Schlenker, Lamberton & Lamberton (2026)

@cite{schlenker-lamberton-lamberton-2026}

Traveling Shots in Language: Towards an Analysis of Dynamic Viewpoints in ASL. To appear in Linguistic Inquiry.

Core Contribution

Extends Iconological Semantics (@cite{schlenker-lamberton-2024}) by showing that viewpoint variables may denote dynamic (traveling) viewpoints — functions from time-world pairs to static viewpoints — not just static observation points.

In ASL, a classifier denoting a static object (e.g., TREE-cl) can move in signing space to represent the object's apparent motion from a moving character's perspective. This is the linguistic analogue of a traveling camera shot in film.

Two Analyses

1. Analysis I (§7): All viewpoint variables can be dynamic. Relative motion arises whenever a viewpoint variable takes a non-constant value.

2. Analysis II (§8): Only viewpoints introduced by Role Shift (as overt context shift) can be dynamic. Standard viewpoint variables denote static viewpoints. Under Role Shift, a distinguished variable π* reads the character's dynamic viewpoint from the shifted context.

The paper leaves both options open, pending a consensus on the definition of Role Shift.

Data

Paradigms were elicited from two Deaf native ASL signers. Acceptability is on a 7-point scale (7 = best, 1 = worst). Classifier direction (left vs. right) systematically determines the character's inferred path.

theorem SchlenkerEtAl2026.static_is_special_case {W : Type u_1} {T : Type u_2} {P : Type u_3} {E : Type u_4} (projects : E → Semantics.Iconic.StaticViewpoint P → Bool) (d : E) (sv : Semantics.Iconic.StaticViewpoint P) (w : W) (t₁ t₂ : T) : Semantics.Iconic.dynamicProjection projects d (Semantics.Iconic.DynamicViewpoint.static sv) w t₁ = Semantics.Iconic.dynamicProjection projects d (Semantics.Iconic.DynamicViewpoint.static sv) w t₂

The static viewpoint analysis is a special case of the dynamic one. When a viewpoint is constant, dynamic projection reduces to time-invariant projection. The dynamic framework is a conservative extension.

def SchlenkerEtAl2026.travelingShotCondition {W : Type u_5} {T : Type u_6} {P : Type u_7} {E : Type u_8} (projects : E → Semantics.Iconic.StaticViewpoint P → Bool) (d : E) (vp : Semantics.Iconic.DynamicViewpoint W T P) (w : W) : Prop

The traveling shot condition: there exist two times at which the object's projection differs, producing apparent motion. This is only possible when the viewpoint is dynamic.

Equations

• SchlenkerEtAl2026.travelingShotCondition projects d vp w = ∃ (t₁ : T) (t₂ : T), Semantics.Iconic.dynamicProjection projects d vp w t₁ ≠ Semantics.Iconic.dynamicProjection projects d vp w t₂

theorem SchlenkerEtAl2026.no_travelingShot_static {W : Type u_5} (T : Type u_6) {P : Type u_7} {E : Type u_8} (projects : E → Semantics.Iconic.StaticViewpoint P → Bool) (d : E) (sv : Semantics.Iconic.StaticViewpoint P) (w : W) : ¬travelingShotCondition projects d (Semantics.Iconic.DynamicViewpoint.static sv) w

A static viewpoint never produces a traveling shot: projection is constant across time, so no apparent motion is possible.

def SchlenkerEtAl2026.ViewpointAssignment (W : Type u_5) (T : Type u_6) (P : Type u_7) : Type (max (max u_7 u_6) u_5)

A viewpoint assignment: maps viewpoint variable indices to dynamic viewpoints. The iconic analogue of an assignment function for pronouns.

Equations

• SchlenkerEtAl2026.ViewpointAssignment W T P = (ℕ → Semantics.Iconic.DynamicViewpoint W T P)

def SchlenkerEtAl2026.resolveViewpoint {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (v : Semantics.Iconic.ViewpointVar) (assign : ViewpointAssignment W T P) (agentVP : E → Semantics.Iconic.DynamicViewpoint W T P) (agent : E) : Semantics.Iconic.DynamicViewpoint W T P

Resolve a viewpoint variable against a viewpoint assignment and an agent. Free variables read from the assignment; the context-bound variable π* reads the dynamic viewpoint associated with the agent.

Under Role Shift (which changes the context's agent to the character), π* yields the character's dynamic viewpoint.

Equations

• SchlenkerEtAl2026.resolveViewpoint (Semantics.Iconic.ViewpointVar.free i) assign agentVP agent = assign i
• SchlenkerEtAl2026.resolveViewpoint Semantics.Iconic.ViewpointVar.contextBound assign agentVP agent = agentVP agent

def SchlenkerEtAl2026.roleShiftCtx {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (character : E) (rsWorld : W) : Core.Context.ContextShift (Core.Context.KContext W E P T)

Role Shift as context shift. Structurally identical to attitudeShift but labeled .roleShift — it changes the agent to the character (and the world to a Role-Shift-accessible world).

The viewpoint consequence is indirect: since π* reads the agent's viewpoint via resolveViewpoint, changing the agent changes what π* denotes.

Equations

• SchlenkerEtAl2026.roleShiftCtx character rsWorld = { apply := (Core.Context.attitudeShift character rsWorld).apply, label := Core.Context.ShiftLabel.roleShift }

theorem SchlenkerEtAl2026.roleShift_is_monster {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (character : E) (rsWorld : W) (c : Core.Context.KContext W E P T) (hAgent : c.agent ≠ character) : Semantics.Reference.Monsters.IsTowerMonster (roleShiftCtx character rsWorld)

Role Shift is a monster (non-identity context shift), connecting to the Kaplan/Schlenker monster debate in Monsters.lean.

theorem SchlenkerEtAl2026.contextBound_under_roleShift {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (assign : ViewpointAssignment W T P) (agentVP : E → Semantics.Iconic.DynamicViewpoint W T P) (character : E) : resolveViewpoint Semantics.Iconic.ViewpointVar.contextBound assign agentVP character = agentVP character

Under Role Shift, π* resolves to the character's viewpoint.

theorem SchlenkerEtAl2026.free_unaffected_by_agent {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (assign : ViewpointAssignment W T P) (agentVP : E → Semantics.Iconic.DynamicViewpoint W T P) (agent₁ agent₂ : E) (i : ℕ) : resolveViewpoint (Semantics.Iconic.ViewpointVar.free i) assign agentVP agent₁ = resolveViewpoint (Semantics.Iconic.ViewpointVar.free i) assign agentVP agent₂

Free viewpoint variables are unaffected by who the agent is — they read from the assignment function regardless.

def SchlenkerEtAl2026.RestrictiveTheory {W : Type u_1} {P : Type u_3} {T : Type u_4} (assign : ViewpointAssignment W T P) : Prop

The restrictive theory: free viewpoint variables always denote static viewpoints. Only context-bound π* (introduced by Role Shift) can be dynamic.

Equations

• SchlenkerEtAl2026.RestrictiveTheory assign = ∀ (i : ℕ), (assign i).isStatic

theorem SchlenkerEtAl2026.restrictive_no_travelingShot {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} (assign : ViewpointAssignment W T P) (agentVP : E → Semantics.Iconic.DynamicViewpoint W T P) (hRestr : RestrictiveTheory assign) (projects : E → Semantics.Iconic.StaticViewpoint P → Bool) (d : E) (i : ℕ) (agent : E) (w : W) : ¬travelingShotCondition projects d (resolveViewpoint (Semantics.Iconic.ViewpointVar.free i) assign agentVP agent) w

Under the restrictive theory, traveling shots are impossible for classifiers with free viewpoint variables.

theorem SchlenkerEtAl2026.dynamicVP_enables_travelingShot {W : Type u_1} {T : Type u_2} (projects : Fragments.ASL.Entity → Semantics.Iconic.StaticViewpoint Fragments.ASL.SigningSpace → Bool) (d : Fragments.ASL.Entity) (charVP : Semantics.Iconic.DynamicViewpoint W T Fragments.ASL.SigningSpace) (w : W) (t₁ t₂ : T) (hDynamic : Semantics.Iconic.dynamicProjection projects d charVP w t₁ ≠ Semantics.Iconic.dynamicProjection projects d charVP w t₂) : travelingShotCondition projects d charVP w

The complete argumentation chain:

1. Role Shift changes the context's agent from signer to character
2. π* reads the agent's viewpoint, so it now reads the character's
3. The character's viewpoint is dynamic (they are moving)
4. Dynamic viewpoint + static object → traveling shot is possible
5. Static viewpoint would make traveling shot impossible

This theorem captures steps 2-5: given that the character's viewpoint is genuinely dynamic (non-constant), the traveling shot condition is satisfiable — there exist times where projection differs.

structure SchlenkerEtAl2026.Judgment : Type

An acceptability judgment on a 7-point scale.

• score : Float
• numSessions : ℕ

@[implicit_reducible]

instance SchlenkerEtAl2026.instReprJudgment : Repr Judgment

Equations

• SchlenkerEtAl2026.instReprJudgment = { reprPrec := SchlenkerEtAl2026.instReprJudgment.repr }

def SchlenkerEtAl2026.instReprJudgment.repr : Judgment → ℕ → Std.Format

Equations

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

structure SchlenkerEtAl2026.Condition : Type

A paradigm condition: classifier direction + Role Shift status.

• classifierDirection : Phenomena.Iconicity.ClassifierDirection
• roleShiftStatus : Phenomena.Iconicity.RoleShiftStatus
• judgment : Judgment

@[implicit_reducible]

instance SchlenkerEtAl2026.instReprCondition : Repr Condition

Equations

• SchlenkerEtAl2026.instReprCondition = { reprPrec := SchlenkerEtAl2026.instReprCondition.repr }

def SchlenkerEtAl2026.instReprCondition.repr : Condition → ℕ → Std.Format

Equations

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

def SchlenkerEtAl2026.paradigm7 : List Condition

Paradigm (7): POLE-cl moving past signer. Ann driving drunk, nearly hits pole. Direction determines which side she nearly hits. No strict Role Shift (no body rotation).

Equations

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

def SchlenkerEtAl2026.paradigm13 : List Condition

Paradigm (13): TREE-cl moving past signer. Ann runs past a tree. Direction determines which side the tree passes on. No strict Role Shift.

Equations

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

def SchlenkerEtAl2026.paradigm19 : List Condition

Paradigm (19): Role-shifted version of (7). Strict Role Shift (body rotation). Same interpretive effect.

Equations

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

def SchlenkerEtAl2026.paradigm7_travelingShot : Phenomena.Iconicity.TravelingShotEffect

Paradigm (7) instantiates the traveling shot: pole is static, classifier moves, motion type is relative.

Equations

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

def SchlenkerEtAl2026.paradigm13_travelingShot : Phenomena.Iconicity.TravelingShotEffect

Paradigm (13) instantiates the traveling shot: tree is static, classifier moves, motion type is relative.

Equations

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

theorem SchlenkerEtAl2026.travelingShot_with_and_without_RS : Option.map (fun (x : Condition) => x.roleShiftStatus) paradigm7.head? = some Phenomena.Iconicity.RoleShiftStatus.broad ∧ Option.map (fun (x : Condition) => x.roleShiftStatus) paradigm19.head? = some Phenomena.Iconicity.RoleShiftStatus.strict

The traveling shot arises both with and without strict Role Shift.

theorem SchlenkerEtAl2026.paradigm7_uses_poleCl (proj : Fragments.ASL.Entity → Semantics.Iconic.StaticViewpoint Fragments.ASL.SigningSpace → Bool) : (Fragments.ASL.poleCl proj).label = "POLE-cl"

The classifier used in paradigm (7) is POLE-cl from the ASL fragment.

theorem SchlenkerEtAl2026.paradigm13_uses_treeCl (proj : Fragments.ASL.Entity → Semantics.Iconic.StaticViewpoint Fragments.ASL.SigningSpace → Bool) : (Fragments.ASL.treeCl proj).label = "TREE-cl"

The classifier used in paradigm (13) is TREE-cl from the ASL fragment.