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Deriving presupposition projection in coordinations of polar questions: a reply to Enguehard 2021

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Abstract

This paper is a response to Enguehard (Natural Language Semantics 29(4):527–578, 2021), who observes that presuppositions project in the same way from coordinations of declaratives and coordinations of polar questions, but existing mechanisms of projection from declaratives (e.g. Schlenker in Theoretical Linguistics 34(3):157–212, 2008, Semantics and Pragmatics 2:1–78, 2009) fail to scale to questions. His solution involves specifying a trivalent inquisitive semantics for (coordinations of) questions that bakes the various asymmetries of presupposition projection into the lexical entry of conjunction/disjunction. However, we argue that such a move faces both theoretical and empirical issues. Instead, we show that the data can be handled without moving to such an asymmetric inquisitive denotation, by adapting the novel pragmatic theory of Limited Symmetry (Kalomoiros in Proceedings of the 52nd annual meeting of the North East linguistic society, GLSA, Amherst, 2022) to an inquisitive framework in a way that leaves the underlying semantics for conjunction symmetric and bivalent, while deriving the projection data.

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Notes

  1. But see van Rooij (2005) for an interesting precursor that examines the general problem of projection from modal subordination environments, and who considers (among other things) a version of E’s data.

  2. E’s original paper makes use of the following example:

    1. (i)

      Is Syladvia a monarchy and is the Syldavian monarch a progressive?

    However, when considering the negation of ‘Syldavia is monarchy’ in the context of negated polar questions, and disjoined questions, E takes the opposite of ‘monarchy’ to be ‘republic’, leading to examples like:

    1. (ii)

      # Is Syldavia a republic and is the Syldavian monarch a progressive?

    Native speakers that we consulted found it hard to keep in mind ‘monarchy’ and ‘republic’ as polar opposites, as they did not consider these two systems to exhaust the types of government. The examples in the current paper are still based on the existential presupposition of definites, but instead exploit the ‘married’ vs. ‘unmarried’ contrast, which was judged to be a lot more straightforward by consultants.

  3. We deviate slightly from Schlenker’s notation who writes \(\underline{p}p'\) for a sentence where \(\underline{p}\) is the presuppositional component and \(p'\) the assertive component.

  4. The assumption that presuppositions are separable from the other entailments of a sentence is implicit in a lot of work on presupposition. For instance Karttunen (1974) talks about the ‘atomic presuppositions’ of a sentence. Moreover, presupposition-triggering algorithms (e.g., Abrusán 2011) assume that a presupposition starts as an entailment that gets marked as a presupposition. We then can view the \(p'\) in \(p'p\) as precisely this entailment to be marked as a presupposition (hence the prime). Nevertheless, it should be noted that this is probably an idealization, and that sometimes separating the entailment which is to be presupposed is not as straightforward (see Schlenker 2010). Nonetheless, we think it’s a useful idealization, and we end up adopting it in our system as well.

  5. An anonymous reviewer wonders under what assumptions this could be made to work in a direct interpretation framework, suggesting that this might require taking presupposition triggers to be syntactically complex in the object language. We share the sense that if someone wanted to use this system to directly interpret a more naturalistic syntax, then taking triggers to form syntactic complexes of the form presupposition + assertion would probably be required. In the case of triggers like factive verbs (e.g., ‘know’) there is a sense in which the presuppositional component is already syntactically separable as it appears in the form of a CP complement to the factive verb. For triggers like ‘stop’, we might end up having to postulate the required syntactic complexity, but take the presuppositional component of ‘stop’ to be unpronounced. For current purposes, we leave this issue aside.

  6. Note that β is a variable over substrings.

  7. An interesting thing to note here is that the strategy of quantifying over possible continuations as a way of making a projection system asymmetric isn’t necessarily tied to the particularities of Transparency. As pointed out in Fox (2008) (see also Chemla and Schlenker 2012), we can use this strategy to incrementalize more familiar trivalent accounts of projection (Kleene 1952, Peters 1979, Beaver and Krahmer 2001, George 2008a). Suppose that we start with the traditional Strong Kleene system, which is fully commutative in its base semantics. For example, here’s Strong Kleene conjunction:

    1. (i)

      p∧q

      T

      F

      #

      T

      T

      F

      #

      F

      F

      F

      F

      #

      #

      F

      #

    Then we can add a constraint like the following:

    1. (ii)

      Given a sentence S = (α∗β), where ∗ is a binary connective, if it’s the case that α receives the # value in some world w, and it’s the case that for all possible constituents γ the truth value of (α∗γ) is constant in w (according to the Strong Kleene table), then assign to S that constant truth value. Otherwise, assign to S the value #. If α doesn’t receive the # value in w, then the value of the entire sentence in w is the one given by the Strong Kleene table.

    In this constraint, good finals are thought of as possible constituents that can substitute for the second argument in (α∗β), and as such the constraint has a more structural nature than the Transparency constraint, where good finals are substrings. However, the effects are similar: by applying this constraint to the Strong Kleene tables, we get the so-called Middle Kleene tables. For example, in (α∧β), if α is # in some w, then there are continuations that make the sentence both 0 (take β = 0) and # (take β = #). So, the truth value of the sentence isn’t constant regardless of continuation in w, and the sentence receives the # value. The full Middle Kleene table for conjunction is as follows:

    1. (iii)

      p∧q

      T

      F

      #

      T

      T

      F

      #

      F

      F

      F

      F

      #

      #

      #

      #

  8. That is not to say that there aren’t issues. In particular, the case of connectives that behave symmetrically (e.g., disjunction) forces Schlenker to say that both symmetric Transparency and asymmetric Transparency are available, with asymmetric Transparency being the preferred default, as it follows the order imposed by incremental interpretation. However, recent experimental results suggest that symmetry is not available to the same extent for all connectives. It is much more readily available in disjunctions than in conjunction; this constitutes a challenge for the idea that all connectives have access to both kinds of Transparency. In this respect, some of the questions that arise in Heim’s theory reappear, in the form of what conditions the choice of one kind of local context over the other. It is exactly this kind of problem that Limited Symmetry was originally designed to solve. See Sect. 3 for some more discussion of this, as well as Kalomoiros and Schwarz (Accepted).

  9. Schlenker (2009) proposes an equivalent formulation of these ideas in the form of his Local Contexts theory. The idea behind that reformulation is that the Karttunen-Heim notion of ‘local context’ (Karttunen 1974; Heim 1983) can be re-conceptualized as the strongest proposition r that we can conjoin to a constituent E such that α(r and E)β is equivalent to αEβ, for all E, and for all β (it should be clear that this requires r to be asymmetrically transparent with respect to E). Since the theory that we use to develop our own ideas in this paper is much more transparently connected to Transparency Theory than to Local Contexts, we limit our presentation here to Transparency. See Schlenker (2009) for more details on Local Contexts.

  10. If there were no such worlds, then all worlds where |q| is false would be worlds where either |p| is true or \(|q'|\) is true; that is, \(|\neg q| \models |p \vee q'|\). Since \(|p| \models |q'|\), this is equivalent to \(|\neg q| \models |q'|\), which is equivalent to \(|\neg q'| \models |q|\), which violates the assumption that |q| and \(|\neg q'|\) are not related by contextual entailment.

  11. E extends this claim to trivalent accounts of presupposition projection like George (2008a). The point is that trivalence ends up operating on the question level in E’s theory, and not just at the declarative level.

  12. Here we present a version of Limited Symmetry that is formalized enough to make the main ideas clear, but is not meant to be comprehensive. For a more comprehensive statement of the theory, see Kalomoiros (2023). An even fuller treatment will hopefully be published in the future.

  13. We use the verbatim font to refer to partial syntactic objects.

  14. As pointed out by an anonymous reviewer, formulating these sets based on true vs. non-true opposition (instead of the true vs. false opposition) has the advantage of allowing the system to be compatible with an underlying semantics that involves truth value gaps/trivalence. We do not pursue this alternative here (since classical bivalent logic is enough to derive our basic results), but it’s an interesting potential extension of the ideas here. See also Kalomoiros (2023) for more.

  15. This assumption does not lead to any loss of generality. If a sentence S has multiple instance of \(p'p\) in it, rewrite the ones after the first instance with other symbols of the \(p_{i}'p_{j}\) form, stipulating that the interpretation of these is the same as the original \(p'p\) (see also Rothschild 2008).

  16. Suppose that at some parsing point, we can determine that for all p, all of the worlds where the sentence S is already true/false for all continuations are worlds where \(S_{p'p/p}\) is also true/false. Then since these worlds are in the set of true/false worlds for all continuations, when the comprehender moves to next parsing point and recalculates these sets, there is no need to include the worlds that they checked on the previous step. For those worlds the constraint holds. So, the comprehender could explicitly remove these worlds from the context as they restart the checking routine. However, encoding this in the definitions above directly would only add to their complexity without any gain/change in the predictions of the theory. Even though we do not pursue this enhancement here, the point is important in the larger scheme of things, as it could help us recover a notion of ‘local context’ parallel to that of Schlenker (2009). We leave a more detailed elaboration of this point for the future.

  17. As before, the language includes conditionals. We do not make use of conditionals in the examples that we study, and the connective is only included here because the semantics of negation are defined via reference to it. Moreover, in Limited Symmetry, conditionals are best represented via an (if (ϕ)(ψ)) syntax, so that the parser knows immediately that they are dealing with a conditional, and not just after they have parsed the entirety of the antecedent. See Kalomoiros (2023) for more information.

  18. Thanks to an anonymous reviewer whose comments helped me clarify this point.

  19. A potentially alternative line of inquiry here is to assume that comprehenders categorize states into the ones that are in the denotation of the dref (and hence resolve the questions positively) vs. ones that are not in the denotation of the dref (and hence are states that either don’t resolve the question, or don’t resolve it positively). In the main text, we develop an approach whereby states are categorized into being in the denotation of the dref or in the denotation of its negation, as this will allow us to straightforwardly derive E’s tripartition pragmatically (see Sect. 4.2).

  20. The exact licensing conditions of polarity particles are not an uncomplicated matter (see Pope 1976, Kramer and Rawlins 2009, Farkas and Bruce 2010, Roelofsen and Farkas 2015, a.o. for more details and references). Polarity particles responses to polar question usually come in the form pol particle + prejacent, and properties of the prejacent (specifically whether or not the prejacent contains a negation) can affect whether a polarity particle is licensed. Consider the following (taken from Roelofsen and Farkas 2015):

    1. (i)

      A: Did Peter not call? B: No, he didn’t. / Yes, he didn’t.

    Putting things somewhat loosely here, Roelofsen and Farkas (2015) argue that ‘yes’ is licensed when the prejacent agrees with the discourse referent introduced by the question (in the sense that the prejacent and the discourse referent express the same proposition) or when the prejacent doesn’t contain a negation. ‘No’ is licensed when the prejacent disagrees with dref or when the prejacent contains a negation. So, in this example, ‘yes’ is licensed because the response agrees with the content of ‘Peter didn’t call’, but ‘no’ is also licensed because ‘Peter didn’t call’ contains a negation.

    To avoid the confound introduced by whether the prejacent contains a negation, our example in (42) contains no negations; in that case, monolectic yes/no responses appear to care solely about agreement vs. diagreement with the dref introduced by the question.

  21. Note the direction of the logic here: if you can answer ‘Yes’, or ‘No’ to a question Q in a given state s, that diagnoses polarity in that state; not being able to give a yes/no response in a given state s tells us nothing about the overall polarity in s.

  22. Since the Roelofsen and Farkas (2015) framework has been quite influential to our thinking here, a few comments on it are warranted. Roelofsen and Farkas (2015) also take polar questions to introduce discourse referents. However, they identify the discourse referents with the positive and negative highlights of a question ?ϕ (see Roelofsen and van Gool 2010), which in turn are possibilities associated with the meaning of ϕ. Possibilities/Alternatives are the maximal states in the denotation of ϕ. Therefore, the drefs that Roelofsen and Farkas (2015) use do not have syntactic status, but rather are semantic in nature. For our purposes, it will be more convenient to have access to a syntactic dref so that we can reason about its possible continuations during the parse.

    Another aspect of the Roelofsen and Farkas (2015) system is that the discourse referents are marked as positive vs. negative. This is needed because they want to account for the distribution of polarity particles like ‘yes’ and ‘no’, which are sensitive to whether the discourse referent introduced by the question contains a negation or not (see fn 20). Since the notion of ‘resolving/not resolving a question positively’ that is of interest to us cares only about agreement with the discourse referent, and not about the presence/absence of negation, we eschew the more complicated definition of highlights in the interest of keeping things simple.

    That said, even if we wanted to use the definitions of highlights to define the relevant notions, there is at least one non-trivial challenge to be overcome. To see this, first consider the definition of highlights:

    1. (i)

      • \([\!\![p ]\!\!]^{+/-} = \langle \{|p|\}, \emptyset \rangle \)

      • \([\!\![\neg \phi ]\!\!]^{+/-} = \langle \ \emptyset , \{\overline{\cup [\!\![\phi ]\!\!]^{+/-}}\}\rangle \)

      • \([\!\![\phi \vee \psi ]\!\!]^{+/-} = \langle [\!\![\phi ]\!\!]^{+}\cup [\!\![\psi ]\!\!]^{+}, [\!\![\phi ]\!\!]^{-}\cup [\!\![\psi ]\!\!]^{-}\rangle \)

      • \([\!\![?\phi ]\!\!]^{+/-} = \begin{cases} \langle \ \emptyset , \{\alpha \}\rangle \ \text{if} \ [\!\![\phi ]\!\!]^{+/-} = \langle \ \emptyset , \{\alpha \}\rangle \\ \langle \{\cup [\!\![\phi ]\!\!]^{+/-}\}, \emptyset \rangle \ \text{otherwise}\end{cases} \)

    The first coordinate of these pairs represents the positive highlight, whereas the second coordinate represents the negative highlight. If we wanted to extend this to conjunction, a reasonable clause to add would be:

    1. (ii)

      \([\!\![\phi \wedge \psi ]\!\!]^{+/-} = \langle [\!\![\phi ]\!\!]^{+}\cap [\!\![\psi ]\!\!]^{+}, [\!\![\phi ]\!\!]^{-}\cap [\!\![\psi ]\!\!]^{-}\rangle \)

    This predicts, for instance, that the highlight introduced by (?p∧?q) will be positive and can be identified with {|p∧q|}. As we have seen, this is the proposition that ‘so’ picks up in an example like (41). However, consider the following:

    1. (iii)

      A: Is Emily unmarried and does she like traveling? B: I think so.

    The ‘so’ here picks up ‘Emily is unmarried and she likes traveling’ as its referent. But our extension does not predict this. If we represent (iii) as (?¬p∧?q), then \([\!\![?\neg p ]\!\!]^{+/-} = \langle \emptyset , \{|\neg p| \} \rangle \), and \([\!\![?q ]\!\!]^{+/-} = \langle \{|q|\}, \emptyset \rangle \). Taking the point-wise intersection, we get \([\!\![?\neg p \wedge ?q ]\!\!]^{+/-} = \langle \emptyset , \emptyset \rangle \). This means that no non-empty possibility is available to be picked up by ‘so’. While there may some way to get correct results here, taking the discourse referent to be syntactic simplifies the situation considerably and avoids such complications.

  23. Note that as in Sect. 3, fn 14, the definition here is not necessarily tied to truth vs. falsity of Decl(S). We could perfectly well define ℕ to be the set of states that support the non-truth of Decl(S), where non-truth could be falsity or undefinedness in a trivalent system. As with the classical Limited Symmetry system, we do not pursue such an alternative here (but see Kalomoiros 2023).

  24. For the constraint in (46) to be fully defined, we need to extend the definition \(S_{p'p/p}\) to \(L^{+}\). Since the extension is routine, we leave it implicit.

  25. We count ?-operators as a basic parsing unit.

  26. Recall that |ϕ| is the classical proposition associated with inquisitive ϕ.

  27. Of course the issue here is the justification. The Strong Kleene truth table for conjunction is also symmetric, but experimental results suggest that projection is rigidly asymmetric in conjunction (Mandelkern et al. 2020). This is exactly the justification that Limited Symmetry aims to provide by deriving symmetric disjunction, but asymmetric conjunction. That said, there are ways to systematically derive trivalent truth tables where conjunction is asymmetric but disjunction is symmetric. George (2008b) proposes the so-called ‘disappointment’ algorithm which derives a symmetric trivalent truth table for disjunction, but an asymmetric one for conjunction. We could state E’s resolution conditions in terms of this system and thus get the right (a-)symmetries in a principled way. Thanks to Patrick Elliot (p.c.) for discussion on this point.

  28. As pointed out by an anonymous reviewer, this feature of the system means that the filtering properties of conjunctions/disjunctions of questions are forced to be the same as the filtering properties of conjunctions/disjunctions below an ?-operator. In a theory where the filtering properties of conjunctions/disjunctions below an ?-operator can be derived by a different mechanism from the one that derives the filtering properties of conjunctions/disjunctions of questions, we might expect less tight filtering parallelisms between the two kinds of constructions. We leave further consideration of this point and its potential empirical consequences for future research.

  29. I take no position here on the correct analysis for closed disjunctive questions, as it is beyond the scope of the projection facts.

  30. Thanks to an anonymous reviewer for suggesting this way of looking at the issues.

  31. The same reviewer also points out that once we move away from the semantics of the question to essentially the semantics of the declarative, we could have applied a theory like Transparency to Decl(?ϕ) and get good results. We chose Limited Symmetry as it offered an interesting hypothesis about what comprehenders go about computing incrementally when parsing polar questions and their conjunctions/disjunctions, and also made interesting predictions about (a-)symmetries between conjunction vs. disjunction.

  32. For example:

    1. (i)

      It’s possible that Mary speaks French, but I don’t think that’s the case.

    The ‘that’ in the second conjunct refers to ‘Mary speaks French’.

  33. van Rooij (2005) proposes a dynamic solution that eschews discourse referents, but the asymmetry is essentially introduced by the update effect that modals have. Simplifying quite a bit, updating with a sentence like ‘It’s possible that John used to smoke’ makes the worlds where ‘John used to smoke’ preferred. In a conjunction then like (80c), the second conjunct is sensitive to these ‘preferred’ worlds. van Rooij’s solution is stated in a dynamic framework where what is presupposed is analyzed as a propositional attitude. The differences between his system and the systems we have been discussing in the present paper are sufficiently large that a detailed comparison will have to await another occasion. See his paper for more details.

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Acknowledgements

This paper derives from my dissertation work, undertaken at the University of Pennsylvania between 2018 - 2023. As such, I am indebted to my supervisor, Florian Schwarz, as well as to my committee members, Julie Legate, Anna Papafragou and Jacopo Romoli, for their support and insightful feedback. Thanks also to my editor Clemens Mayr, as well as to two anonymous NALS reviewers for very helpful discussion. Thanks are also due to the audience of SuB 27 for providing useful feedback on a previous version of this work. Throughout my work on this paper, I have also benefitted greatly from discussions with Andrea Beltrama, Patrick Elliot, Phillipe Schlenker, Muffy Siegel, Benjamin Spector and Jeremy Zehr, and from presenting this work to the members of the Penn Semantics Lab. Needless to say that Phillipe Schlenker’s work, as well as the original paper by Émile Enguehard that prompted the present response, have been deep sources of inspiration for me. Of course, all errors are my own.

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  1. Department of Linguistics, University of Pennsylvania, Philadelphia, USA

    Alexandros Kalomoiros

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Kalomoiros, A. Deriving presupposition projection in coordinations of polar questions: a reply to Enguehard 2021. Nat Lang Semantics 31, 253–290 (2023). https://doi.org/10.1007/s11050-023-09206-z

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