Steedman 2000: The Syntactic Process #

CCG predictions from [Ste00a], one section per phenomenon:

Word order: slash direction in lexical categories enforces English SVO.
Non-constituent coordination: type-raising + composition make "John likes" a constituent (S/NP), and generalized conjunction delivers the conjunctive interpretation (modeled on the book's "Anna married, and I detest, Manny").
Gapping: [Ros70]'s word-order/gapping-direction generalization, recovered from the type-raising directions a language's verb categories license.
Cross-serial dependencies: Dutch verb clusters ([BKPZ82]) with cross-serial NP-verb bindings, via the book's leftward argument categories and forward crossed composition.
Verb clusters and quantifier scope (§6.8): verb-raising orders are scope-ambiguous, verb-projection-raising orders surface-only; predictions are computed via CCG.Scope.analyzeDerivation and checked against the §6.8 judgments in Linglib.Data.Examples.Steedman2000 ([Bay96], [Kay98], [HvR86], [Hae92] are credited per example in the JSON).

Word order #

Slash direction encodes word order: TV = (S\NP)/NP looks right for the object NP first, then the resulting S\NP looks left for the subject, enforcing SVO.

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def Steedman2000.mary_eats_pizza :

CCG.DerivStep

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def Steedman2000.he_sees_her :

CCG.DerivStep

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def Steedman2000.the_cat_eats_pizza :

CCG.DerivStep

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theorem Steedman2000.mary_eats_pizza_cat :

mary_eats_pizza.cat = some CCG.S

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theorem Steedman2000.he_sees_her_cat :

he_sees_her.cat = some CCG.S

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theorem Steedman2000.the_cat_eats_pizza_cat :

the_cat_eats_pizza.cat = some CCG.S

Non-constituent coordination #

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theorem Steedman2000.john_likes_and_mary_hates_beans_cat :

CCG.john_likes_and_mary_hates_beans.cat = some CCG.S

CCG derives "John likes and Mary hates beans" (modeled on the book's "Anna married, and I detest, Manny") with category S: "John likes" is a constituent S/NP via type-raising + composition.

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def Steedman2000.john_sleeps_and_mary_sleeps :

CCG.DerivStep

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theorem Steedman2000.opCount_standardCoord_lt_nonConstituentCoord :

john_sleeps_and_mary_sleeps.opCount < CCG.john_likes_and_mary_hates_beans.opCount

Non-constituent coordination requires more combinatory operations than standard coordination. Reading operation count as processing difficulty is this formalization's linking hypothesis, not a claim of [Ste00a].

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theorem Steedman2000.opCount_simple_lt_standardCoord :

CCG.john_sleeps.opCount < john_sleeps_and_mary_sleeps.opCount

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def Steedman2000.toySemLexicon :

CCG.SemLexicon Semantics.Montague.ToyEntity Unit

Toy semantic lexicon over the toy English fragment ("likes"/"hates" reuse sees_sem as placeholder denotations).

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Steedman2000.toySemLexicon "John" (CCG.Cat.atom CCG.Atom.NP) = some { cat := CCG.NP, meaning := Semantics.Montague.ToyEntity.john }
Steedman2000.toySemLexicon "Mary" (CCG.Cat.atom CCG.Atom.NP) = some { cat := CCG.NP, meaning := Semantics.Montague.ToyEntity.mary }
Steedman2000.toySemLexicon "beans" (CCG.Cat.atom CCG.Atom.NP) = some { cat := CCG.NP, meaning := Semantics.Montague.ToyEntity.pizza }
Steedman2000.toySemLexicon "sleeps" ((CCG.Cat.atom CCG.Atom.S).lslash (CCG.Cat.atom CCG.Atom.NP)) = some { cat := CCG.IV, meaning := Semantics.Montague.ToyLexicon.sleeps_sem }
Steedman2000.toySemLexicon "laughs" ((CCG.Cat.atom CCG.Atom.S).lslash (CCG.Cat.atom CCG.Atom.NP)) = some { cat := CCG.IV, meaning := Semantics.Montague.ToyLexicon.laughs_sem }
Steedman2000.toySemLexicon word cat = none

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theorem Steedman2000.getMeaning_john_sleeps :

CCG.getMeaning (CCG.john_sleeps.interp toySemLexicon) = some True

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theorem Steedman2000.getMeaning_john_sees_mary :

CCG.getMeaning (CCG.john_sees_mary.interp toySemLexicon) = some True

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def Steedman2000.john_sees_mary_via_tr :

CCG.DerivStep

"John sees Mary" with a type-raised subject: the raised subject CCG.john_tr : S/(S\NP) uses forward application, and the derivation produces the same truth value as the canonical one.

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Steedman2000.john_sees_mary_via_tr = CCG.john_tr.fapp ((CCG.DerivStep.lex { form := "sees", cat := CCG.TV }).fapp (CCG.DerivStep.lex { form := "Mary", cat := CCG.NP }))

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theorem Steedman2000.getMeaning_john_sees_mary_via_tr :

CCG.getMeaning (john_sees_mary_via_tr.interp toySemLexicon) = some True

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def Steedman2000.coordMeaningAt (e : Semantics.Montague.ToyEntity) :

Option Prop

The predicate "John likes and Mary hates" (category S/NP) evaluated at an entity.

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Steedman2000.coordMeaningAt e = Option.map (fun (x : Semantics.Montague.ToyEntity → Prop) => x e) (CCG.getPredicateMeaning (CCG.john_likes_and_mary_hates.interp Steedman2000.toySemLexicon))

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def Steedman2000.pointwiseConjAt (e : Semantics.Montague.ToyEntity) :

Option Prop

The pointwise conjunction of "John likes" and "Mary hates" at an entity.

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theorem Steedman2000.coordMeaningAt_eq_pointwiseConjAt (e : Semantics.Montague.ToyEntity) :

coordMeaningAt e = pointwiseConjAt e

Generalized conjunction delivers the conjunctive interpretation: ⟦John likes and Mary hates⟧(e) = ⟦John likes⟧(e) ∧ ⟦Mary hates⟧(e).

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theorem Steedman2000.getMeaning_john_likes_and_mary_hates_beans :

CCG.getMeaning (CCG.john_likes_and_mary_hates_beans.interp toySemLexicon) = some (Semantics.Montague.ToyLexicon.sees_sem Semantics.Montague.ToyEntity.pizza Semantics.Montague.ToyEntity.john ∧ Semantics.Montague.ToyLexicon.sees_sem Semantics.Montague.ToyEntity.pizza Semantics.Montague.ToyEntity.mary)

The truth conditions of "John likes and Mary hates beans" are the conjunction of the two predications (in the toy model, likes = hates = sees).

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def Steedman2000.john_likes_beans_and_mary_hates_beans :

CCG.DerivStep

The spelled-out paraphrase "John likes beans and Mary hates beans".

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theorem Steedman2000.nonConstituentCoord_eq_spelledOut :

CCG.getMeaning (CCG.john_likes_and_mary_hates_beans.interp toySemLexicon) = CCG.getMeaning (john_likes_beans_and_mary_hates_beans.interp toySemLexicon)

The non-constituent coordination and its spelled-out paraphrase receive the same truth conditions — the book's claim that the composed derivation yields the same predicate-argument structure as the canonical one.

The coordinator's `role` is truth-conditionally load-bearing #

interp reads the coordinator's role off the .coord node — it no longer hardcodes conjunction — so which coordinator a derivation uses is part of its truth conditions. Using the actual English fragment coordinators, conjoining a true sentence p and a false sentence q with and_ (role = .j) gives p ∧ q (false), while or_ (role = .disj) gives p ∨ q (true). They differ, so the marking's role field is load-bearing — flipping English.Coordination.and_.role to .disj would break the theorem below, rather than no theorem depending on it.

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theorem Steedman2000.coord_role_load_bearing :

CCG.getMeaning ((CCG.DerivStep.coord English.Coordination.and_.role Steedman2000.dp✝ Steedman2000.dq✝).interp Steedman2000.pqLex✝) ≠ CCG.getMeaning ((CCG.DerivStep.coord English.Coordination.or_.role Steedman2000.dp✝ Steedman2000.dq✝).interp Steedman2000.pqLex✝)

The coordinator's role flips the truth conditions: English and_ yields p ∧ q, or_ yields p ∨ q, and these differ at p = ⊤, q = ⊥. Flipping a fragment coordinator's role collapses the inequality, so the role marking is not decorative.

Gapping #

[Ros70]'s generalization — gapping direction tracks word order — which [Ste00a] derives from the Principles of Adjacency, Consistency, and Inheritance together with the order-preserving constraint on type-raising. Deriving predictedGappingPattern from the slash directions of CCG.Gapping's gapped categories is TODO. (Dutch licensing both directions is mixed_allows_both.)

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inductive Steedman2000.WordOrder :

Type

Basic word order of a transitive clause (S = subject, V = verb, O = object).

SOV : WordOrder
SVO : WordOrder
VSO : WordOrder
VOS : WordOrder
OVS : WordOrder
OSV : WordOrder

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@[implicit_reducible]

instance Steedman2000.instDecidableEqWordOrder :

DecidableEq WordOrder

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Steedman2000.instDecidableEqWordOrder x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def Steedman2000.instReprWordOrder.repr :

WordOrder → ℕ → Std.Format

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@[implicit_reducible]

instance Steedman2000.instReprWordOrder :

Repr WordOrder

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Steedman2000.instReprWordOrder = { reprPrec := Steedman2000.instReprWordOrder.repr }

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inductive Steedman2000.GappingDirection :

Type

Direction of gapping in a coordinate structure: forward gapping leaves the gap in the non-initial conjunct ("Dexter ate bread, and Warren, potatoes"); backward gapping leaves it in the non-final conjunct (Japanese "Ken-ga Naomi-o, Erika-ga Sara-o tazuneta").

forward : GappingDirection
backward : GappingDirection

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@[implicit_reducible]

instance Steedman2000.instDecidableEqGappingDirection :

DecidableEq GappingDirection

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Steedman2000.instDecidableEqGappingDirection x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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@[implicit_reducible]

instance Steedman2000.instReprGappingDirection :

Repr GappingDirection

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Steedman2000.instReprGappingDirection = { reprPrec := Steedman2000.instReprGappingDirection.repr }

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def Steedman2000.instReprGappingDirection.repr :

GappingDirection → ℕ → Std.Format

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structure Steedman2000.GappingPattern :

Type

The gapping directions a language allows.

allowsForward : Prop
allowsBackward : Prop
decAllowsForward : Decidable self.allowsForward
decAllowsBackward : Decidable self.allowsBackward

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def Steedman2000.GappingPattern.forwardOnly :

GappingPattern

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Steedman2000.GappingPattern.forwardOnly = { allowsForward := True, allowsBackward := False, decAllowsForward := instDecidableTrue, decAllowsBackward := instDecidableFalse }

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def Steedman2000.GappingPattern.backwardOnly :

GappingPattern

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Steedman2000.GappingPattern.backwardOnly = { allowsForward := False, allowsBackward := True, decAllowsForward := instDecidableFalse, decAllowsBackward := instDecidableTrue }

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def Steedman2000.GappingPattern.both :

GappingPattern

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Steedman2000.GappingPattern.both = { allowsForward := True, allowsBackward := True, decAllowsForward := instDecidableTrue, decAllowsBackward := instDecidableTrue }

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def Steedman2000.GappingPattern.neither :

GappingPattern

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Steedman2000.GappingPattern.neither = { allowsForward := False, allowsBackward := False, decAllowsForward := instDecidableFalse, decAllowsBackward := instDecidableFalse }

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def Steedman2000.HasRightwardVerbs :

WordOrder → Prop

The order's transitive verbs seek (at least one of) their arguments rightward.

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Steedman2000.HasRightwardVerbs Steedman2000.WordOrder.VSO = True
Steedman2000.HasRightwardVerbs Steedman2000.WordOrder.SVO = True
Steedman2000.HasRightwardVerbs Steedman2000.WordOrder.VOS = True
Steedman2000.HasRightwardVerbs x✝ = False

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@[implicit_reducible]

instance Steedman2000.instDecidablePredWordOrderHasRightwardVerbs :

DecidablePred HasRightwardVerbs

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def Steedman2000.HasLeftwardVerbs :

WordOrder → Prop

The order's transitive verbs seek their arguments leftward.

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Steedman2000.HasLeftwardVerbs Steedman2000.WordOrder.SOV = True
Steedman2000.HasLeftwardVerbs Steedman2000.WordOrder.OVS = True
Steedman2000.HasLeftwardVerbs Steedman2000.WordOrder.OSV = True
Steedman2000.HasLeftwardVerbs x✝ = False

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@[implicit_reducible]

instance Steedman2000.instDecidablePredWordOrderHasLeftwardVerbs :

DecidablePred HasLeftwardVerbs

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def Steedman2000.predictedGappingPattern (order : WordOrder) :

GappingPattern

The gapping directions CCG predicts for a word order: forward gapping needs a leftward-looking gapped conjunct, available through backward type-raising over rightward-seeking verbs (T\(T/NP)); backward gapping needs forward raising over leftward-seeking verbs (T/(T\NP)).

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theorem Steedman2000.predictedGappingPattern_iff_rossOriginal (order : WordOrder) :

((predictedGappingPattern order).allowsForward ↔ (rossOriginal order).allowsForward) ∧ ((predictedGappingPattern order).allowsBackward ↔ (rossOriginal order).allowsBackward)

The CCG-predicted pattern coincides with Ross's generalization.

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theorem Steedman2000.predictedGappingPattern_svo_iff_vso :

((predictedGappingPattern WordOrder.SVO).allowsForward ↔ (predictedGappingPattern WordOrder.VSO).allowsForward) ∧ ((predictedGappingPattern WordOrder.SVO).allowsBackward ↔ (predictedGappingPattern WordOrder.VSO).allowsBackward)

SVO patterns with VSO: both license forward but not backward gapping.

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theorem Steedman2000.no_backward_gapping_in_english :

¬HasLeftwardVerbs WordOrder.SVO

English (SVO) has no leftward-looking transitive verb category, so the rightward-looking gapped conjunct a backward gap needs cannot be built: "*Warren, potatoes and Dexter ate bread" (instantiating Steedman's *SO and SVO schema; the book's attested forward counterpart is "Dexter ate bread and Warren, potatoes").

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structure Steedman2000.ClauseOrderProfile :

Type

Main- vs subordinate-clause word order, for languages whose two clause types diverge.

mainClause : WordOrder
subClause : WordOrder

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def Steedman2000.instReprClauseOrderProfile.repr :

ClauseOrderProfile → ℕ → Std.Format

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@[implicit_reducible]

instance Steedman2000.instReprClauseOrderProfile :

Repr ClauseOrderProfile

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Steedman2000.instReprClauseOrderProfile = { reprPrec := Steedman2000.instReprClauseOrderProfile.repr }

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def Steedman2000.rossRevised (profile : ClauseOrderProfile) :

GappingPattern

Steedman's revision of [Ros70]: gapping availability tracks the lexical availability of verb categories, not a single "underlying" word order — forward gapping needs rightward-combining verbs, backward gapping leftward-combining verbs in either clause type.

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def Steedman2000.dutch :

ClauseOrderProfile

Dutch: SVO main clauses, SOV subordinate clauses. The mixed profile licenses both gapping directions — forward in main clauses ("Wil jij een ijsje en Marietje limonade?"), backward in subordinate clauses ("...dat Jan Syntactic Structures en Piet Aspects gelezen heeft").

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Steedman2000.dutch = { mainClause := Steedman2000.WordOrder.SVO, subClause := Steedman2000.WordOrder.SOV }

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theorem Steedman2000.mixed_allows_both :

(rossRevised dutch).allowsForward ∧ (rossRevised dutch).allowsBackward

A mixed-order language like Dutch licenses both gapping directions.

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inductive Steedman2000.EllipsisType :

Type

Steedman's taxonomy of elliptical constructions.

gapping : EllipsisType
"Dexter ate bread, and Warren, potatoes"
stripping : EllipsisType
"Dexter ran away, and Warren (too)"
vpEllipsis : EllipsisType
"Dexter ate bread, and Warren did too"
sluicing : EllipsisType
"Dexter did something, but I don't know what"

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@[implicit_reducible]

instance Steedman2000.instDecidableEqEllipsisType :

DecidableEq EllipsisType

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Steedman2000.instDecidableEqEllipsisType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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@[implicit_reducible]

instance Steedman2000.instReprEllipsisType :

Repr EllipsisType

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Steedman2000.instReprEllipsisType = { reprPrec := Steedman2000.instReprEllipsisType.repr }

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def Steedman2000.instReprEllipsisType.repr :

EllipsisType → ℕ → Std.Format

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def Steedman2000.isSyntacticallyMediated :

EllipsisType → Prop

Gapping and stripping are syntactically mediated via CCG; VP ellipsis and sluicing are purely anaphoric.

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instance Steedman2000.instDecidablePredEllipsisTypeIsSyntacticallyMediated :

DecidablePred isSyntacticallyMediated

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def Steedman2000.HasWordOrderConstraints :

EllipsisType → Prop

Only the syntactically mediated ellipsis types exhibit word-order constraints; VP ellipsis and sluicing pattern alike across languages.

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@[implicit_reducible]

instance Steedman2000.instDecidablePredEllipsisTypeHasWordOrderConstraints :

DecidablePred HasWordOrderConstraints

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@[implicit_reducible]

instance Steedman2000.instHasDepthEllipsisType :

Anaphor.HasDepth EllipsisType

All four of Steedman's elliptical constructions are surface anaphora in Hankamer & Sag's sense ([HS76]): each deletes internal structure under identity with a linguistic antecedent. Steedman's taxonomy contains no deep anaphor (no do so-type pro-form), so the depth axis is constant .surface over it.

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Steedman2000.instHasDepthEllipsisType = { depth := fun (x : Steedman2000.EllipsisType) => Anaphor.Depth.surface }

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theorem Steedman2000.surface_not_syntacticallyMediated :

Anaphor.HasDepth.IsSurface EllipsisType.vpEllipsis ∧ ¬isSyntacticallyMediated EllipsisType.vpEllipsis

Cross-framework non-alignment. Steedman's CCG cut isSyntacticallyMediated (gapping/stripping derived by category composition; VP-ellipsis/sluicing handled anaphorically) is not Hankamer & Sag's deep/surface cut. VP-ellipsis is the paradigm surface anaphor ([HS76]; Landau's own surface baseline in [Lan26]) yet CCG treats it as non-mediated — so the two frameworks partition the very same constructions differently.

Cross-serial dependencies #

Dutch verb clusters ([BKPZ82]) with cross-serial NP-verb bindings, using the surface-faithful derivations of CCG.CrossSerial: cluster verbs carry leftward NP slots and the cluster composes by forward crossed composition, per the book's own Dutch fragment, so the yield matches the attested word order.

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structure Steedman2000.AnnotatedDerivation :

Type

A CCG derivation annotated with which NP binds to which verb. TODO: compute binding from deriv's composition structure instead of annotating it by hand.

n : ℕ
Number of NP-verb pairs
deriv : CCG.Classical.Derivation
words : List String
Surface words
binding : Features.VerbClusterBinding self.n
The NP-verb binding permutation

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def Steedman2000.instReprAnnotatedDerivation.repr :

AnnotatedDerivation → ℕ → Std.Format

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@[implicit_reducible]

instance Steedman2000.instReprAnnotatedDerivation :

Repr AnnotatedDerivation

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Steedman2000.instReprAnnotatedDerivation = { reprPrec := Steedman2000.instReprAnnotatedDerivation.repr }

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def Steedman2000.dutch_jan_piet_zag_zwemmen :

AnnotatedDerivation

"Jan Piet zag zwemmen" with cross-serial bindings: Jan is the subject of "zag", Piet the argument bound into the cluster.

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def Steedman2000.dutch_jan_piet_marie_zag_helpen_zwemmen :

AnnotatedDerivation

"Jan Piet Marie zag helpen zwemmen": zag >B× (helpen zwemmen) makes the cluster a leftward-seeking 3-place predicate; Marie binds helpen's slot, Piet zag's object slot, Jan the subject — the cross-serial binding pattern, in the attested word order.

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theorem Steedman2000.dutch_jan_piet_zag_zwemmen_binding :

dutch_jan_piet_zag_zwemmen.binding = BresnanEtAl1982.dutch_2np_2v.binding

The annotated binding agrees with the empirical datum.

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theorem Steedman2000.dutch_jan_piet_marie_zag_helpen_zwemmen_binding :

dutch_jan_piet_marie_zag_helpen_zwemmen.binding = BresnanEtAl1982.dutch_3np_3v.binding

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theorem Steedman2000.dutch_jan_piet_zag_zwemmen_yield :

dutch_jan_piet_zag_zwemmen.deriv.yield = dutch_jan_piet_zag_zwemmen.words

The derivations spell out exactly the annotated surface words.

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theorem Steedman2000.dutch_jan_piet_marie_zag_helpen_zwemmen_yield :

dutch_jan_piet_marie_zag_helpen_zwemmen.deriv.yield = dutch_jan_piet_marie_zag_helpen_zwemmen.words

Verb clusters and quantifier scope (§6.8) #

Scope tracks word order: in the verb-raising order the cluster forms by composition, so a quantified argument combines with a function containing the tensed verb and can take scope over it; in the verb-projection-raising order it combines with the embedded verb alone. The derivations below are category-checked DerivStep trees: the verb-raising cluster forms by forward crossed composition (CCG.forwardCompX), the verb-projection-raising order by plain application — the composed-cluster vs. applied-cluster contrast driving the account. (The toy Cat still drops the book's features, e.g. the VP₋SUB restriction on >B×.)

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inductive Steedman2000.VerbOrder :

Type

Word order in a West Germanic verb cluster ([Ste00a] §6.8).

verbRaising : VerbOrder
Object precedes the whole verb cluster: NP … V_emb V_matrix.
verbProjectionRaising : VerbOrder
Object follows the matrix verb: V_matrix … NP V_emb.

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@[implicit_reducible]

instance Steedman2000.instDecidableEqVerbOrder :

DecidableEq VerbOrder

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Steedman2000.instDecidableEqVerbOrder x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

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def Steedman2000.instReprVerbOrder.repr :

VerbOrder → ℕ → Std.Format

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@[implicit_reducible]

instance Steedman2000.instReprVerbOrder :

Repr VerbOrder

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Steedman2000.instReprVerbOrder = { reprPrec := Steedman2000.instReprVerbOrder.repr }

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@[implicit_reducible]

instance Steedman2000.instInhabitedVerbOrder :

Inhabited VerbOrder

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Steedman2000.instInhabitedVerbOrder = { default := Steedman2000.instInhabitedVerbOrder.default }

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def Steedman2000.verbRaisingDeriv :

CCG.DerivStep

Verb-raising order, Dutch (99a): the cluster probeert te zingen forms by crossed composition before taking the object to its left.

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def Steedman2000.verbProjectionRaisingDeriv :

CCG.DerivStep

Verb-projection-raising order, Dutch (99b): the matrix verb applies to an already-saturated embedded VP, so the quantified object never combines with a function containing the tensed verb.

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