Lu, Pan and Degen (2025): Evidence for a Discourse Account of Manner-of-Speaking Islands

This file formalizes the backgroundedness account of manner-of-speaking islands that Lu, Pan and Degen support in five acceptability experiments. A constituent is foregrounded when its alternatives are among the answers to the question under discussion, (3), with alternative sets and answers after Roberts, and backgrounded otherwise (Foregrounded), which is the question deciding each of the constituent's alternatives (Setoid.le_ker_iff_forall_decides). A communication event has a manner and a content, and the manner question backgrounds the content (mannerQUD, contentQUD, not_foregrounded_content_mannerQUD). Movement foregrounds the moved element, so moving it out of a backgrounded complement is the information-structural clash of Erteschik-Shir: the embedded object is an island exactly when the complement is backgrounded under the question under discussion (Island).

Prosodic focus sets that question, focus on the matrix predicate raising the manner question and focus on the embedded object the content question. Without focus the predicate sets it: a manner-of-speaking verb carries a manner component, whisper being say in a whispering manner, which makes the manner question the default, while the light say leaves the content question (activeQUD, island_iff). The experiments' findings follow for each predicate: embedded focus removes the island of a manner-of-speaking verb, Experiment 1 (island_whisper_iff); focus on say creates one, Experiment 2a (island_say_iff); and a manner adverb makes say behave as a manner-of-speaking verb, by default in Experiment 3a and under focus in 3b (island_sayAdverb_iff_island_whisper). The manner component is read from the verb's Levin class in Fragments/English (MatrixPredicate.hasManner_of_mannerOfSpeaking, MatrixPredicate.hasManner_say_iff).

Implementation notes

(3) asks the alternatives relative to a constituent to be among the complete answers to the question. Over partition questions, whose cells are the complete answers, this is rendered as the question settling the constituent: two events in one cell agree on it, so the question decides each of its alternatives. The paper takes one question to be under discussion at a time, which is why focus overrides the predicate's default.

The negation test (7) of earlier work is not formalized: the paper counts it a test of projection, correlated with backgroundedness but distinct from it, and probes the embedded object's backgroundedness with a comprehension task instead. The subjacency and verb-frame-frequency accounts the paper argues against are described in prose: prosodic focus changes neither structure nor frequency, and the say plus adverb contrast holds the verb constant. The residual difference between manner-of-speaking verbs and say under one prosody in Experiment 2a, the default backgroundedness contrast of Experiment 2b, and the rating means are not represented; the paper notes that the account makes no prediction about the obligatory overt complementizer of manner-of-speaking complements (22).

TODO

The stimuli of Data/Examples/LuPanDegen2025 are printed unmarked; which member of each contrast is degraded is a rating result of the experiments, for Data/Experiments, and the island rule is not yet checked against those results.

References

• [LPD25]
• [Rob96]
• [Rob12]
• [ES73]
• [Lev93]

Foregrounding (3)

def LuPanDegen2025.Foregrounded {M : Type u_1} {A : Type u_2} (q : Setoid M) (π : M → A) : Prop

A dimension π of the events is foregrounded under the question q, (3): its alternatives are among the answers, so two events in one cell agree on it. A dimension that is not foregrounded is backgrounded.

Equations

• LuPanDegen2025.Foregrounded q π = (q ≤ Setoid.ker π)

Communication events

structure LuPanDegen2025.CommEvent (Manner : Type u_1) (Content : Type u_2) : Type (max u_1 u_2)

A communication event: how it was said and what was said.

• manner : Manner

  How it was said.

• content : Content

  What was said.

def LuPanDegen2025.mannerQUD {Manner : Type u_1} {Content : Type u_2} : Setoid (CommEvent Manner Content)

The manner question, how did John say it?: events in one cell share a manner.

Equations

• LuPanDegen2025.mannerQUD = Setoid.ker LuPanDegen2025.CommEvent.manner

def LuPanDegen2025.contentQUD {Manner : Type u_1} {Content : Type u_2} : Setoid (CommEvent Manner Content)

The content question, what did John say?: events in one cell share a content.

Equations

• LuPanDegen2025.contentQUD = Setoid.ker LuPanDegen2025.CommEvent.content

theorem LuPanDegen2025.foregrounded_manner_mannerQUD {Manner : Type u_1} {Content : Type u_2} : Foregrounded mannerQUD CommEvent.manner

The manner question foregrounds the manner.

theorem LuPanDegen2025.foregrounded_content_contentQUD {Manner : Type u_1} {Content : Type u_2} : Foregrounded contentQUD CommEvent.content

The content question foregrounds the content.

theorem LuPanDegen2025.not_foregrounded_content_mannerQUD {Manner : Type u_1} {Content : Type u_2} [Nonempty Manner] [Nontrivial Content] : ¬Foregrounded mannerQUD CommEvent.content

The manner question backgrounds the content, given two contents to choose from.

The question under discussion and the island

structure LuPanDegen2025.MatrixPredicate : Type

The matrix predicate: a verb of the fragment, and whether a manner adverb modifies it.

• verb : English.Verbs.Verb

  The matrix verb.

• mannerAdverb : Bool

  Whether a manner adverb modifies the verb.

def LuPanDegen2025.MatrixPredicate.HasManner (p : MatrixPredicate) : Prop

The predicate carries a manner component, as a manner-of-speaking verb of [Lev93] or by a manner adverb.

Equations

• p.HasManner = (ArgumentStructure.LevinClass.mannerOfSpeaking ∈ p.verb.levinClasses ∨ p.mannerAdverb = true)

@[instance_reducible]

instance LuPanDegen2025.MatrixPredicate.instDecidablePredHasManner : DecidablePred HasManner

Equations

• x✝.instDecidablePredHasManner = { decide := decide (ArgumentStructure.LevinClass.mannerOfSpeaking ∈ x✝.verb.levinClasses) || decide (x✝.mannerAdverb = true), reflects_decide := ⋯ }

theorem LuPanDegen2025.MatrixPredicate.hasManner_of_mannerOfSpeaking {v : English.Verbs.Verb} (h : ArgumentStructure.LevinClass.mannerOfSpeaking ∈ v.levinClasses) (b : Bool) : { verb := v, mannerAdverb := b }.HasManner

A verb of the manner-of-speaking class carries manner however it is modified.

theorem LuPanDegen2025.MatrixPredicate.hasManner_say_iff {v : English.Verbs.Verb} (h : v.levinClasses = {ArgumentStructure.LevinClass.say}) (b : Bool) : { verb := v, mannerAdverb := b }.HasManner ↔ b = true

A verb of the say class carries manner only by an adverb.

inductive LuPanDegen2025.FocusCondition : Type

Where the context puts prosodic focus: on the matrix predicate, its verb or its manner adverb, on the embedded object, or nowhere.

• predicate : FocusCondition
• embedded : FocusCondition
• unmarked : FocusCondition

@[instance_reducible]

instance LuPanDegen2025.instDecidableEqFocusCondition : DecidableEq FocusCondition

Equations

• LuPanDegen2025.instDecidableEqFocusCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def LuPanDegen2025.activeQUD (Manner : Type u_1) (Content : Type u_2) (p : MatrixPredicate) : FocusCondition → Setoid (CommEvent Manner Content)

The question under discussion: focus on the predicate raises the manner question, the alternatives of a verb of saying being its manners, and focus on the embedded object the content question; without focus a predicate with a manner component raises the manner question and the light say the content question.

Equations

• LuPanDegen2025.activeQUD Manner Content p LuPanDegen2025.FocusCondition.predicate = LuPanDegen2025.mannerQUD
• LuPanDegen2025.activeQUD Manner Content p LuPanDegen2025.FocusCondition.embedded = LuPanDegen2025.contentQUD
• LuPanDegen2025.activeQUD Manner Content p LuPanDegen2025.FocusCondition.unmarked = if p.HasManner then LuPanDegen2025.mannerQUD else LuPanDegen2025.contentQUD

def LuPanDegen2025.Island (Manner : Type u_1) (Content : Type u_2) (p : MatrixPredicate) (f : FocusCondition) : Prop

The embedded object is an island when the complement is backgrounded under the question under discussion: movement foregrounds the moved element, which clashes with the backgrounded complement it leaves ([ES73]).

Equations

• LuPanDegen2025.Island Manner Content p f = ¬LuPanDegen2025.Foregrounded (LuPanDegen2025.activeQUD Manner Content p f) LuPanDegen2025.CommEvent.content

theorem LuPanDegen2025.not_island_embedded {Manner : Type u_1} {Content : Type u_2} (p : MatrixPredicate) : ¬Island Manner Content p FocusCondition.embedded

Focus on the embedded object foregrounds the complement whatever the predicate.

theorem LuPanDegen2025.island_iff {Manner : Type u_1} {Content : Type u_2} [Nonempty Manner] [Nontrivial Content] (p : MatrixPredicate) (f : FocusCondition) : Island Manner Content p f ↔ f = FocusCondition.predicate ∨ f = FocusCondition.unmarked ∧ p.HasManner

The complement is an island exactly when the predicate is focused, or nothing is and the predicate carries manner.

theorem LuPanDegen2025.island_whisper_iff {Manner : Type u_1} {Content : Type u_2} [Nonempty Manner] [Nontrivial Content] (f : FocusCondition) : Island Manner Content { verb := English.Verbs.whisper, mannerAdverb := false } f ↔ f ≠ FocusCondition.embedded

Who did John whisper that Mary met with? is degraded unless the embedded object is focused, Experiment 1.

theorem LuPanDegen2025.island_say_iff {Manner : Type u_1} {Content : Type u_2} [Nonempty Manner] [Nontrivial Content] (f : FocusCondition) : Island Manner Content { verb := English.Verbs.say, mannerAdverb := false } f ↔ f = FocusCondition.predicate

Who did John say that Mary met with? is degraded exactly when say is focused, Experiment 2a.

theorem LuPanDegen2025.island_sayAdverb_iff_island_whisper {Manner : Type u_1} {Content : Type u_2} [Nonempty Manner] [Nontrivial Content] (f : FocusCondition) : Island Manner Content { verb := English.Verbs.say, mannerAdverb := true } f ↔ Island Manner Content { verb := English.Verbs.whisper, mannerAdverb := false } f

A manner adverb makes say behave as a manner-of-speaking verb under every focus condition, Experiments 3a and 3b.

The stimulus rows

def LuPanDegen2025.rowPredicate (e : Datum) : Option MatrixPredicate

The matrix predicate of a stimulus row: whisper for the manner-of-speaking items, say and say softly for the others.

Equations

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

def LuPanDegen2025.rowFocus (e : Datum) : Option FocusCondition

The focus condition of a stimulus row.

Equations

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

theorem LuPanDegen2025.rows_parse (e : Datum) : e ∈ Examples.all → (rowPredicate e).isSome = true ∧ (rowFocus e).isSome = true

Every row has a predicate and a focus condition.