Voice Semantics: Compositional Operations on Argument Structure #
@cite{beavers-udayana-2022} @cite{kratzer-1996} @cite{alexiadou-schaefer-2015}
Voice heads are type-changing compositional functions: they take a VP
denotation and return a clause-level meaning with modified argument
structure. This file defines the semantic operations; the theta-role
assignments are in VoiceTheta.lean (an independent interface).
Independence from VoiceTheta #
This file and VoiceTheta.lean are independent interfaces from the
syntactic voice head:
- VoiceTheta: Voice → theta role label (what the ext arg IS)
- VoiceSemantics: Voice → compositional operation (what the voice head DOES)
Same theta role, different operations: Agent is projected (active) or suppressed-coreferent (reflexive). Same operation, different theta roles: suppression can target agents (passive) or patients (antipassive).
Key insight #
The three Indonesian voice denotations have different Montague types:
- ⟦meN-⟧ :
(e ⇒ τ) → (e ⇒ τ)— identity (preserves all arguments) - ⟦di-⟧ :
(e ⇒ e ⇒ t) → (e ⇒ t)— existentially binds external arg - ⟦ber-⟧ :
(e ⇒ τ) → τ— saturates firste-arg with open variable
The type change IS the argument-structure change. Active voice preserves both arguments; passive and middle reduce arity by one.
Polymorphism of ber- #
berSemG is parametric in the result type τ. When applied to a VP of
type e ⇒ t (after FA with an object DP), it yields type t — the
external argument (agent) was suppressed. When applied to a VP of type
e ⇒ e ⇒ t (after noun incorporation), it yields type e ⇒ t — the
internal argument (patient) was suppressed and the agent remains as the
surface subject.
One Lean definition, two surface argument structures. The 2×2 typology of @cite{beavers-udayana-2022} is a consequence of Montague composition, not a stipulated data structure.
Active voice is the identity on VP meanings: it preserves the full argument structure.
⟦meN-⟧ = λP[P] (@cite{beavers-udayana-2022}, (39a))
In a type-driven system, "doing nothing" is itself a semantic contribution — it commits to projecting ALL arguments as DPs.
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Argument suppression at a specific value: saturates the first
e-argument of a VP with entity z.
suppressArg z VP = VP(z) — the rest of the meaning is preserved.
This is ⟦ber-⟧ evaluated at a particular assignment where the open
variable has value z.
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Assignment-relative argument suppression: the suppressed argument is
a free variable g(n), interpreted relative to an assignment function.
⟦ber-⟧ₙ(VP)(g) = VP(g(n))(g)
This is the paper's (43): ⟦ber-⟧ = λP_{⟨e,α⟩}[P(z̲)], where z̲ is
the open variable g(n).
The result type τ is parametric — Lean's implicit type argument
captures the paper's subscript ⟨e,α⟩:
τ = .t: VP wase ⇒ t(post-FA with object) → agent suppressedτ = .e ⇒ .t: VP wase ⇒ e ⇒ t(post-incorporation) → patient suppressed, agent remains as surface subject
Equations
- Theories.Interfaces.SyntaxSemantics.VoiceSemantics.berSemG n vp g = vp g (g n)
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berSemG at a specific assignment is just suppressArg with g(n).
Passive voice existentially binds the external argument (Prop-valued).
⟦di-⟧ₙ(VP)(patient)(g) = ∃x. VP(g[n↦x])(x)(patient)
Simplified from the paper's (39b), omitting the presuppositional content (disjoint reference, ∂-operator) and event variables.
The structural contrast with ber-: di- BINDS the suppressed variable; ber- leaves it FREE. This explains the diagnostic difference: di- passives license oleh 'by' phrases (the existential can be made explicit) while ber- middles do not (the variable is unbound).
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Noun incorporation: conjoins an NP predicate with the VP's internal argument, preserving both argument positions.
⟦V_I⟧(P)(obj)(subj) = ⟦V⟧(obj)(subj) ∧ P(obj)
Simplified from the paper's (49). The NP predicate P narrows the referent of the object position without saturating it. Both argument positions remain open — the difference from FA, where the object position is fully saturated.
After incorporation, ber- suppresses the first argument (object), leaving the subject free for the agent. After FA, ber- suppresses the remaining argument (subject), making the patient the surface subject. Same ber-, different VP shape, different surface structure.
Equations
- Theories.Interfaces.SyntaxSemantics.VoiceSemantics.incorporate verb np obj subj = (verb obj subj && np obj)
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Active voice preserves argument count: the output type matches the input.
Suppression after FA: when the VP has had its object saturated
(type e ⇒ t), suppression yields a proposition (type t).
The suppressed argument was the agent — the only remaining argument after FA. The patient (the FA-applied argument) becomes the surface subject. This is the dispositional/passive middle.
Suppression after incorporation: when the VP retains both arguments
(type e ⇒ e ⇒ t), suppression yields a property (type e ⇒ t).
The suppressed argument was the object (first position). The agent (second position) remains as the surface subject. This is the incorporation middle.
The core unification: suppressArg is the SAME function in both
derivations. The difference in surface argument structure comes
entirely from the type of the VP input, not from any difference in
the suppression operation.
This is the formal content of @cite{beavers-udayana-2022}'s claim that ber- is ONE operation producing FOUR surface types.
Incorporation preserves both arguments: the incorporated VP still
has type e ⇒ e ⇒ t, unlike FA which reduces to e ⇒ t.
Assignment-relative suppression: berSemG does not fix how the open variable is interpreted — different assignments yield different values for g(n). The root class determines the DEFAULT assignment (coreferent or disjoint), but the operation itself is agnostic.