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A Choice Function Analysis of Either in the Either/or Construction

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New Frontiers in Artificial Intelligence (JSAI-isAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12331))

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Abstract

In this paper, I propose an analysis that covers both the wide scope or reading of the either/or construction and the availability of Alternative Question and Yes/No Question readings, namely a hybrid of an ellipsis analysis and a choice function analysis of either. After presenting two sets of data, I introduce two hybrid analyses that combine an ellipsis analysis and a choice function analysis. The two differ from each other in terms of the item that introduces the choice function variable: in the first analysis, the disjunction particle or introduces the choice function variable while in the second analysis, either has that semantic role. It is demonstrated that the two analyses both account for the either/or construction data, whereas only the second hybrid analysis, in which either introduces the choice function variable, explains the Alternative Question and Yes/No Question data. Finally, I review another account proposed in previous research, namely the focus alternative semantics analysis, and point out its problems.

I am indebted to Akira Watanabe, Noriko Imanishi, Christopher Tancredi, audience at LENLS 16, and two anonymous reviewers for helpful comments and suggestions. All remaining errors are my own. This study was supported by Grant-in-Aid for Young Scientists (#18K12414) from the Japan Society for the Promotion of Science, to which I am grateful.

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Notes

  1. 1.

    Another, often cited, analysis of the semantics of AltQs is [11]’s analysis that makes use of focus alternative semantics. I take up the analysis in Sect. 3.

  2. 2.

    There are several other lines of research regarding the semantics of YNQs. [12], for example, takes the assumption that the denotation of a YNQ is a singleton set of its literal meaning (declarative meaning) as in (i).

    (i) [[ Can Jack come to tea ]] = {Jack can come to tea}

    Here, however, I maintain the simplest idea that questions denote the set of their possible answers and adopt the semantics of the YNQ operator in (20).

  3. 3.

    Note that this semantics for wh-Questions and AltQs does not account for the AltQ/YNQ data discussed in the previous section, under either the first or the second version of the hybrid analysis. If we adopt the semantics in (34) in the first hybrid analysis, the choice function variable is closed via Existential Closure and the IP always denotes a single proposition. The semantics of the question would be the singleton set of this proposition. However, this is not the intended AltQ reading. A similar problem arises if we adopt (34) for the second hybrid analysis too.

  4. 4.

    According to [17], the denotation of or is set-theoretic union in both (36a) and (36b). In (36a), or takes the ordinary semantic value of the disjuncts, in this case two propositions, and gives back their union. This is equivalent to the meaning in (36a), a set of worlds where the program executed or the computer crashed. In (36b), on the other hand, or takes the focus semantic value of the disjuncts, namely two singleton sets, and gives back their union. This is equivalent to (36b), a set of the focus semantic values of the disjuncts. Here I use the original analysis of [17] in (36), and not the version of [11] in which the focus semantic value of a DisjP is a set containing the two ordinary meanings of the disjuncts.

  5. 5.

    Note that there is another, perhaps a more salient reading, in which John only saw Bill, among other candidates, or John only saw Sue, among other candidates, but the speaker forgot which John actually saw. This reading falls out from the present analysis by assuming that the covert either floats up to a higher position and (46) can have the LF representation in (i).

    (i) Opi eitheri [John only saw BillF or John only saw SueF]

  6. 6.

    It seems, however, that the intervention effect of only cannot be obtained without a focus alternative semantics for questions. Since, as noted in footnote 3, a focus alternative semantics for questions does not account for AltQ/YNQ data, this point remains as a problem. I leave this point for future research.

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  1. Nagoya University of Commerce and Business, Nisshin, Aichi, Japan

    Mioko Miyama

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  1. Mioko Miyama
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  1. The University of Electro-Communications, Tokyo, Japan

    Maki Sakamoto

  2. Tokyo Institute of Technology, Tokyo, Japan

    Naoaki Okazaki

  3. Keio University, Tokyo, Japan

    Koji Mineshima

  4. National Institute of Informatics, Tokyo, Japan

    Ken Satoh

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Miyama, M. (2020). A Choice Function Analysis of Either in the Either/or Construction. In: Sakamoto, M., Okazaki, N., Mineshima, K., Satoh, K. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2019. Lecture Notes in Computer Science(), vol 12331. Springer, Cham. https://doi.org/10.1007/978-3-030-58790-1_19

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  • DOI: https://doi.org/10.1007/978-3-030-58790-1_19

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