyo Conference on psycholinguistics (TCP 2002), 1–25. Tokyo: Hituzi Syobo.Search in Google Scholar

Krifka, Manfred. 2001. Quantifying into question acts. Natural Language Semantics 9. 1–40. https://doi.org/10.3765/salt.v9i0.2830.Search in Google Scholar

Ladusaw, William. 1979. Polarity Sensitivity as inherent scope relation. PhD dissertation. Austin: University of Texas.Search in Google Scholar

Linebarger, Marcia. 1987. Negative polarity and grammatical representation. Linguistics and Philosophy 10. 325–387. https://doi.org/10.1007/bf00584131.Search in Google Scholar

Nicolae, Andreea. 2013. Any questions? Polarity as a Window into the Structure of questions. Doctoral Dissertation. Cambridge, MA: Harvard University.Search in Google Scholar

Nicolae, Andreea. 2015. Questions with NPIs. Natural Language Semantics 23(1). 21–76. https://doi.org/10.1007/s11050-014-9110-8.Search in Google Scholar

Parsons, Terence. 1990. Events in the Semantics of English. Cambridge: MIT Press.Search in Google Scholar

Pruitt, Kathryn & Floris Roelofsen. 2013. The interpretation of prosody in disjunctive questions. Linguistic Inquiry 44. 632–650. https://doi.org/10.1162/ling_a_00141.Search in Google Scholar

Rooth, Mats & Barbara Partee. 1982. Conjunction, type ambiguity and wide scope or. In Daniel Flickinger, Marlys Macken & Nancy Wiegand (eds.), Proceedings of WCCFL 1, stanford: Department of linguistics: Stanford University.Search in Google Scholar

Schein, Barry. 2017. And’: Conjunction reduction redux. Cambridge, MA: MIT Press.10.7551/mitpress/10488.001.0001Search in Google Scholar

van Rooij, Robert. 2008. Towards a uniform analysis of ’any. Natural Language Semantics 16(4). 297–315. https://doi.org/10.1007/s11050-008-9035-1.Search in Google Scholar

Published Online: 2025-04-09

Published in Print: 2025-03-26

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/ip-2025-0003

Keywords for this article

alternative-interrogatives; which-interrogatives; question presuppositions; fragment replies