Slot/Filler Verification #
@cite{dunn-2025} @cite{kay-fillmore-1999} @cite{goldberg-shirtz-2025}
Per-datum verification that derivedSpecificity (computed from the typed
slot structure) matches the Specificity values stipulated in existing
construction definitions.
Concrete TypedForm instantiations for six constructions verify:
abstractionLevelcomputes the correct open-slot proportionderivedSpecificityagrees with stipulatedSpecificityConstructionSlot.toSlotround-trips through embeddingrefGroupCountandhasConstraintdetect WXDY's structural properties- WXDY coinstantiation: X and Y share refIdx 2 (subject control)
Ditransitive typed form: [Subj_NP V Obj1_NP Obj2_NP].
All four slots are open — the construction constrains categories and roles but not specific lexemes.
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must-VERB typed form: [fixed("must") V N].
"must" is a fixed lexeme; the verb and noun slots are open. "a must-see movie", "a must-read book".
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Let alone typed form: [A_NP fixed("let") fixed("alone") B_NP].
Simplified from the full form F⟨X A Y let alone B⟩ to highlight the fixed/open distinction. "let" and "alone" are fixed; the focus positions are open.
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Veggie-wrap: a fully lexically specified compound (@cite{goldberg-2003}:220).
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Ditransitive: 4/4 open slots → abstraction level 1.
must-VERB: 2/3 open slots → abstraction level 2/3.
Let alone: 2/4 open slots → abstraction level 1/2.
Veggie-wrap: 0/2 open slots → abstraction level 0.
These theorems verify that derivedSpecificity (computed from slot
structure) matches the Specificity values stipulated in the existing
construction definitions. This makes the connection true by verification
rather than by construction.
Ditransitive: derived .fullyAbstract matches stipulated.
Let alone: derived .partiallyOpen matches stipulated.
must-VERB: derived .partiallyOpen matches stipulated.
Veggie-wrap: derived .lexicallySpecified (all fixed).
The ditransitive TypedForm matches the existing ArgStructureConstruction's
slots projected through toTypedForm.
@cite{kay-fillmore-1999} formalize the WXDY construction as a hierarchical AVM with valence sets, grammatical functions, coreference indices (#1, #2), and feature constraints ([loc -], [neg -], [ref ∅]). This flat projection captures the key structural properties while losing the nesting.
**Coinstantiation** (Figure 13, §4.2) is a general construction
expressing subject control: the matrix subject and the complement's
subject share a coreference index. WXDY's X–Y coindexation is an
instance of this pattern.
WXDY construction typed form (@cite{kay-fillmore-1999}, Figure 12).
Flat projection of the hierarchical AVM. The five positions:
- X (subject of BE): open NP, coindexed with Y via refIdx 2
- BE (head): auxiliary headed by be
- doing (complement): VP headed by doing, cannot be negated
- what (object of doing): fixed, left-isolated, nonreferential
- Y (secondary predicate): open, coindexed with X via refIdx 2
The coindexation (refIdx 2) captures the paper's #2: X is the understood subject of Y (coinstantiation / subject control).
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Coinstantiation construction (@cite{kay-fillmore-1999}, Figure 13, §4.2).
A general pattern for subject control: the matrix subject and the complement's subject share a coreference index.
"She tried to leave": the subject of try (#1) = the understood subject of leave (#1). This is the mechanism underlying WXDY's X–Y coindexation.
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Abstraction and specificity #
WXDY: 2/5 open slots → abstraction level 2/5.
WXDY is partiallyOpen: mix of open, headed, and fixed slots.
Coinstantiation is fully abstract (all slots open).
Coreference constraints #
WXDY has exactly one coreference group (the X–Y coinstantiation).
X (first slot) and Y (last slot) share coreference index 2: X is the understood subject of Y.
Coinstantiation has exactly one coreference group.
Syntactic constraints #
WXDY-what is left-isolated ([loc -]) and nonreferential ([ref ∅]). These two constraints together explain why WXDY-what cannot take else modification and is not a true interrogative pronoun.
WXDY-doing cannot be negated ([neg -]): "*What's X not doing Y?" is ungrammatical on the incredulity reading.
Neither the ditransitive nor let alone bear any slot constraints — the enriched constraint machinery is specific to constructions like WXDY that have fine-grained syntactic restrictions.