Dalrymple and Haug, constraints on reciprocal scope (2024)

A reciprocal in a complement clause has a narrow-scope we-reading and a wide-scope I-reading, and Dalrymple and Haug survey constructions in which properties of its local antecedent, the embedded pronoun rather than the matrix subject, fix the scope. On the quantificational analysis of Heim, Lasnik and May the reciprocal contains a distributive quantifier that raises to the scope position and binds the local antecedent in situ; on the relational analysis of Haug and Dalrymple it is a pronoun anaphoric on the local antecedent, so that under wide scope the local antecedent is bound by the matrix subject and interpreted with the reciprocal in the matrix clause. Bound and nonbound antecedents, collective conjuncts and control constructions come out alike on both analyses; an explicit distributor on the antecedent and a logophoric antecedent separate them, and only the relational analysis fits the data.

We state each analysis by its two commitments, where it interprets the local antecedent under each reading and whether the reciprocal distributes, derive the readings each admits for each construction, and check them against the paper's judgments.

Implementation notes

• A construction is represented by its local antecedent alone: the denotation its form or predicate forces, whether it is a logophor, the locus of an explicit distributor, and the number of the matrix argument. Partial control forces no denotation, since PRO may properly include the controller or coincide with it.
• A simple sentence has only the in-situ reading, so (18b)–(20) are the narrow reading with the distributor at the low locus.

TODO

• (17) is analysed, with the paper, as exhaustive control, but Landau2015.derivedControlTier puts intend (and decide of (14)) on the partial-control tier; a semantics for partial control would decide the case.
• (25) is headed wide scope but read by the paper as a crossed reading; a crossed value in Scope would make it a row and reach the substrate's ScopeReading.crossed.

References

• M. Dalrymple and D. T. T. Haug, Constraints on reciprocal scope (2024)
• D. T. T. Haug and M. Dalrymple, Reciprocity: Anaphora, scope, and quantification (2020)
• I. Heim, H. Lasnik and R. May, Reciprocity and plurality (1991)
• J. Higginbotham, Reciprocal interpretation (1980)
• T. Nishigauchi, Syntax of reciprocals in Japanese (1992)
• G. Rákosi, Reciprocal anaphors in singular constructions in Hungarian (2019)
• W. Tay, K. New, M. Dalrymple and D. Haug, Reciprocal scope in Mandarin (2021)
• I. Landau, Elements of control (2000)
• I. Landau, A two-tiered theory of control (2015)
• K. Safir, One true anaphor (2014)
• L. Champollion, Overt distributivity in algebraic event semantics (2016)

Analyses and local antecedents

inductive DalrympleHaug2024.Grain : Type

What the local antecedent denotes under a reading ((5), (8)).

• individual : Grain

  An individual, as a bound variable (=).

• plurality : Grain

  The plurality, under group identity (∪) with the matrix subject.

@[instance_reducible]

instance DalrympleHaug2024.instDecidableEqGrain : DecidableEq Grain

Equations

• DalrympleHaug2024.instDecidableEqGrain x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance DalrympleHaug2024.instReprGrain : Repr Grain

Equations

• DalrympleHaug2024.instReprGrain = { reprPrec := DalrympleHaug2024.instReprGrain.repr }

def DalrympleHaug2024.instReprGrain.repr : Grain → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def DalrympleHaug2024.antecedentGrain (r : Reciprocal.Scope) : Grain

The denotation of the local antecedent under a scope reading, read off the antecedent relation of its cell, bound under wide scope and group-identical under narrow scope on both analyses ((4), (6)–(8)).

Equations

• One or more equations did not get rendered due to their size.

@[simp]

theorem DalrympleHaug2024.antecedentGrain_narrow : antecedentGrain Reciprocal.Scope.narrow = Grain.plurality

@[simp]

theorem DalrympleHaug2024.antecedentGrain_wide : antecedentGrain Reciprocal.Scope.wide = Grain.individual

def DalrympleHaug2024.Grain.ofNumber? : Number → Option Grain

The denotation a pronoun's number forces: a singular pronoun denotes an individual and so must be bound, a plural pronoun may be bound or group-identical ((10b)).

Equations

• DalrympleHaug2024.Grain.ofNumber? Number.singular = some DalrympleHaug2024.Grain.individual
• DalrympleHaug2024.Grain.ofNumber? x✝ = none

structure DalrympleHaug2024.Antecedent : Type

The local antecedent of a reciprocal in a complement clause, by the properties the paper surveys.

• grain : Option Grain

  The denotation its form or its predicate forces, if any.

• logophoric : Bool

  A logophor, interpreted inside the report (§6).

• distributor : Option Reciprocal.Locus

  The locus of an explicit distributor on it, if any (§5).

• matrixPlural : Bool

  Whether the matrix argument it is anaphoric to is a plurality.

def DalrympleHaug2024.instReprAntecedent.repr : Antecedent → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance DalrympleHaug2024.instReprAntecedent : Repr Antecedent

Equations

• DalrympleHaug2024.instReprAntecedent = { reprPrec := DalrympleHaug2024.instReprAntecedent.repr }

def DalrympleHaug2024.Antecedent.ofNumber (n : Option Number) : Antecedent

A pronoun of number n as local antecedent.

Equations

• DalrympleHaug2024.Antecedent.ofNumber n = { grain := n.bind DalrympleHaug2024.Grain.ofNumber? }

def DalrympleHaug2024.Antecedent.ofLogophor (p : LogophoricPronoun) : Antecedent

A logophoric pronoun as local antecedent: its number, interpreted inside the report.

Equations

• One or more equations did not get rendered due to their size.

structure DalrympleHaug2024.Analysis : Type

An analysis of reciprocal scope, by what it commits the local antecedent to under each reading.

• antecedentLocus : Reciprocal.Scope → Reciprocal.Locus

  Where the local antecedent is interpreted under each reading.

• distributes : Bool

  Whether the reciprocal contributes a distributive quantifier at the reading's locus.

def DalrympleHaug2024.quantificational : Analysis

On the quantificational analysis the quantifier part of the reciprocal raises to the reading's locus and binds the local antecedent in situ ((2), (4)).

Equations

• DalrympleHaug2024.quantificational = { antecedentLocus := fun (x : Reciprocal.Scope) => Reciprocal.Locus.low, distributes := true }

def DalrympleHaug2024.relational : Analysis

On the relational analysis the reciprocal is a pronoun anaphoric on the local antecedent, which is therefore interpreted where the reciprocal is ((3), (6)–(9)).

Equations

• DalrympleHaug2024.relational = { antecedentLocus := fun (r : Reciprocal.Scope) => r.reading.locus, distributes := false }

def DalrympleHaug2024.Available (A : Analysis) (a : Antecedent) (r : Reciprocal.Scope) : Prop

Reading r is available for the local antecedent a on analysis A: r gives the local antecedent the denotation its form forces, a logophor stays inside the report, a distributing reciprocal scopes below any explicit distributor, and a wide-scope reciprocal takes the matrix argument as its plural antecedent.

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance DalrympleHaug2024.instDecidableAvailable (A : Analysis) (a : Antecedent) (r : Reciprocal.Scope) : Decidable (Available A a r)

Equations

• DalrympleHaug2024.instDecidableAvailable A a r = id inferInstance

def DalrympleHaug2024.label : Reciprocal.Scope → String

The label of a reading in Data/Examples/DalrympleHaug2024.json.

Equations

• DalrympleHaug2024.label Reciprocal.Scope.narrow = "narrow"
• DalrympleHaug2024.label Reciprocal.Scope.wide = "wide"

def DalrympleHaug2024.Attested (e : Datum) (r : Reciprocal.Scope) : Prop

The paper records reading r of example e as available.

Equations

• DalrympleHaug2024.Attested e r = (List.lookup (DalrympleHaug2024.label r) e.readings = some Judgment.acceptable)

@[instance_reducible]

instance DalrympleHaug2024.instDecidableAttested (e : Datum) (r : Reciprocal.Scope) : Decidable (Attested e r)

Equations

• DalrympleHaug2024.instDecidableAttested e r = id inferInstance

def DalrympleHaug2024.Covers (A : Analysis) (a : Antecedent) (e : Datum) : Prop

Every reading the paper records for e is available on A with local antecedent a.

Equations

• DalrympleHaug2024.Covers A a e = ∀ (r : Reciprocal.Scope), DalrympleHaug2024.Attested e r → DalrympleHaug2024.Available A a r

@[instance_reducible]

instance DalrympleHaug2024.instDecidableCovers (A : Analysis) (a : Antecedent) (e : Datum) : Decidable (Covers A a e)

Equations

• DalrympleHaug2024.instDecidableCovers A a e = id inferInstance

def DalrympleHaug2024.Fits (A : Analysis) (a : Antecedent) (e : Datum) : Prop

A reading is available on A with local antecedent a exactly when the paper records it for e.

Equations

• DalrympleHaug2024.Fits A a e = ∀ (r : Reciprocal.Scope), DalrympleHaug2024.Available A a r ↔ DalrympleHaug2024.Attested e r

@[instance_reducible]

instance DalrympleHaug2024.instDecidableFits (A : Analysis) (a : Antecedent) (e : Datum) : Decidable (Fits A a e)

Equations

• DalrympleHaug2024.instDecidableFits A a e = id inferInstance

def DalrympleHaug2024.FitsSimple (A : Analysis) (a : Antecedent) (e : Datum) : Prop

A simple sentence has only the in-situ reading, and is acceptable on A exactly when that reading is available.

Equations

• DalrympleHaug2024.FitsSimple A a e = (DalrympleHaug2024.Available A a Reciprocal.Scope.narrow ↔ e.judgment = Judgment.acceptable)

@[instance_reducible]

instance DalrympleHaug2024.instDecidableFitsSimple (A : Analysis) (a : Antecedent) (e : Datum) : Decidable (FitsSimple A a e)

Equations

• DalrympleHaug2024.instDecidableFitsSimple A a e = id inferInstance

Where the analyses agree

theorem DalrympleHaug2024.available_iff_of_none {A B : Analysis} {a : Antecedent} (hd : a.distributor = none) (hl : a.logophoric = false) (r : Reciprocal.Scope) : Available A a r ↔ Available B a r

Without an explicit distributor or a logophoric antecedent the readings do not depend on the analysis: the constraints of §§2–4 are equally predicted by both.

theorem DalrympleHaug2024.fits_iff_of_none {A B : Analysis} {a : Antecedent} (hd : a.distributor = none) (hl : a.logophoric = false) (e : Datum) : Fits A a e ↔ Fits B a e

theorem DalrympleHaug2024.covers_iff_of_none {A B : Analysis} {a : Antecedent} (hd : a.distributor = none) (hl : a.logophoric = false) (e : Datum) : Covers A a e ↔ Covers B a e

theorem DalrympleHaug2024.narrow_of_plurality {A : Analysis} {a : Antecedent} (h : a.grain = some Grain.plurality) {r : Reciprocal.Scope} (hr : Available A a r) : r = Reciprocal.Scope.narrow

Wide scope binds the local antecedent, so a form that must denote the plurality has narrow scope only ((11), (12)).

theorem DalrympleHaug2024.wide_of_individual {A : Analysis} {a : Antecedent} (h : a.grain = some Grain.individual) {r : Reciprocal.Scope} (hr : Available A a r) : r = Reciprocal.Scope.wide

Narrow scope makes the local antecedent the plurality, so a form that must denote an individual has wide scope only ((10)).

Bound and nonbound antecedents (§2)

def DalrympleHaug2024.hungarian : Antecedent

The Hungarian complement subject, a null pronoun whose number is the singular agreement on its verb, Rákosi's bound-variable construction ((10)), his (17): the verb agreement recorded on that row.

Equations

• DalrympleHaug2024.hungarian = DalrympleHaug2024.Antecedent.ofNumber (some (if Rakosi2019.Examples.ex_17.feature? "verb" = some "pl" then Number.plural else Number.singular))

theorem DalrympleHaug2024.hungarian_fits (A : Analysis) : Fits A hungarian Examples.ex_10

A singular null pronoun must be bound, so (10) has wide scope only on every analysis.

def DalrympleHaug2024.japanese : Antecedent

The plural reflexive zibun-tati, which resists a bound reading and takes group identity (Nishigauchi), so denotes the plurality ((11)).

Equations

• DalrympleHaug2024.japanese = { grain := some DalrympleHaug2024.Grain.plurality }

theorem DalrympleHaug2024.japanese_fits (A : Analysis) : Fits A japanese Examples.ex_11

A plural reflexive that cannot be bound leaves narrow scope only on every analysis.

Collectivity (§3)

def DalrympleHaug2024.collectiveConjunct : Antecedent

The subject of a coordinated collective predicate, meet at the tennis court, which needs the plurality (Tay, New, Dalrymple and Haug) ((12)).

Equations

• DalrympleHaug2024.collectiveConjunct = { grain := some DalrympleHaug2024.Grain.plurality }

theorem DalrympleHaug2024.collectiveConjunct_fits (A : Analysis) : Fits A collectiveConjunct Examples.ex_12

A bound local antecedent offers no plurality to the collective conjunct, so (12) has narrow scope only on every analysis.

Control (§4)

def DalrympleHaug2024.pro (exhaustive collective matrixPlural : Bool) : Antecedent

PRO as local antecedent: a collectively read matrix predicate makes PRO the group, under exhaustive control with a distributive reading PRO is the individual controller, and under partial control PRO is semantically plural and may properly include the controller, so no denotation is forced.

Equations

• One or more equations did not get rendered due to their size.

theorem DalrympleHaug2024.control_tiers : Landau2015.derivedControlTier English.Verbs.want.toVerb = some Landau2015.Tier.logophoric ∧ Landau2015.derivedControlTier English.Verbs.try_.toVerb = some Landau2015.Tier.predicative ∧ Landau2015.derivedControlTier English.Verbs.manage.toVerb = some Landau2015.Tier.predicative ∧ Landau2015.derivedControlTier English.Verbs.intend.toVerb = some Landau2015.Tier.logophoric ∧ Landau2015.derivedControlTier English.Verbs.decide_.toVerb = some Landau2015.Tier.logophoric

Landau's tiers on the paper's control verbs: want of (13) and (15) selects an attitude complement and admits partial control, try and manage of (16) force exhaustive control, and intend of (17) and decide of (14) fall with want, although the paper's argument from (17) assumes exhaustive control.

def DalrympleHaug2024.partialPlural : Antecedent

PRO of a partial-control verb with a plural matrix subject ((13)).

Equations

• DalrympleHaug2024.partialPlural = DalrympleHaug2024.pro false false true

theorem DalrympleHaug2024.partial_narrow (A : Analysis) : Available A partialPlural Reciprocal.Scope.narrow

A partial-control verb makes a narrow reading available on every analysis, the paper's §4 generalization applied to want ((13)).

theorem DalrympleHaug2024.not_fits_received_judgment (A : Analysis) : ¬Fits A partialPlural Examples.ex_13

The wide-only judgment recorded for (13) since Higginbotham is therefore not what any analysis predicts for a partial-control verb.

theorem DalrympleHaug2024.collective_narrow (A : Analysis) (exhaustive : Bool) (r : Reciprocal.Scope) : Available A (pro exhaustive true true) r ↔ r = Reciprocal.Scope.narrow

A collectively read matrix predicate leaves narrow scope only, whatever the control type, the first of the two readings Heim, Lasnik and May attribute to (14).

def DalrympleHaug2024.exhaustiveDistributive : Antecedent

PRO of an exhaustive-control verb whose plural matrix subject is read distributively, the second reading of (14) and the paper's reading of (17), whose adjunct forces the distributive reading.

Equations

• DalrympleHaug2024.exhaustiveDistributive = DalrympleHaug2024.pro true false true

theorem DalrympleHaug2024.exhaustiveDistributive_wide (A : Analysis) (r : Reciprocal.Scope) : Available A exhaustiveDistributive r ↔ r = Reciprocal.Scope.wide

Under exhaustive control a distributively read matrix subject leaves wide scope only.

theorem DalrympleHaug2024.intend_fits (A : Analysis) : Fits A exhaustiveDistributive Examples.ex_17

The paper's construal of (17) as exhaustive control fits on every analysis.

def DalrympleHaug2024.partialSingular : Antecedent

PRO of a partial-control verb with a singular matrix subject, a plurality including the subject that the reciprocal takes as antecedent in situ ((15)).

Equations

• DalrympleHaug2024.partialSingular = DalrympleHaug2024.pro false false false

theorem DalrympleHaug2024.partialSingular_fits (A : Analysis) : Fits A partialSingular Examples.ex_15a ∧ Fits A partialSingular Examples.ex_15b

Every analysis fits (15): narrow scope, and no wide scope for want of a plural matrix antecedent.

def DalrympleHaug2024.exhaustiveSingular : Antecedent

PRO of an exhaustive-control verb with a singular matrix subject, the subject itself ((16)).

Equations

• DalrympleHaug2024.exhaustiveSingular = DalrympleHaug2024.pro true false false

theorem DalrympleHaug2024.not_available_exhaustiveSingular (A : Analysis) (r : Reciprocal.Scope) : ¬Available A exhaustiveSingular r

An individual PRO cannot antecede a narrow reciprocal and a singular matrix subject cannot antecede a wide one, so (16) has no reading on any analysis.

theorem DalrympleHaug2024.exhaustiveSingular_fits (A : Analysis) : Fits A exhaustiveSingular Examples.ex_16a ∧ Fits A exhaustiveSingular Examples.ex_16b

Every analysis fits the ungrammaticality of (16).

Distributive operators (§5)

def DalrympleHaug2024.plural : Antecedent

The plural pronoun they as local antecedent ((1)).

Equations

• DalrympleHaug2024.plural = DalrympleHaug2024.Antecedent.ofNumber English.Pronouns.they.number

theorem DalrympleHaug2024.plural_fits (A : Analysis) : Fits A plural Examples.ex_1

(1) is ambiguous on every analysis.

def DalrympleHaug2024.distributed (d : Reciprocal.Locus) : Antecedent

The plural pronoun with an explicit distributor at locus d, they each, each of them, neither of them ((18)–(20), (24)–(26)).

Equations

• One or more equations did not get rendered due to their size.

theorem DalrympleHaug2024.narrow_of_distributes_high {A : Analysis} (hA : A.distributes = true) {a : Antecedent} (hd : a.distributor = some Reciprocal.Locus.high) {r : Reciprocal.Scope} (h : Available A a r) : r = Reciprocal.Scope.narrow

A distributing reciprocal cannot scope at or above an explicit distributor, so a matrix distributor leaves narrow scope only, the judgment of Heim, Lasnik and May on (18a) derived from their analysis.

theorem DalrympleHaug2024.not_available_of_distributes_low {A : Analysis} (hA : A.distributes = true) {a : Antecedent} (hd : a.distributor = some Reciprocal.Locus.low) (r : Reciprocal.Scope) : ¬Available A a r

A distributor in the clause of a distributing reciprocal leaves no reading, the ungrammaticality of (18b), and of (24)–(25), on the quantificational analysis.

theorem DalrympleHaug2024.available_iff_of_not_distributes {A : Analysis} (hA : A.distributes = false) (a : Antecedent) (r : Reciprocal.Scope) : Available A a r ↔ Available A { grain := a.grain, logophoric := a.logophoric, matrixPlural := a.matrixPlural } r

A pronominal reciprocal is blind to explicit distributors, since it accesses the group denoted by the antecedent even when the antecedent is distributed on, so its readings are those of the undistributed antecedent ((27)).

theorem DalrympleHaug2024.hlm_judgments : Fits quantificational (distributed Reciprocal.Locus.high) Examples.ex_18a ∧ FitsSimple quantificational (distributed Reciprocal.Locus.low) Examples.ex_18b

The quantificational analysis reproduces the judgments of Heim, Lasnik and May on (18).

theorem DalrympleHaug2024.simple_distributors : (FitsSimple relational (distributed Reciprocal.Locus.low) Examples.ex_19a ∧ FitsSimple relational (distributed Reciprocal.Locus.low) Examples.ex_19b ∧ FitsSimple relational (distributed Reciprocal.Locus.low) Examples.ex_20a ∧ FitsSimple relational (distributed Reciprocal.Locus.low) Examples.ex_20b) ∧ ¬FitsSimple quantificational (distributed Reciprocal.Locus.low) Examples.ex_19a ∧ ¬FitsSimple quantificational (distributed Reciprocal.Locus.low) Examples.ex_19b ∧ ¬FitsSimple quantificational (distributed Reciprocal.Locus.low) Examples.ex_20a ∧ ¬FitsSimple quantificational (distributed Reciprocal.Locus.low) Examples.ex_20b

Simple sentences with a distributor on the reciprocal's antecedent are attested, admitted by the relational analysis and excluded by the quantificational one ((19)–(20)).

theorem DalrympleHaug2024.corpus_distributors : (Covers relational (distributed Reciprocal.Locus.low) Examples.ex_24a ∧ Covers relational (distributed Reciprocal.Locus.low) Examples.ex_24b ∧ Covers relational (distributed Reciprocal.Locus.high) Examples.ex_26a ∧ Covers relational (distributed Reciprocal.Locus.high) Examples.ex_26b) ∧ ¬Covers quantificational (distributed Reciprocal.Locus.low) Examples.ex_24a ∧ ¬Covers quantificational (distributed Reciprocal.Locus.low) Examples.ex_24b ∧ ¬Covers quantificational (distributed Reciprocal.Locus.high) Examples.ex_26a ∧ ¬Covers quantificational (distributed Reciprocal.Locus.high) Examples.ex_26b

Narrow scope is attested with the distributor in the complement clause and wide scope with a matrix distributor, which the relational analysis covers and the quantificational analysis does not ((24), (26)).

Logophoricity (§6)

def DalrympleHaug2024.logophor : Antecedent

The Wan plural logophor mɔ̄ as local antecedent, which can itself be bound, as (31) shows, but cannot leave the report with the reciprocal ((28)).

Equations

• DalrympleHaug2024.logophor = DalrympleHaug2024.Antecedent.ofLogophor Wan.Reciprocals.logPl

def DalrympleHaug2024.ordinary : Antecedent

The ordinary plural pronoun à̰ as local antecedent ((32)).

Equations

• DalrympleHaug2024.ordinary = DalrympleHaug2024.Antecedent.ofNumber Wan.Reciprocals.ordinaryPl.number

theorem DalrympleHaug2024.narrow_of_logophoric {A : Analysis} (hA : ∀ (r : Reciprocal.Scope), A.antecedentLocus r = r.reading.locus) {a : Antecedent} (ha : a.logophoric = true) {r : Reciprocal.Scope} (h : Available A a r) : r = Reciprocal.Scope.narrow

On an analysis that interprets the local antecedent where the reciprocal is, a logophoric antecedent leaves narrow scope only, since under wide scope the reciprocal would drag it out of the report ((29)).

theorem DalrympleHaug2024.available_iff_of_in_situ {A : Analysis} (hA : ∀ (r : Reciprocal.Scope), A.antecedentLocus r = Reciprocal.Locus.low) (a : Antecedent) (r : Reciprocal.Scope) : Available A a r ↔ Available A { grain := a.grain, distributor := a.distributor, matrixPlural := a.matrixPlural } r

An analysis that binds the local antecedent in situ is blind to a logophoric antecedent, since logophoricity constrains only where the antecedent is interpreted, so its readings for a logophor are those for the ordinary pronoun ((30)).

theorem DalrympleHaug2024.logophor_fits : Fits relational logophor Examples.ex_28 ∧ ¬Fits quantificational logophor Examples.ex_28

Only the relational analysis fits (28).

theorem DalrympleHaug2024.ordinary_covers (A : Analysis) : Covers A ordinary Examples.ex_32

With the ordinary pronoun the wide reading of (32) is available on every analysis.