The Anaphoric Potential of Indefinites under Negation and Disjunction Lisa Hofmann (UC Santa Cruz) . Amsterdam Colloquium 2019 1 Introduction This talk A generalization • Presents an analysis of the above cases in intensional Compositional DRT (CDRT, following Muskens (1996); Brasoveanu (2010)) based on the assumption that a pronoun can be co-referential Indefinite DPs under non-veridical operators such as negation do not usually introduce a discourseref- with a preceding DP only if the referent of the DP exists in the worlds of evaluation of the pronoun erent (dref) that is available for subsequent reference (Karttunen (1969)): – Uses analyses of modal subordination in terms of simultaneous reference to sets of possible (1) There is [no bathroom]υ in this house. worlds (propositions) and individuals #Itυ is in a weird place. (Stone (1999); Stone and Hardt (1999); Brasoveanu (2007, 2010)) – Extends them to disjunction, double negation and disagreement cases

Some counterexamples 2 The account (2) a. Double negation: (Karttunen (1969); Krahmer and Muskens (1995)) The intuition behind the analysis υ1 It’s not true that there is [no bathroom] in this house. Itυ1 is just in a weird place. • Counterfactual drefs under negation: Speaker committed to their non-existence b. Disjunction: (Krahmer and Muskens (1995)) (cf. hypothetical drefs in Stone (1999); Stone and Hardt (1999)) υ2 Either there is [no bathroom] in this house, or itυ is in a weird place. 2 • Pronoun presupposes existence of a referent c. Modal subordination: (Roberts (1989)) υ3 There is [no bathroom] in this house. Itυ3 would be easier to find. • Use of a pronoun in veridical contexts is inconsistent with counterfactual dref antecedent d. Disagreement: • BUT: Pronoun can co-refer with counterfactual dref if A: There’s [no bathroom]υ4 in this house. – It is in a counterfactual context (Modal subordination) B: (What are you talking about?) Itυ4 is right over there. – The discourse segments of the antecedent and pronoun do not have to be consistent (disjunc- tion, disagreement) Krahmer and Muskens (1995) The account in a nutshell Note that standard Discourse Representation Theory (DRT, Kamp (1981); Kamp and Reyle (1993)) (and • Antecedents and pronouns are interpreted relative to their local intensional context other classic dynamic semantic frameworks) don’t account for the counterexamples • Relativizing individual drefs to sets of worlds where they refer (Stone (1999); Stone and Hardt • Negation is externally static, indefinites in its scope never introduce global drefs (1999)) – In DRT, it introduces a subordinated discourse representation structure (DRS) – Gives rise to accessibility condition, capturing that pronouns presuppose existence of a ref- – Only drefs introduced in the same DRS or a superordinate DRS are accessible erent and are infelicitous otherwise • Sentential operators introduce drefs for sets of worlds providing a local context for interpretation of their prejacent K & M introduce an account of double negation and disjunction cases, based on… – Relation between local and global context sets is constrained semantically by the interpreta- • Semantics for negation that symmetrically switches between the extension and anti-extension of tion of linguistic expressions an expression Karttunen (1973); Heim (1983) • Semantics for disjunction that analogizes it to conditionals, truth-conditionally and dynamically – And pragmatically by set of worlds compatible with a speaker’s commitments • Doesn’t extend to cases w/o overt negation or disjunction (disagreement, modal subordination) Stalnaker (1978, 2002); Gunlogson (2004)

1 December 18, 2019 The Anaphoric Potential of Indefinites under Negation and Disjunction Lisa Hofmann

2.1 Intensional CDRT ϕ, ϕ : υ1, υ2

υ1 = Marye (3) Mary has a car ⇝ CDRT with propositional discourse referents Muskens (1996); Brasoveanu (2007, 2010) carϕ{υ2} { } • Four basic types: haveϕ υ1, υ2 t (truth-values), e (entities), w (possible worlds), and s (variable assignments) Relative variable update • Variable assignments Individual drefs map to an individual for all worlds in which their referent exists, and to an indeterminate – Objects manipulated and updated in context value #e in all other worlds (cf Stone (1999); Stone and Hardt (1999)) – In classic static systems: Functions from variables to entities (4) i[ϕ : υ]j, where ϕ ∈ Term , υ ∈ Term , holds iff the conjunction of the following holds: – Here: Basic type s (discourse states) s(wt) s(we) • Discourse referents (drefs) •i[υ]j

′ – Functions from assignments to referents •∀ww.(ϕ(j)(w) → υ (i)(w) ≠ # – Individual drefs: type s(we) •∀ww.(¬ϕ(j)(w) → υ(j)(w) = #) ∗ Functions from assignments is and worlds ww to individuals xe ∗ Drefs for individual concepts j is an update of i with υ in relation to ϕ, iff ∗ Variables: υ, υ1, υ2,... • j is an update of i that differs at most wrt the value assigned to υ – Propositional drefs: type s(wt) • for each world w in ϕ(j), υ(j)(w) doesn’t map to # (but an individual) ∗ Drefs for sets of worlds • for each world w not in ϕ(j), υ(j)(w) maps to # ∗ Variables: ϕ, ϕ1, ϕ2,... Negation • Sentence meanings Negation introduces a counterfactual set of worlds wrt which its prejacent is interpreted – Conceptualized in terms of their context-change potential – Binary relations between discourse states: Type s(st) (5) S: Mary doesn’t sleep. – Anaphoric potential: Updating variable assignments ϕ1, ϕ1 : υ, ϕ2 ⊆ – Truth-conditions: Imposing conditions on propositional drefs ϕDCS ϕ1 S :(not(Mary sleep)) ⇝ υ = Marye

ϕ1 = ϕ2 { } sleepϕ2 υ

2.2 Drefs in relation to their local context • New drefs: • Conditions:

– Matrix ϕ1 – ϕ1 is entailed by the commitments of S DRSs and Relativizing individual drefs ϕDC – not: Embedded ϕ2 S • A DRS contains a list of new drefs (ϕ, ϕ : υ1, . . . , υn) – Mary: υ – Mary: υ refers to marye – Where individual drefs are introduced relative to propositional ones – not: ϕ1 and ϕ2 are complements

• and a series of conditions of type st, i.e. properties of the output state (C1,...,Cn) – Verb: υ sleeps in ϕ2

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Accessibility condition on pronominal reference: The hypothetical bathroom • A dref is accessible for reference by a variable, iff the referent exists in the local context ofthe υ variable. (7) S: There is [no bathroom] 1 . (9). S: It would be (more) accessible. • Local context defined wrt the evaluation of DRS conditions: ϕ1, ϕ2, ϕ2 : υ1 ϕ3 ⊆ ⊆ ϕDCS ϕ1 ϕDCS ϕ3 (6) Predicates with their arguments as conditions (type st): { } { } ∀ ∈ ϕ1 = ϕ2 wouldϕ3 underlineϕ4 carϕ υ2 := λis. w ϕ(i).car(υ2(i)(w))(w) { } { } bathroomϕ2 υ1 accessibleϕ4 υ2 – υ2 is a car in ϕ wrt the variable assignment i, iff – Each world w in ϕ(i) is s.t. • Modal subordination: (Stone (1999); Stone and Hardt (1999); Brasoveanu (2007, 2010)) ∗ υ2(i)(w) ≠ # (i.e. a referent of υ2 wrt i exists in w) and ∗ υ2(i)(w) is a car in w – would is anaphoric to a proposition that is not taken to be true in ϕDCS , this can be the counterfactual ϕ2 • A dref is an accessible antecedent for a variable in the context of is, ϕs(wt) iff the dref refers to something other than # (i.e. an actual individual) in each world in ϕ, wrt i – The local set of worlds for the interpretation of its prejacent is provided compositionally { } • Now we have accessibleϕ2 υ2 , so we get υ1 = υ2 2.3 Drefs under negation

The non-existent bathroom The optional bathroom

υ1 (7) S: There is [no bathroom] . (8) # S: Itυ3=υ1 is in a weird place. υ1 (10) S: Either there is [no bathroom] ,or itυ =υ is in a weird place. ϕ1, ϕ2, ϕ2 : υ1 ϕ3, ϕ3 : υ2 3 1 ⊆ ⊆ ϕ1, ϕ2, ϕ3, ϕ4, ϕ4 : υ1, ϕ3 : υ2 ϕDCS ϕ1 ϕDCS ϕ3 ϕDC ⊆ ϕ1 ϕ1 = ϕ2 placeϕ {υ2} S 3 ϕ = ϕ ∪ ϕ bathroom {υ } weird {υ } 1 2 3 ϕ2 1 ϕ3 2 ϕ = ϕ { } 2 4 inϕ3 υ3, υ2 { } bathroomϕ4 υ1 place {υ } • New drefs: • Conditions: ϕ3 2 { } weirdϕ3 υ2 – Matrix ϕ1 – ϕ1 is entailed by the commitments of S (ϕDCS ) { } inϕ3 υ3, υ2 – Embedded ϕ2 – ϕ1 and ϕ2 are complements • Assertion compatible with speaker’s commitments – υ1 exists in ϕ2 – υ1 is a bathroom in ϕ2 • Disjunction introduces two local sets of worlds that don’t have to be compatible • υ exists in all and only the counterfactual ϕ -worlds 1 2 • First disjunct: Analogous to the above negative sentences • υ1 doesn’t exist in any worlds in ϕ1, the complement of ϕ2 – υ1 exists in all and only the ϕ4-worlds, and in none of the worlds in ϕ2 { } • υ3 is interpreted in the condition inϕ3 υ3, υ2 • Second disjunct:

• For υ1 to be an antecedent for υ3, υ1 needs to exist in all ϕ3-worlds – For υ1 to be an antecedent for υ3, υ1 needs to exist in all ϕ3-worlds ∩ ∩ ∅ • ϕDCS contains only worlds that are in ϕ1 ϕ3 • Compatible with an output discourse state, s.t. υ1 exists in ϕ3, i.e. the one where ϕ2 ϕ3 = , and υ3 can be resolved as υ1 • So, there are ϕ1-worlds in ϕ3, i.e. worlds where υ1 doesn’t exist

• υ3 can’t refer to υ1

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The contested bathroom 4 Conclusion • The paper presents an analysis results in a flat-update dynamic semantics that globally introduces υ1 (7) S: There is [no bathroom] . (11). B: Itυ1 is (right over) there. anti-veridical drefs along with the information about the sets of worlds in which they exist : ϕ1, ϕ2, ϕ2 υ1 ϕ3 • The analysis provides an understanding of when the surrounding context allows for an anaphoric ϕ ⊆ ϕ ⊆ DCS 1 ϕDCB ϕ3 relation between expressions introducing anaphora and potential antecedents ϕ1 = ϕ2 there {υ } ϕ3 2 • It constitutes a step forward from previous approaches to anaphoric accessibility in classical DRT bathroomϕ {υ1} 2 (Kamp and Reyle (1993)), as well as analyses of modal subordination (Stone (1999)) and the double negation and disjunction cases (Krahmer and Muskens (1995)), by extending the empirical coverage. ⊆ ⊆ • Since the two speakers disagree, ϕDCS ϕ1 and ϕDCB ϕ2 don’t have to be compatible with each other References

• This allows for the possibility that υ1 exists in ϕ3, i.e. the one where ϕ1 ∩ ϕ3 = ∅, similar to the disjunction case Adrian Brasoveanu. Structured Nominal and Modal Reference. Doctoral dissertation, Rutgers University, 2007. Adrian Brasoveanu. Decomposing Modal Quantification. Journal of Semantics, 27(4):437–527, 2010. 3 Discussion Christine Gunlogson. True to Form : Rising and Falling Declaratives as Questions in English. Routledge, Upshot June 2004. An indefinite in the scope of negation is available for subsequent reference only if the pronoun making Irene Heim. On the Projection Problem for Presuppositions. In Proceedings of the Second West Coast reference to it is interpreted wrt a set of worlds in which the referent of the indefinite exists Conference on Formal Linguistics, pages 114–125, 1983. • That can be the case, if Hans Kamp. A theory of truth and semantic representation. Formal semantics-the essential readings, pages 189–222, 1981. – Anaphoric would anaphorically retrieves a hypothetical (/counterfactual) set of worlds for the interpretation of its prejacent (like in Stone (1999) analysis of modal subordination). Hans Kamp and Uwe Reyle. From Discourse to Logic. Dordrecht: Kluwer Academic Publishers, 1993. – The discourse segments including the pronoun and the anaphor aren’t required to becom- Lauri Karttunen. Discourse Referents. 1969. patible with each other (like in the disjunction or disagreement cases). Lauri Karttunen. Presuppositions of compound sentences. Linguistic Inquiry, 4:169–93, 1973. Emiel Krahmer and Reinhard Muskens. Negation and Disjunction in Discourse Representation Theory. 3.1 Propositional anaphora under negation and disjunction Journal of Semantics, 12(4):357–376, 1995. Reinhard Muskens. Combining Montague Semantics and Discourse Representation. Linguistics and Phi- Propositional anaphora present a challenge: losophy, 19(2):143–186, 1996. (12) a. If Mary is sick, she knows that. Craige Roberts. Modal subordination and pronominal anaphora in discourse. Linguistics and Philosophy, b. Either Mary is not sick, or she #(is and) knows that. 12(6):683–721, December 1989. • We might expect the propositional dref in the scope of negation (where Mary is sick) to be accessible in the Robert Stalnaker. Assertion. In P. Cole, editor, Pragmatics, number 9 in Syntax and Semantics, pages second disjunct 315–332. London: Academic Press, 1978. • Krahmer and Muskens (1995): Disjunctions and conditionals are dynamically equivalent, asymmetry ruled out Robert Stalnaker. Common ground. Linguistics and Philosophy, 25:701–721, 2002. • Present account leaves room for an explanation, since disjunctions and conditionals have distinct semantic representations Matthew Stone. Reference to possible worlds. RuCCS Report, 46, 1999. • Therefore provides a vantage point over asymmetries between individual and propositional anaphora, tobe Matthew Stone and Daniel Hardt. Dynamic discourse referents for tense and modals.In Computing explored in future research meaning, pages 301–319. Springer, 1999.

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