Abstract
Certain propositional anaphora, like the Polarity Particles and Polar Additives discussed in this paper, are sensitive to the polarity of their antecedent clause. The paper establishes that discourse polarity—the polarity of the antecedent clause for the purposes of licensing subsequent anaphora—is influenced by complex factors, some of them syntactic, semantic, and pragmatic in nature.
The hyperintensional dynamic framework presented here gives a formal foundation to a distinction of polarity for propositional discourse referents and captures some of the central generalizations. It uses discourse referents for hyperintensional propositions, providing a level of representation that connects information from the discourse context, the proposition’s semantic content, and the information about the polarity of the antecedent clause. Therefore, it constitutes a step towards an analysis capturing the heterogeneous factors influencing discourse polarity.
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Notes
- 1.
Ahn (2015) suggests that additive either/too is anaphoric to a proposition in the discourse which serves as grounds for satisfying the additive presupposition, which we adopt here for neither/so. Additive so is semantically distinct from propositional so-anaphora, which can occupy CP-positions (e.g. I believe so). The latter do not come with an additive inference (see e.g. Hankamer and Sag 1976).
- 2.
for \(\upsilon \in {\textbf {Term}}_{s(we)}\), \(\pi \in {\textbf {Term}}_{sp}\), where \(p \in \{p^+, p^-\}\)
- 3.
An anonymous reviewer points out that Fox and Lappin (2008) show that Thomason’s intentional logic cannot do what it is intended to do, viz. distinguishing between distinct, but logically equivalent, propositions. This is shown based on the algebraic properties of the used meaning postulates, which relate hyperintensional propositions to truth-values (\(D_p \mapsto 2\)). Unlike intentional logic, hyperintensional CDRT has an intensional layer, and a content-function (\((D_{p^+} \cup D_{p^-}) \mapsto D_{wt}\)). This allows distinct propositional objects to be related to the same content and avoids the problems Fox and Lappins identify for Thomason’s intentional logic.
- 4.
- 5.
Since this is a hypothetical local update in the scope of the quantifier, the embedded \(\pi ^+_2\) is predicted to never be accessible outside of the scope of the quantifier. The current system does not provide a way of capturing the constraints (and possibilities) for anaphora to quantified content. See Brasoveanu (2006; 2010b) for an account that can handle anaphora to quantified content by making use of selectively distributive dynamic quantification and structural dependencies between plural drefs.
- 6.
A formal treatment of the additive presupposition requires additional machinery to deal with presuppositions, and focus alternatives, and is glossed over here. I am also not accounting for (interaction with) VP-ellipsis at this point.
- 7.
An anonymous reviewer suggests that instead of sentential mood, one might attribute the introduction of a propositional dref to a TP-level sentential operator, as in e.g. Roeper (2011; Krifka (2013); van Elswyk (2018). This may have some empirical weaknesses as noted in Snider (2017), but it would include polar interrogatives in the analysis more straightforwardly.
- 8.
The superscript \(\phi \)-variables indicate the introduction of (here not necessarily hyperintensional) propositional drefs, and the lowercase instances of these variables indicate that they are being picked up anaphorically.
- 9.
The idea that anaphoric accessibility is constrained in terms of local contextual entailment of a referent is also found for individual anaphora in Stone (1999); Brasoveanu (2010a); Hofmann (2019). See also work in Elliott (2020; 2022); Mandelkern (2022), which develops the intuition of contextual entailment for individual anaphora on a global discourse level.
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Acknowledgments
This paper is a revised version of Hofmann (2019), presented at ESSLLI student session 2019. It grew out of work during my graduate studies at UCSC. I am grateful for Adrian Brasoveanu’s and Donka Farkas’ invaluable guidance and feedback. Thank you also to Jorge Hankamer, Amanda Rysling, Chris Barker, Morwenna Hoeks for helpful comments and discussion, the participants of the UCSC 2019 Research Seminar, and anonymous reviewers from ESSLLI for insightful feedback. Special thanks to Jim McCloskey for inspiring my interest in this phenomenon.
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Hofmann, L. (2024). Sentential Negativity and Anaphoric Polarity-Tags: A Hyperintensional Account. In: Pavlova, A., Pedersen, M.Y., Bernardi, R. (eds) Selected Reflections in Language, Logic, and Information. ESSLLI 2019. Lecture Notes in Computer Science, vol 14354. Springer, Cham. https://doi.org/10.1007/978-3-031-50628-4_7
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