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Composing alternatives


There is a prominent line of work in natural language semantics, rooted in the work of Hamblin, in which the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions—a set of alternatives. This allows for a more fine-grained view on meaning, which has led to improved analyses of a wide range of linguistic phenomena. However, this approach also faces a number of problems. We focus here on two of these, in our view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstraction; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin’s proposal with the more orthodox type-theoretic framework rooted in the work of Montague in such a way that both the explanatory utility of the former and the solid formal foundations of the latter are preserved. Our proposal builds on insights from recent work on inquisitive semantics, and it also contributes to the further development of this framework by specifying how the inquisitive meaning of a sentence may be built up compositionally.


  1. Achimova, A., Deprez, V., & Musolino, J. (2010). What makes pair list answers available: An experimental approach. In NELS 41 Proceedings. United States: University of Pennsylvania.

  2. Aloni M. (2007) Free choice, modals and imperatives. Natural Language Semantics, 15(1): 65–94

    Article  Google Scholar 

  3. Alonso-Ovalle, L. (2006). Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst.

  4. Brasoveanu A., Farkas D. F. (2011) How indefinites choose their scope. Linguistics and Philosophy, 34: 1–55

    Article  Google Scholar 

  5. Champollion L. (2016) Ten men and women got married today: Noun coordination and the intersective theory of conjunction. Journal of Semantics, 33(3): 561–622

    Article  Google Scholar 

  6. Charlow, S. (2014). On the semantics of exceptional scope. Ph.D. thesis, New York University.

  7. Chierchia G. (1993) Questions with quantifiers. Natural Language Semantics, 1(2): 181–234

    Article  Google Scholar 

  8. Chierchia, G., Fox, D., & Spector, B. (2009). Hurford’s constraint and the theory of scalar implicatures: Evidence for embedded implicatures. Presuppositions and implicatures (pp. 47–62). Cambridge, MA: MIT Press.

  9. Chomsky, N. (1977). On wh-movement. In P. Culicover, A. Akmajian & T. Wasow (Eds.), Formal syntax (pp. 71–132). New York: Academic Press.

  10. Chomsky, N. (1995). The minimalist program (Vol. 1765). Cambridge: Cambridge University Press.

  11. Ciardelli, I., & Roelofsen, F. (2015). Alternatives in Montague grammar. In E. Csipak & H. Zeijlstra (Eds.), Proceedings of Sinn und Bedeutung, Göttingen, pp. 161–178.

  12. Ciardelli, I. & Roelofsen, F. (2016). Hurford’s constraint, the semantics of disjunctions, and the nature of alternatives. Manuscript, available on the Semantics Archive.

  13. Ciardelli I., Groenendijk J., & Roelofsen F. (2013) Inquisitive semantics: A new notion of meaning. Language and Linguistics Compass, 7(9): 459–476

    Article  Google Scholar 

  14. Ciardelli, I., Groenendijk, J., & Roelofsen, F. (2015). Inquisitive semantics. ESSLLI lecture notes. Available via

  15. Farkas D. (1981) Quantifier scope and syntactic islands. Proceedings of CLS, 7: 59–66

    Google Scholar 

  16. Fodor J. D., Sag I. A. (1982) Referential and quantificational indefinites. Linguistics and Philosophy, 5: 355–398

    Article  Google Scholar 

  17. Groenendijk, J. & Stokhof, M. (1984). Studies on the semantics of questions and the pragmatics of answers. Ph.D. thesis, University of Amsterdam.

  18. Hagstrom, P. A. (1998). Decomposing questions. Ph.D. thesis, MIT.

  19. Haida, A. & Repp, S. (2013). Disjunction in wh-questions. In Proceedings of NELS 40.

  20. Hamblin C.L. (1973) Questions in Montague English. Foundations of Language, 10(1): 41–53

    Google Scholar 

  21. Higginbotham, J. (1991). Interrogatives I. In L. Cheng & H. Demirdash (Eds.), More papers on wh-movement. MIT Working Papers in Linguistics.

  22. Hurford J. (1974) Exclusive or inclusive disjunction. Foundations of Language, 11(3): 409–411

    Google Scholar 

  23. Jacobson P. (1999) Towards a variable-free semantics. Linguistics and Philosophy, 22(2): 117–185

    Article  Google Scholar 

  24. Jäger, G. (2007). Partial variables and specificity. In U. Sauerland & P. Stateva (Eds.), Presupposition and implicature in compositional semantics (pp. 121–162). New York: Palgrave Macmillan.

  25. Karttunen L. (1977) Syntax and semantics of questions. Linguistics and Philosophy, 1: 3–44

    Article  Google Scholar 

  26. Katzir R., Singh R. (2013) Hurford disjunctions: Embedded exhaustification and structural economy. Proceedings of Sinn und Bedeuting, 18: 201–216

    Google Scholar 

  27. Keenan, E. L., & Faltz, L. M. (1985). Boolean semantics for natural language. New York: Springer.

  28. Kratzer, A. & Shimoyama, J. (2002). Indeterminate pronouns: The view from Japanese. In Y. Otsu (Ed.), Proceedings of the third Tokyo conference on psycholinguistics, pp. 1–25.

  29. Krifka M. (2001) Quantifying into question acts. Natural Language Semantics, 9(1): 1–40

    Article  Google Scholar 

  30. May, R. (1985). Logical Form: Its structure and derivation (Vol. 12). Cambridge, MA: MIT Press.

  31. Menéndez-Benito, P. (2005). The grammar of choice. Ph.D. thesis, University of Massachusetts, Amherst.

  32. Montague R. (1970) Universal grammar. Theoria, 36(3): 373–398

    Article  Google Scholar 

  33. Montague, R. (1973). The proper treatment of quantification in ordinary English. In J. Hintikka, J. Moravcsik, & P. Suppes (Eds.), Approaches to natural language (pp. 221–242). Dordrecht: Springer.

  34. Novel M., Romero M. (2010) Movement, variables and Hamblin alternatives. Proceedings of Sinn und Bedeutung, 14: 322–338

    Google Scholar 

  35. Onea E. (2015) Why indefinites can escape scope islands. Linguistics and Philosophy, 38(3): 1–31

    Article  Google Scholar 

  36. Partee, B. H., & Rooth, M. (1983). Generalized conjunction and type ambiguity. In R. Bäuerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use and interpretation of language (pp. 115–143). Berlin: De Gruyter.

  37. Poesio, M. (1996). Semantic ambiguity and perceived ambiguity. In K. van Deemter & S. Peters (Eds.), Semantic ambiguity and underspecification (pp. 231–250). Stanford, CA: CSLI.

  38. Rawlins, K. (2008). (Un)conditionals: an investigation in the syntax and semantics of conditional structures. Ph.D. thesis, University of California, Santa Cruz.

  39. Reinhart T. (1997) Quantifier scope: How labor is divided between QR and choice functions. Linguistics and Philosophy, 20(4): 335–397

    Article  Google Scholar 

  40. Rizzi, L. (2006). On the form of chains: Criterial positions and ECP effects. In L. Cheng & N. Corver (Eds.), Wh-movement: Moving on (pp. 97–134). Cambridge, MA: MIT Press.

  41. Roelofsen F. (2013) Algebraic foundations for the semantic treatment of inquisitive content. Synthese, 190(1): 79–102

    Article  Google Scholar 

  42. Roelofsen, F. (2015). Two alternatives for disjunction: an inquisitive reconciliation. Manuscript, submitted for publication. Available via

  43. Roelofsen, F. & van Gool, S. (2010). Disjunctive questions, intonation, and highlighting. In M. Aloni, H. Bastiaanse, T. de Jager, & K. Schulz (Eds.), Logic, language, and meaning: Selected papers from the seventeenth Amsterdam colloquium (pp. 384–394). New York: Springer.

  44. Rooth, M. (1985). Association with focus. Ph.D. thesis, University of Massachusetts, Amherst.

  45. Ross, J. R. (1967). Constraints on variables in syntax. Ph.D. thesis, Massachusetts Institute of Technology.

  46. Shan, C.-C. (2004). Binding alongside Hamblin alternatives calls for variable-free semantics. In Proceedings of semantics and linguistic theory (SALT 14) (pp. 289–304).

  47. Shimoyama, J. (2001). Wh-constructions in Japanese. Ph.D. thesis, University of Massachusetts, Amherst.

  48. Shimoyama J. (2006) Indeterminate phrase quantification in Japanese. Natural Language Semantics, 14(2): 139–173

    Article  Google Scholar 

  49. Simons M. (2005) Dividing things up: The semantics of or and the modal/or interaction. Natural Language Semantics, 13(3): 271–316

    Article  Google Scholar 

  50. Szabolcsi, A. (1987). Bound variables in syntax: Are there any? In Proceedings of the 6th Amsterdam colloquium (pp. 331–353).

  51. Szabolcsi, A. (1997). Quantifiers in pair-list readings. In A. Szabolcsi (Ed.), Ways of scope taking (pp. 311–347). New York: Springer.

  52. Theiler, N. (2014). A multitude of answers: Embedded questions in typed inquisitive semantics. MSc thesis, University of Amsterdam.

  53. von Stechow, A. (1991). Focusing and backgrounding operators. In W. Abraham (Ed.), Discourse particles: Descriptive and theoretical investigations on the logical, syntactic and pragmatic properties of discourse particles in German (pp. 37–84). Amsterdam: John Benjamins.

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

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Correspondence to Floris Roelofsen.

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This paper integrates and extends ideas and results from Theiler (2014) and Ciardelli and Roelofsen (2015). We are grateful to two anonymous reviewers for their useful feedback, to Andreas Haida, Reinhard Muskens, Wataru Uegaki, and Yimei Xiang for helpful comments on earlier presentations of this material, and especially to Maria Aloni, Lucas Champollion, Liz Coppock, Donka Farkas, Jeroen Groenendijk, Edgar Onea, and Anna Szabolcsi for extensive discussion. Financial support from the Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged.

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Ciardelli, I., Roelofsen, F. & Theiler, N. Composing alternatives. Linguist and Philos 40, 1–36 (2017).

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  • Alternative semantics
  • Inquisitive semantics
  • Type-theoretic semantics
  • Compositionality