Pickering & Barry (1991)

[PB91]

Sentence Processing without Empty Categories. Language and Cognitive Processes, 6(3), 229–259.

Core Thesis

Processing of unbounded dependencies does not involve empty categories (traces). Fillers associate directly with their subcategorizing verbs — filler-verb association — without intermediary gap sites. Processing difficulty is determined by the nesting pattern of filler-verb associations:

• Nested (abba): must hold first filler while processing inner pairs → hard
• Disjoint (aabb): each pair completed before the next begins → easy

This single distinction correctly predicts processing difficulty across four sentence types (Table 2), where the trace-based account (requiring separate filler-gap and gap-verb association patterns) makes incorrect predictions for multiple pied-piping constructions.

Connection to CCG

The gap-free account is made possible by CCG's forward composition (the B combinator), which allows partial constituents like S/NP for "John saw" without positing a gap after "saw." In the derivation of "Sue wonders whom John saw" (ex 84):

• John : NP type-raises to S/(S\NP) via T
• saw : (S\NP)/NP
• T(John) >B saw yields S/NP — a sentence missing an object
• whom : Q/(S/NP) combines with S/NP to form Q

No empty category is needed because composition creates the filler-verb association directly. This is the subject_verb_composition theorem in CCG.Combinators.

Sections

• §1: Association patterns and the two competing analyses
• §2: The four sentence types with empirical difficulty
• §3: Table 2 — the gap-free classification and its processing predictions
• §4: Contrast with the trace-based analysis (Table 1)
• §5: Bridges to ProcessingProfile, BresnanEtAl1982, and CCG

inductive PickeringBarry1991.NestingPattern : Type

Nesting pattern of associations in a sentence.

Two concurrent associations can be nested (abba: the second pair is enclosed within the first) or disjoint (aabb: each pair completed before the next begins).

This is the central formal object of [PB91].

• nested : NestingPattern
• disjoint : NestingPattern

@[implicit_reducible]

instance PickeringBarry1991.instDecidableEqNestingPattern : DecidableEq NestingPattern

Equations

• PickeringBarry1991.instDecidableEqNestingPattern x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance PickeringBarry1991.instReprNestingPattern : Repr NestingPattern

Equations

• PickeringBarry1991.instReprNestingPattern = { reprPrec := PickeringBarry1991.instReprNestingPattern.repr }

def PickeringBarry1991.instReprNestingPattern.repr : NestingPattern → ℕ → Std.Format

Equations

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

inductive PickeringBarry1991.AnalysisType : Type

Under the gap-free account, there is only one type of association: filler-verb. Under the trace account, there are two: filler-gap and gap-verb.

The trace account must classify both patterns independently, while the gap-free account needs only one.

• gapFree : AnalysisType
• traceBased : AnalysisType

@[implicit_reducible]

instance PickeringBarry1991.instDecidableEqAnalysisType : DecidableEq AnalysisType

Equations

• PickeringBarry1991.instDecidableEqAnalysisType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def PickeringBarry1991.instReprAnalysisType.repr : AnalysisType → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance PickeringBarry1991.instReprAnalysisType : Repr AnalysisType

Equations

• PickeringBarry1991.instReprAnalysisType = { reprPrec := PickeringBarry1991.instReprAnalysisType.repr }

def PickeringBarry1991.AnalysisType.associationTypes : AnalysisType → ℕ

Number of independent association types required by each analysis.

Equations

• PickeringBarry1991.AnalysisType.gapFree.associationTypes = 1
• PickeringBarry1991.AnalysisType.traceBased.associationTypes = 2

theorem PickeringBarry1991.gapFree_simpler : AnalysisType.gapFree.associationTypes < AnalysisType.traceBased.associationTypes

The gap-free analysis is simpler: fewer association types to track.

inductive PickeringBarry1991.SentenceType : Type

The four sentence types classified in Tables 1 and 2 (p. 242, 246).

Each involves multiple extractions and exhibits characteristic processing difficulty that discriminates between the two analyses.

• engMultiSubjRel : SentenceType

  "I saw the farmer who owned the dog which chased the cat." (ex 44) Subject extracted from each relative clause.

• engMultiObjRel : SentenceType

  "The cat which the dog which the farmer owned chased fled." (ex 45) Object extracted from each relative clause (center-embedded).

• gerMultiSubjRel : SentenceType

  "Der Bauer der das Mädchen das den Jungen küßte schlug ging." (ex 48) German: subject extracted, verb-final order creates nesting.

• engMultiPiedPiping : SentenceType

  "John found the saucer on which Mary put the cup into which I poured the tea." (ex 42) Pied-piped PPs, successive relatives.

@[implicit_reducible]

instance PickeringBarry1991.instDecidableEqSentenceType : DecidableEq SentenceType

Equations

• PickeringBarry1991.instDecidableEqSentenceType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def PickeringBarry1991.instReprSentenceType.repr : SentenceType → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance PickeringBarry1991.instReprSentenceType : Repr SentenceType

Equations

• PickeringBarry1991.instReprSentenceType = { reprPrec := PickeringBarry1991.instReprSentenceType.repr }

inductive PickeringBarry1991.Difficulty : Type

Observed processing difficulty.

• easy : Difficulty
• hard : Difficulty

@[implicit_reducible]

instance PickeringBarry1991.instDecidableEqDifficulty : DecidableEq Difficulty

Equations

• PickeringBarry1991.instDecidableEqDifficulty x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance PickeringBarry1991.instReprDifficulty : Repr Difficulty

Equations

• PickeringBarry1991.instReprDifficulty = { reprPrec := PickeringBarry1991.instReprDifficulty.repr }

def PickeringBarry1991.instReprDifficulty.repr : Difficulty → ℕ → Std.Format

Equations

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

def PickeringBarry1991.observedDifficulty : SentenceType → Difficulty

Empirical processing difficulty for each sentence type.

Subject relatives and pied-piping are easy to extend with further relative clauses (exx 51, 54–55); object relatives and German subject relatives become rapidly incomprehensible (exx 52–53).

Equations

• PickeringBarry1991.observedDifficulty PickeringBarry1991.SentenceType.engMultiSubjRel = PickeringBarry1991.Difficulty.easy
• PickeringBarry1991.observedDifficulty PickeringBarry1991.SentenceType.engMultiObjRel = PickeringBarry1991.Difficulty.hard
• PickeringBarry1991.observedDifficulty PickeringBarry1991.SentenceType.gerMultiSubjRel = PickeringBarry1991.Difficulty.hard
• PickeringBarry1991.observedDifficulty PickeringBarry1991.SentenceType.engMultiPiedPiping = PickeringBarry1991.Difficulty.easy

def PickeringBarry1991.fillerVerbPattern : SentenceType → NestingPattern

Filler-verb association pattern under the gap-free analysis (Table 2).

This is the ONLY association type needed. The annotation scheme from p. 245:

• Subject relative (ex 56): [who]₁ [owned]₁ ... [which]₂ [chased]₂ → disjoint (1122)
• Object relative (ex 57): [which]₁ ... [which]₂ [owned]₂ [chased]₁ → nested (1221)
• German subj rel (ex 58): [der]₁ [das]₂ [küßte]₂ [schlug]₁ → nested (1221)
• Pied-piping (ex 59): [on which]₁ [put]₁ [into which]₂ [poured]₂ → disjoint (1122)

Equations

• PickeringBarry1991.fillerVerbPattern PickeringBarry1991.SentenceType.engMultiSubjRel = PickeringBarry1991.NestingPattern.disjoint
• PickeringBarry1991.fillerVerbPattern PickeringBarry1991.SentenceType.engMultiObjRel = PickeringBarry1991.NestingPattern.nested
• PickeringBarry1991.fillerVerbPattern PickeringBarry1991.SentenceType.gerMultiSubjRel = PickeringBarry1991.NestingPattern.nested
• PickeringBarry1991.fillerVerbPattern PickeringBarry1991.SentenceType.engMultiPiedPiping = PickeringBarry1991.NestingPattern.disjoint

def PickeringBarry1991.isNestedConstruction : SentenceType → Prop

Is the construction nested in Chomsky's (1965) sense?

Under the gap-free analysis (no empty categories), the definition simplifies: a construction is nested iff its filler-verb associations are nested. This collapse is the central result.

Equations

• PickeringBarry1991.isNestedConstruction PickeringBarry1991.SentenceType.engMultiSubjRel = False
• PickeringBarry1991.isNestedConstruction PickeringBarry1991.SentenceType.engMultiObjRel = True
• PickeringBarry1991.isNestedConstruction PickeringBarry1991.SentenceType.gerMultiSubjRel = True
• PickeringBarry1991.isNestedConstruction PickeringBarry1991.SentenceType.engMultiPiedPiping = False

@[implicit_reducible]

instance PickeringBarry1991.instDecidablePredSentenceTypeIsNestedConstruction : DecidablePred isNestedConstruction

Equations

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

theorem PickeringBarry1991.table2_correspondence (s : SentenceType) : fillerVerbPattern s = NestingPattern.nested ↔ isNestedConstruction s

Table 2 correspondence (p. 246): under the gap-free analysis, the filler-verb pattern directly determines construction nestedness.

Table 1 (trace-based) has three independent columns (filler-gap pattern, gap-verb pattern, construction type) with no systematic relationship. Table 2 collapses to two identical columns.

def PickeringBarry1991.gapFreePrediction (s : SentenceType) : Difficulty

Gap-free processing prediction: nested filler-verb associations are hard, disjoint are easy.

Equations

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

theorem PickeringBarry1991.gapFree_all_correct (s : SentenceType) : gapFreePrediction s = observedDifficulty s

The gap-free analysis correctly predicts all four observations.

def PickeringBarry1991.fillerGapPattern : SentenceType → NestingPattern

Filler-gap pattern under the trace-based analysis (Table 1).

Equations

• PickeringBarry1991.fillerGapPattern PickeringBarry1991.SentenceType.engMultiSubjRel = PickeringBarry1991.NestingPattern.disjoint
• PickeringBarry1991.fillerGapPattern PickeringBarry1991.SentenceType.engMultiObjRel = PickeringBarry1991.NestingPattern.nested
• PickeringBarry1991.fillerGapPattern PickeringBarry1991.SentenceType.gerMultiSubjRel = PickeringBarry1991.NestingPattern.disjoint
• PickeringBarry1991.fillerGapPattern PickeringBarry1991.SentenceType.engMultiPiedPiping = PickeringBarry1991.NestingPattern.nested

def PickeringBarry1991.gapVerbPattern : SentenceType → NestingPattern

Gap-verb pattern under the trace-based analysis (Table 1).

Equations

• PickeringBarry1991.gapVerbPattern PickeringBarry1991.SentenceType.engMultiSubjRel = PickeringBarry1991.NestingPattern.disjoint
• PickeringBarry1991.gapVerbPattern PickeringBarry1991.SentenceType.engMultiObjRel = PickeringBarry1991.NestingPattern.disjoint
• PickeringBarry1991.gapVerbPattern PickeringBarry1991.SentenceType.gerMultiSubjRel = PickeringBarry1991.NestingPattern.nested
• PickeringBarry1991.gapVerbPattern PickeringBarry1991.SentenceType.engMultiPiedPiping = PickeringBarry1991.NestingPattern.nested

def PickeringBarry1991.traceBasedPrediction (s : SentenceType) : Difficulty

Trace-based prediction: a construction is hard if EITHER filler-gap or gap-verb associations are nested.

Equations

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

theorem PickeringBarry1991.traceBased_piedPiping_wrong : traceBasedPrediction SentenceType.engMultiPiedPiping ≠ observedDifficulty SentenceType.engMultiPiedPiping

The trace-based analysis incorrectly predicts pied-piping is hard. It has nested filler-gap AND nested gap-verb (Table 1), yet the construction is easy to process and easily extensible (exx 54–55).

theorem PickeringBarry1991.gapFree_piedPiping_correct : gapFreePrediction SentenceType.engMultiPiedPiping = observedDifficulty SentenceType.engMultiPiedPiping

The gap-free analysis correctly predicts pied-piping is easy — the critical case where it outperforms the trace-based account.

theorem PickeringBarry1991.table1_columns_disagree : fillerGapPattern SentenceType.gerMultiSubjRel = NestingPattern.disjoint ∧ gapVerbPattern SentenceType.gerMultiSubjRel = NestingPattern.nested ∧ isNestedConstruction SentenceType.gerMultiSubjRel

Table 1 has no systematic relationship between its three columns. The filler-gap pattern, gap-verb pattern, and construction type are all independent. German subject relatives are nested constructions with disjoint filler-gap associations — the columns disagree.

Bridge to ProcessingProfile

def PickeringBarry1991.nestingProfile : NestingPattern → ProcessingModel.ProcessingProfile

Map nesting pattern to ProcessingProfile.

Nested associations require holding unfinished fillers in working memory while forming inner associations — higher locality (longer dependency span) and referential load (more intervening material to track).

Equations

• PickeringBarry1991.nestingProfile PickeringBarry1991.NestingPattern.nested = { locality := 4, boundaries := 2, referentialLoad := 2, ease := 0 }
• PickeringBarry1991.nestingProfile PickeringBarry1991.NestingPattern.disjoint = { locality := 2, boundaries := 0, referentialLoad := 0, ease := 1 }

@[implicit_reducible]

instance PickeringBarry1991.instHasProcessingProfileSentenceType : ProcessingModel.HasProcessingProfile SentenceType

Equations

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

theorem PickeringBarry1991.nested_harder_than_disjoint : (nestingProfile NestingPattern.nested).compare (nestingProfile NestingPattern.disjoint) = ProcessingModel.CompareResult.harder

Nested associations are Pareto-harder than disjoint.

def PickeringBarry1991.orderingPredictions : List (ProcessingModel.OrderingPrediction SentenceType)

Processing ordering predictions verified via Pareto dominance.

Equations

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

theorem PickeringBarry1991.all_orderings_verified : orderingPredictions.all ProcessingModel.verifyOrdering = true

Bridge to cross-serial dependencies

theorem PickeringBarry1991.german_nested_consistent : fillerVerbPattern SentenceType.gerMultiSubjRel = NestingPattern.nested ∧ BresnanEtAl1982.german_3np_3v.binding.pattern = Features.BindingPattern.nested

German verb-final order produces nested filler-verb associations, consistent with the nested dependency pattern in German verb clusters (BresnanEtAl1982.german_3np_3v). Both German constructions — subject relatives and verb clusters — exhibit nesting because the verb that closes each dependency comes in reverse order.

[BBMW86] confirms the processing prediction: German nested constructions are hard, like their Dutch cross-serial counterparts (though for different structural reasons).

Bridge to CCG combinators

The gap-free account requires a grammar that can establish filler-verb associations without positing gap positions. CCG achieves this via forward composition (B) and type-raising (T):

subject_verb_composition in CCG.Combinators proves: B (T subj) verb obj = verb obj subj

This is exactly derivation (84) in the paper: "John saw" becomes a constituent S/NP via rule (80a) (type-raising + composition), and "whom" : Q/(S/NP) combines with S/NP to form Q — no trace needed. The variable-free semantics (ccgVariableFree in CCG.Combinators) guarantees that all semantic operations use combinators rather than bound variables, which is the formal counterpart of "no empty categories."