Sentential negativity and polarity-sensitive anaphora A hyperintensional account Lisa Hofmann University of California Santa Cruz 1 Introduction This paper is concerned with an asymmetry between positive and negative sen- tences in discourse.1 The licensing of certain propositional anaphora is contin- gent on the polarity of their antecedent clause. I call them Polarity-Sensitive Anaphora (PSAs). Among these are polar additives (Klima (1964)) and polarity particles (Farkas and Bruce (2010); Roelofsen and Farkas (2015)). (1) Polar additives (2) Agreement with polarity particles a. Mary slept. a. Mary slept. (i) So did Dalia. (i) Yes, she slept. (ii) #Neither did Dalia. (ii) #No, she slept. b. Mary didn’t sleep. b. Mary didn’t sleep. (i) #So did Dalia. (i) Yes, she didn’t sleep. (ii) Neither did Dalia. (ii) No, she didn’t sleep. Polar additives are polarity-sensitive in their licensing: Positive polar ad- ditives with so are available with a positive antecedent (1-a), but not with a negative one (1-b), whereas neither shows the opposite pattern. Polarity parti- cles (PolPs) are polarity-sensitive in their interpretation. In a positive context (2-a), only yes, but not no can be used to agree with the antecedent. In the negative context, this contrast is neutralized (Ginzburg and Sag (2000); Roelof- sen and Farkas (2015)) and either polarity particle can be used to agree. These asymmetries lead me to two questions: 1. How can the polarity-sensitivity of PSAs be accounted for? 2. What renders a sentence positive/negative for the purposes of discourse and how might that be captured theoretically? 1. PSAs: Following analyses of PolPs as anaphora to propositional content (Ginzburg and Sag (2000); Krifka (2013); Roelofsen and Farkas (2015)), I am treating PSAs as propositional anaphora. A minimal semantic theory of propo- sitional anaphora would be based on a standard conception in terms of sets of worlds, an unstructured representation, which couldn’t make the relevant polar- ity distinctions. 1 This paper grew out of the work for my second quanlifying paper at UCSC. I am indebted to Adrian Brasoveanu and Donka Farkas for invaluable guidance and feed- back. Thank you also to Jorge Hankamer, Chris Barker, Morwenna Hoeks for helpful comments and discussion, as well as the participants of the Winter 2019 290 Research Seminar at UCSC. Special thanks to Jim McCloskey for inspiring my interest in this phenomenon. 2. Discourse polarity: The phenomenon of discourse negativity is influ- enced by syntactic, semantic and pragmatic factors. Klima (1964) argued that licensing contexts for negative PSAs should be characterized in syntactic terms, based on the fact that they couldn’t be licensed by lexical entailments. (3) Non-licensing by lexical entailments: A: Peter failed the test. B: # Neither did I. Peter didn’t pass the test. (I didn’t pass the test either) ↔ # No, he didn’t. (Agreeing) A’s utterance in (3) introduces the proposition that Peter failed the test. Given satisfaction of the presuppositions, (3) should be equivalent to the negative para- phrase Peter didn’t pass the test. If PSAs involved propositional anaphora that could be formalized purely in terms of sets of worlds, we might expect this con- text to license negative PSAs, which is not the case. Further, negative PSAs may be licensed by sentences in which negation is outscoped by another operator. (4) a. High-scoping modals: A: I shouldn’t go alone. (□ > ), ( > □) B: Me neither. (I shouldn’t go alone either.) ¬ ¬ ̸ No, you really shouldn’t. b. Quantified pronouns: A: We all didn’t sleep. ( > ), ( > ) B: Me neither. (I didn’t sleep either.) ∀ ¬ ¬ ̸ ∀ No, you truly didn’t Horn (1989) suggests that cases like (4-a) pose problems for any purely semantic (i.e. non-syntactic) account of sentential negation. Note that nega- tion is outscoped not only in the antecedent, but also in the interpretation of the anaphoric expression. The content that is picked up anaphorically includes the meaning components introduced by negation and the outscoping operator. Therefore, this data provides a challenge to semantic accounts that assume that negative PSAs are anaphoric to a proposition that is in the scope of negation. While non-licensing by entailment and the outscoping-cases pressure towards an account that can capture the relevant surface-based generalizations, other li- censing contexts pressure against a purely syntactic account. These are cases where negative PSAs are licensed by antecedents that do not contain overt negation, like the cases that Kroll (2016) identifies as contexts licensing polarity- reversals in sluicing, such as contexts involving neg-raising. (5) Neg-raising: I don’t think Mary exercises, … a. …and neither do I. (I don’t exercise either.) b. …No, she really doesn’t. (Mary really doesn’t exercise.) If we assume that neg-raising is a meaning-based phenomenon that isn’t derived syntactically (following Gajewski (2007)), the neg-raising cases pose a serious challenge for a syntactic characterization of sentential negativity that imposes constraints on the morphosyntactic expression of negation.2 The heterogeneity of factors influencing discourse polarity suggests a seman- tic level of representation that may capture both contextual influences and rele- vant morphosyntactic factors. To achieve this, I introduce a representation of the polarity of propositional anaphora in the framework of Compositional Discourse Representation Theory (CDRT, cf. Muskens (1996)) enriched with hyperinten- sional propositional discourse referents (based on Thomason (1980)). 2 Informal Account CDRT with hyperintensional propositional discourse referents (drefs) provides a way of making reference to positive and negative propositions in discourse, connecting information from the linguistic context, the semantic content of the proposition, and the information whether the proposition was introduced by a negative sentence. Roelofsen and Farkas (2015) (R&F) suggest representing polarity on the level of propositional discourse referents, analogously to Farkas and Zec’s (1995) treatment of gender features on pronouns, in which discourse referents function as a level of representation that incorporate both semantic and morphosyntactic sources of gender specification. The account presented here gives a formal foundation to the [+/ ] distinction for polarity of propositional anaphora suggested in R&F. − This distinction is conceptualized here in terms of propositional drefs as re- ferring to hyperintensional propositions in the sense of Thomason (1980), i.e. atomic propositional objects. In Thomason’s spirit, I add not one, but two basic types for positive and negative propositions. Propositions are related to their truth-conditional content (i.e. a set of worlds) by means of a content-function. This provides a way of making reference to propositional content in discourse, while referencing the information whether the propositional dref was introduced by a positive or a negative sentence. The lexical entries of natural language expressions guarantee that a sentence involving negation introduces a negative propositional dref and a sentence without negation introduces a positive propo- sitional dref. This is achieved on the level of type-theory, as the interpretation of the discourse would otherwise result in a type-mismatch. 2 Other cases that could be viewed as cases of contextually introduced negativity are given in (i). Unlike neg-raising, these cases receive mixed acceptability judgments and require further empirical study. (i) a. after Kroll (2016): 1) I don’t remember being scared. And neither was my dog. 2) Love yourself, or neither will anybody else. b. Jim McCloskey (p.c.): However, he moved here without knowing a word of English, and neither did his mom or his sister. 3 Outline of the formal account 3.1 Hyperintensional CDRT Thomason (1980) introduced hyperintensionality to account for non-closure un- der entailment for complements of belief-statements. Entailment is defined over sets of worlds, and introducing a basic type of propositions p as primitive objects achieves that propositions don’t participate in entailment relations any more. Similarly, proportional polarity can be distinguished on the level of type the- ory, if we assume a two-sorted domain of basic propositional objects: + . Dp ,Dp− We yield hyperintensional propositional drefs, which allow us to make reference to propositions of a certain polarity in discourse. A negative dref couldn’t be derived by entailment from a positive one, or vice versa. The analysis captures the selective nature of PSAs, and rules out cases where they are not licensed as type mismatches. Hyperintensional propositions are related to their truth-conditional content (represented as a set of worlds) by a content-function, which assigns a relation wt for each proposition p D + D . ∈ p ∪ p− (6) Content function: + Contp(wt), for p p , p− , s.t. for any proposition p, Cont(p) is the set of worlds that∈ is { the ‘content’} of p, i.e. the set of worlds in which p is true. (6) only defines the shape of the function, i.e. its type. Whatever actually isthe set of worlds associated with a basic propositional object will be constrained by the interpretation of linguistic expression in discourse. The formalization of the proposed hyperintensional dynamic system adapts the dynamic Ty2 Logic introduced as the Logic of Change in Muskens (1996). Including reference to propositions, I am closely following Brasoveanu’s (2010) implementation of this system.3 The system uses six basic types: t (truth-values), e (entities), w (possible + worlds), p (positive propositions), p− (negative propositions), and s (variable assignments). A dref for individuals υ is a function of type se from assignments is to individuals xe (subscripts on terms indicate their type). Accordingly, the individual υse(is) is the individual that the assignment i assigns to the dref υ.A + + dref for positive propositions π is a function of type sp from assignments is + to positive propositions p . and a dref for negative propositions π− is a function of type sp− from assignments is to negative propositions p−.