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Branching Quantifiers

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Quantifiers and Cognition: Logical and Computational Perspectives

Part of the book series: Studies in Linguistics and Philosophy ((SLAP,volume 96))

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Abstract

This chapter is devoted to a particularly intriguing quantifier construction: branching. Branching interpretations of some natural language sentences are intractable, and therefore, their occurrence in natural language is far from obvious. I start by discussing the thesis formulated by Hintikka, which says that certain natural language sentences require nonlinear quantification to express their meaning. Then, I discuss a novel alternative reading for potentially branching sentences, the so-called two-way reading. This reading is expressible by a linear formula and is tractable. I compare the two-way reading to other possible interpretations and argue that it is the best representation for the meaning of Hintikka-like sentences. Next, I describe an experiment providing empirical support for the two-way reading. The basic assumption here is that a criterion for the adequacy of a meaning representation is its compatibility with sentence truth-conditions. This can be established by observing the linguistic behavior of language users. I report on experiments showing that people tend to interpret sentences similar to Hintikka’s sentence in a way consistent with the two-way interpretation.

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Notes

  1. 1.

    The idea of branching is more visible in the case of simpler quantifier prefixes, like in sentence (8) discussed in Sect. 9.3.2.

  2. 2.

    See: Jackendoff (1972), Gabbay and Moravcsik (1974), Guenthner and Hoepelman (1976), Hintikka (1976), Stenius (1976), Barwise (1979), Bellert (1989), May (1989), Sher (1990), Mostowski (1994), Liu (1996), Beghelli et al. (1997), Janssen (2002), Mostowski and Wojtyniak (2004), Schlenker (2006), Janssen and Dechesne (2006), Gierasimczuk and Szymanik (2009). Related discussion on the ambiguity of sentences with multiple quantifiers has been vivid in the more philosophically oriented tradition (see Bach 1982; Jaszczolt 2002; Kempson and Cormack 1981a, b, 1982; May 1985; Tennant 1981).

  3. 3.

    See Chap. 8 for more discussion of reciprocity.

  4. 4.

    Godziszewski and Kalociński (2015) study the computational complexity of various interpretations of ‘the...the...’ construction. This is analogical to our investigation of reciprocal expressions in Chap. 8.

  5. 5.

    See Sevenster (2006) and Sect. 7.3 for a discussion of the computational complexity of branching quantifiers.

  6. 6.

    This statement can be given independent psychological support (see, e.g., Frixione 2001 and Sect. 8.5).

  7. 7.

    See Gierasimczuk and Szymanik (2009) for details.

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  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Jakub Szymanik

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Szymanik, J. (2016). Branching Quantifiers. In: Quantifiers and Cognition: Logical and Computational Perspectives. Studies in Linguistics and Philosophy, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-28749-2_9

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  • DOI: https://doi.org/10.1007/978-3-319-28749-2_9

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