Bhatt & Takahashi 2011: Reduced and Unreduced Phrasal Comparatives

@cite{bhatt-takahashi-2011} @cite{bhatt-pancheva-2004} @cite{bresnan-1973} @cite{lechner-2001} @cite{lechner-2004} @cite{merchant-2009} @cite{takahashi-hulsey-2009} @cite{heim-2006}

Rajesh Bhatt and Shoichi Takahashi. Reduced and Unreduced Phrasal Comparatives. Natural Language & Linguistic Theory 29(3): 581–620.

What this file is

A paper-faithful study of B&T 2011, the successor paper to @cite{bhatt-pancheva-2004} that reverses B&P's central typological claim about English phrasal comparatives. It also delivers the diagnostic battery that the B&P 2004 file's closing prose flagged as needed for a syntactic-structure verdict.

The diagnostic schema (BindingDatum, RAPredictsCoref, DAPredictsCoref, realizesReduction, realizesDirect, HeadAvailability, headAvailabilityFromBinding) lives in Lechner2004.lean — B&T fn. 4 explicitly attributes (11)–(13) to @cite{lechner-2004}'s disjoint-reference battery. This file imports that schema and instantiates it on B&T's English and Hindi-Urdu data.

B&T's two-analyses framework (§1)

Phrasal "John is taller than Bill" admits two competing analyses:

• Reduction Analysis (RA) — phrasal than NP derives from clausal than [NP is Adj] via reduction (gapping, conjunction reduction, TP-ellipsis, stripping). Uses the 2-place degree head, which combines with degree predicates.
• Direct Analysis (DA) — phrasal than NP is genuinely phrasal; the 'than'-phrase combines with an individual. Uses the 3-place degree head, which combines with two individuals plus a predicate of individuals and degrees.

The walked-back B&P 2004 claim

@cite{bhatt-pancheva-2004} §1.1.1 fn. 4 rejected @cite{bresnan-1973}'s reduction analysis of English phrasal comparatives. B&T 2011 §2's binding diagnostic establishes the opposite for English: the standard is c-commanded by everything that c-commands the associate, which is the structural signature of RA, not DA. The 3-place '-er' is needed for Hindi-Urdu §3, not English.

The cross-tradition bridge bt2011_agrees_with_bresnan_against_bp2004 witnesses that B&T's "reduction" and Bresnan's "maximal deletion" are the same kind of analysis — both derive surface phrasal forms from underlying clausal sources via deletion.

The diagnostic battery (§2, §3.4)

The B&P 2004 file's closing note says formalizing the Bresnan disagreement "would need either Bhatt & Takahashi 2011's diagnostic battery or a richer syntactic interface." This file supplies the former for the binding component:

• §2 English binding generalization (B&T (10)) — six minimal-pair entries from B&T (11)–(13), checked against realizesReduction / realizesDirect.
• §3.4 Hindi-Urdu binding contrast — captured by hindiUrduBindingPairs and the corresponding realization theorems.

Scope (§4), the Single Standard Restriction (§3.2), and the Precedence Constraint (§3.3) are noted in prose; their formalization would require richer syntactic infrastructure than the Lechner-style binding minimal pairs.

The typology proposal (B&T (63))

B&T's central crosslinguistic claim: both 2-place and 3-place degree heads are universally available in principle. Crosslinguistic variation in which is realized is determined by:

1. The subcategorization of the comparative marker (than / yori / -se): does it accept DPs, CPs, or both?
2. A preference for minimal structure: when a DP is locally available, the language prefers the smaller analysis.

For English and Hindi-Urdu the per-language HeadAvailability is derived from the binding data via headAvailabilityFromBinding (anti-stipulation). Japanese, where both analyses are realized, is stipulated with an explicit comment: B&T's §5 multiple-standard diagnostics (which would witness RA-realization for Japanese) require infrastructure not present here.

def BhattTakahashi2011.englishBindingPairs : List Lechner2004.BindingDatum

B&T §2 English minimal pairs (11)–(13). Each pair contrasts a pronominal that c-commands the associate (blocking coref into the standard) with a no-c-command baseline (allowing coref).

UNVERIFIED: judgments paraphrased; the binary pattern matches B&T's reported data. (13b) is recorded with .marginal acceptability per B&T fn. 5 (which describes some speakers as finding it "(?)mildly deviant" — corefAttested := true because the binding relation is licensed for the prediction direction).

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theorem BhattTakahashi2011.english_data_realizes_reduction : Lechner2004.realizesReduction englishBindingPairs

B&T (10), formalized: the English data is consistent with RA on every minimal pair. Coreference is grammatical iff the matrix pronoun does not c-command the associate.

theorem BhattTakahashi2011.english_data_rules_out_direct : ¬Lechner2004.realizesDirect englishBindingPairs

The Direct Analysis predicts uniform coreference availability, contradicted by the c-command-blocks-coref data points (11a), (12a), (13a). DA cannot be the analysis at work in English.

def BhattTakahashi2011.hindiUrduBindingPairs : List Lechner2004.BindingDatum

B&T §3.4 Hindi-Urdu data. The standard's binding properties are independent of the associate's: even when the matrix pronoun c-commands the associate (because it precedes the standard in the head-final word order), coreference with an R-expression in the standard is grammatical, because the standard is an external PP that the matrix pronoun never c-commands.

UNVERIFIED: B&T (35) supplies the key positive-coref-with-c-command example; the second entry is the no-c-command baseline.

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theorem BhattTakahashi2011.hindi_urdu_data_realizes_direct : Lechner2004.realizesDirect hindiUrduBindingPairs

B&T §3.4: Hindi-Urdu data is consistent with DA. The key data point is (35), where coreference is grammatical even though the matrix pronoun c-commands the associate.

theorem BhattTakahashi2011.hindi_urdu_data_rules_out_reduction : ¬Lechner2004.realizesReduction hindiUrduBindingPairs

Hindi-Urdu data rules out RA: at the (35) data point, RA predicts no coreference (matrix pronoun c-commands the associate, hence c-commands the standard's R-expression), but coreference is in fact attested.

def BhattTakahashi2011.englishAnalysisPerBhattTakahashi2011 : Lechner2004.PhrasalAnalysis

B&T 2011's verdict for English (§2): only the Reduction Analysis is available.

Equations

• BhattTakahashi2011.englishAnalysisPerBhattTakahashi2011 = Lechner2004.PhrasalAnalysis.reduction

def BhattTakahashi2011.englishAnalysisPerBhattPancheva2004 : Lechner2004.PhrasalAnalysis

@cite{bhatt-pancheva-2004} §1.1.1 fn. 4's verdict for English, restated in B&T's vocabulary: phrasal "than NP" is genuinely phrasal (DA), not a reduction of clausal "than [NP is Adj]".

Equations

• BhattTakahashi2011.englishAnalysisPerBhattPancheva2004 = Lechner2004.PhrasalAnalysis.direct

theorem BhattTakahashi2011.bp2004_bt2011_disagree_about_english : englishAnalysisPerBhattPancheva2004 ≠ englishAnalysisPerBhattTakahashi2011

The two papers genuinely disagree about English.

theorem BhattTakahashi2011.bt2011_verdict_matches_data_bp2004_verdict_does_not : Lechner2004.realizesReduction englishBindingPairs ∧ ¬Lechner2004.realizesDirect englishBindingPairs

The empirical content of the disagreement: B&T's verdict for English (RA) is the analysis whose predictions match the §2 data; B&P's verdict (DA) makes the wrong prediction at the c-command-blocks-coref data points.

structure BhattTakahashi2011.ScopeDatum : Type

A B&T §4 scope datum: a ScopeBinding paired with an observational record of whether than-internal scope is attested for the configuration. The qpBasePosition field of the binding is what (43) keys on (not the surface-scope qpHeight).

• citationId : String
• binding : Minimalist.DegreeMovement.ScopeBinding
• thanInternalScopeAttested : Bool

@[implicit_reducible]

instance BhattTakahashi2011.instReprScopeDatum : Repr ScopeDatum

Equations

• BhattTakahashi2011.instReprScopeDatum = { reprPrec := BhattTakahashi2011.instReprScopeDatum.repr }

def BhattTakahashi2011.instReprScopeDatum.repr : ScopeDatum → ℕ → Std.Format

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def BhattTakahashi2011.englishScopeData : List ScopeDatum

B&T §4 (43) English scope data. The structural prediction is RA's: than-internal scope is attested iff the QP's base position is at or below the DegP (B&T's "doesn't c-command the degree trace from the base").

UNVERIFIED: examples paraphrased; the binary pattern matches B&T's reported English data. (44a) is the in-situ existential case (base = degH); (44b) is the raised universal blocking than-internal scope.

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def BhattTakahashi2011.hindiUrduScopeData : List ScopeDatum

B&T §4 (43) Hindi-Urdu scope data. RA predicts than-internal scope should be available for low-base QPs, but Hindi-Urdu forces scope-out: than-internal scope is unattested even when the base position is at or below the DegP.

UNVERIFIED: data point reflects B&T §4.2's verdict that Hindi-Urdu obligatorily scopes out, not RA-internal scope.

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

def BhattTakahashi2011.RAPredictsThanInternalScope (d : ScopeDatum) : Prop

RA's prediction for a single scope datum: than-internal scope is attested iff the QP's base position is at or below the DegP.

Equations

• BhattTakahashi2011.RAPredictsThanInternalScope d = (Minimalist.DegreeMovement.IsBhattTakahashiScopeLicit d.binding ↔ d.thanInternalScopeAttested = true)

@[implicit_reducible]

instance BhattTakahashi2011.instDecidableRAPredictsThanInternalScope (d : ScopeDatum) : Decidable (RAPredictsThanInternalScope d)

Equations

• BhattTakahashi2011.instDecidableRAPredictsThanInternalScope d = id inferInstance

def BhattTakahashi2011.scopeRealizesReduction (data : List ScopeDatum) : Prop

A language's scope data realizes RA iff every datum matches the B&T (43) biconditional prediction.

Equations

• BhattTakahashi2011.scopeRealizesReduction data = ∀ d ∈ data, BhattTakahashi2011.RAPredictsThanInternalScope d

@[implicit_reducible]

instance BhattTakahashi2011.instDecidableScopeRealizesReduction (data : List ScopeDatum) : Decidable (scopeRealizesReduction data)

Equations

• BhattTakahashi2011.instDecidableScopeRealizesReduction data = id (List.decidableBAll BhattTakahashi2011.RAPredictsThanInternalScope data)

theorem BhattTakahashi2011.english_scope_matches_RA : scopeRealizesReduction englishScopeData

Parallel to english_data_realizes_reduction for the binding diagnostic: English scope data also matches RA.

theorem BhattTakahashi2011.hindi_urdu_scope_rules_out_RA : ¬scopeRealizesReduction hindiUrduScopeData

Parallel to hindi_urdu_data_rules_out_reduction: Hindi-Urdu scope data also rules out RA. The low-base configuration would license than-internal scope under RA, but Hindi-Urdu data shows scope-out is obligatory.

def BhattTakahashi2011.isReductionStyleBT : Lechner2004.PhrasalAnalysis → Bool

B&T's reduction and Bresnan's partialDeletion/maximalDeletion are the same kind of analysis: surface forms derive from underlying clausal sources via syntactic deletion.

Equations

• BhattTakahashi2011.isReductionStyleBT Lechner2004.PhrasalAnalysis.reduction = true
• BhattTakahashi2011.isReductionStyleBT Lechner2004.PhrasalAnalysis.direct = false

def BhattTakahashi2011.isReductionStyleBresnan : Bresnan1973.BresnanThanClauseAnalysis → Bool

Bresnan's two clausal-source pathways are both "reduction-style" in B&T's vocabulary: both posit a clausal underlying structure that is reduced by deletion to surface form.

Equations

• BhattTakahashi2011.isReductionStyleBresnan Bresnan1973.BresnanThanClauseAnalysis.partialDeletion = true
• BhattTakahashi2011.isReductionStyleBresnan Bresnan1973.BresnanThanClauseAnalysis.maximalDeletion = true

theorem BhattTakahashi2011.bt2011_agrees_with_bresnan_against_bp2004 : isReductionStyleBT englishAnalysisPerBhattTakahashi2011 = true ∧ isReductionStyleBresnan (Bresnan1973.bresnanAnalysisOf Semantics.Degree.ThanClause.ThanClauseType.phrasal) = true ∧ isReductionStyleBT englishAnalysisPerBhattPancheva2004 = false

Cross-tradition bridge: B&T 2011's verdict for English (RA) re-vindicates @cite{bresnan-1973}'s analysis of English phrasal comparatives (maximalDeletion) against @cite{bhatt-pancheva-2004}'s direct analysis. The agreement is at the level of analytic style — both posit a clausal source for surface phrasal "than NP", differing only in vocabulary.

def BhattTakahashi2011.englishHeadAvailability : Lechner2004.HeadAvailability

English (B&T §2): head-availability derived from the §2 binding data. RA is consistent with the data; DA is ruled out.

Equations

• BhattTakahashi2011.englishHeadAvailability = Lechner2004.headAvailabilityFromBinding BhattTakahashi2011.englishBindingPairs

def BhattTakahashi2011.hindiUrduHeadAvailability : Lechner2004.HeadAvailability

Hindi-Urdu (B&T §3): head-availability derived from the §3.4 binding data. DA is consistent with the data; RA is ruled out.

Equations

• BhattTakahashi2011.hindiUrduHeadAvailability = Lechner2004.headAvailabilityFromBinding BhattTakahashi2011.hindiUrduBindingPairs

theorem BhattTakahashi2011.english_head_availability_derived : englishHeadAvailability = { reductionRealized := true, directRealized := false }

Anti-stipulation witness for English: the derived head-availability is ⟨true, false⟩ (RA realized, DA not realized). The Bool values are computed from the data; this theorem just exposes them so downstream code can read them off.

theorem BhattTakahashi2011.hindi_urdu_head_availability_derived : hindiUrduHeadAvailability = { reductionRealized := false, directRealized := true }

Anti-stipulation witness for Hindi-Urdu: the derived head-availability is ⟨false, true⟩ (RA ruled out, DA realized).

def BhattTakahashi2011.japaneseHeadAvailability : Lechner2004.HeadAvailability

Japanese (B&T §5): both analyses realized. UNVERIFIED-AS-DERIVED: B&T's §5 argument that Japanese realizes RA rests on multiple-standard data and yori's subcategorization for CPs; those diagnostics require infrastructure not present in this file. The DA-realization side could in principle be derived from Japanese binding data parallel to Hindi-Urdu's, but B&T do not give the relevant minimal pairs in the cited form. So Japanese is stipulated, with an explicit note that the derivation is owed.

Equations

• BhattTakahashi2011.japaneseHeadAvailability = { reductionRealized := true, directRealized := true }

def BhattTakahashi2011.surveyedLanguages : List (String × Lechner2004.HeadAvailability)

B&T's surveyed languages, in citation order. The list is the unit of cross-linguistic generalization; per-pair distinctness theorems are derived over its elements.

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theorem BhattTakahashi2011.all_surveyed_languages_realize_some_analysis (p : String × Lechner2004.HeadAvailability) : p ∈ surveyedLanguages → p.2.reductionRealized = true ∨ p.2.directRealized = true

B&T (63a) restated as a surveyed-language fact: every surveyed language realizes at least one of the two analyses. (B&T's stronger universal claim — that no language lacks either underlying head — is not directly observable from binding data alone.)

theorem BhattTakahashi2011.surveyed_languages_pairwise_distinct : List.Pairwise (fun (a b : String × Lechner2004.HeadAvailability) => a.2 ≠ b.2) surveyedLanguages

B&T's central typological observation: the surveyed languages populate three of the four cells of the 2×2 RA-by-DA grid; no two are identical. The unattested cell is ⟨false, false⟩ — no language is reported to lack both analyses.