Napoli & Nespor (1976): Negatives in Comparatives

Italian non appears in some comparative clauses without truth-conditional effect: Maria è più intelligente di quanto non sia Carlo 'Maria is more intelligent than Carlo (is)'. Earlier accounts treated this non₂ as a pleonastic element ([AP71]) or as surface evidence that than-clauses are underlyingly negative ([Seu69]). [NN76] (Language 52(4), 811–838) reject both: non₂ is real negation, licensed by a discourse condition — the speaker presupposes that the assertion contradicts a prior belief, the move is assertive, the matrix is unnegated, and neither the contradicted belief nor the construction involves precise knowledge. The licensing predicate is formalized once as Pragmatics.Bias.BiasLicensingProfile.licenses; this file is its first historical attestation, applied to the paper's Italian data. The paper's own implementation — a Generative Semantics abstract higher clause hosting non₂, optionally deleted — is historical; only the licensing predicate and its surface diagnostics are preserved.

Main declarations

• Non2Datum, paradigm: the paper's acceptability paradigm — dialogue contexts, comparative environments, and indirect questions, each pairing a bias profile with the reported judgment for non₂;
• paradigm_licenses_iff_non2Ok: the licensing predicate reproduces every judgment in the paradigm;
• predictedMood, predictedSpecificity, complementizerAdmissible, cliticAdmissible, neancheConjunctionAdmissible, weakNPIAdmissible: morphosyntactic diagnostics for underlying negation.

The acceptability paradigm

The licensing conditions are established through an acceptability paradigm. Four dialogues between Dario and Paolo vary the speaker's epistemic state: non₂ is felicitous exactly when the assertion contradicts a belief inferred from the interlocutor's prior discourse. Construction-level environments then isolate the remaining conditions (equality and explicit-degree comparatives both fail the precision condition; meno-comparatives are the positive control), and indirect questions show the condition is a property of the discourse move, not of comparative syntax.

structure NapoliNespor1976.Non2Datum : Type

One row of the acceptability paradigm: a dialogue context or construction, its bias-licensing profile, and the reported acceptability of non₂.

• profile : Pragmatics.Bias.BiasLicensingProfile
• non2Ok : Bool

  Whether the paper reports non₂ as felicitous.

@[instance_reducible]

instance NapoliNespor1976.instReprNon2Datum : Repr Non2Datum

Equations

• NapoliNespor1976.instReprNon2Datum = { reprPrec := NapoliNespor1976.instReprNon2Datum.repr }

def NapoliNespor1976.instReprNon2Datum.repr : Non2Datum → ℕ → Std.Format

Equations

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

def NapoliNespor1976.noOpinionContext : Non2Datum

Dario gives no opinion of Maria or Carlo; Paolo asserts Maria > Carlo: no prior belief to contradict.

Equations

• NapoliNespor1976.noOpinionContext = { profile := Pragmatics.Bias.noContradictionProfile, non2Ok := false }

def NapoliNespor1976.chessContext : Non2Datum

Dario implies Carlo would beat Maria at chess; Paolo asserts Maria is more intelligent: the contradicted belief is inferred.

Equations

• NapoliNespor1976.chessContext = { profile := Pragmatics.Bias.licensedProfile, non2Ok := true }

def NapoliNespor1976.explicitCriticismContext : Non2Datum

Dario explicitly calls Maria stupid; Paolo disagrees: the contradicted belief is explicitly stated rather than inferred, failing the imprecise/inferred condition.

Equations

• NapoliNespor1976.explicitCriticismContext = { profile := Pragmatics.Bias.preciseProfile, non2Ok := false }

def NapoliNespor1976.complaintContext : Non2Datum

Dario's complaint implies he expects Maria cannot help; Paolo asserts she is smart enough to ask: the contradicted belief is inferred.

Equations

• NapoliNespor1976.complaintContext = { profile := Pragmatics.Bias.licensedProfile, non2Ok := true }

def NapoliNespor1976.questionedComparative : Non2Datum

È più intelligente di quanto non sia Carlo? 'Is she more intelligent than Carlo?': questioning is non-assertive.

Equations

• NapoliNespor1976.questionedComparative = { profile := Pragmatics.Bias.questionedProfile, non2Ok := false }

def NapoliNespor1976.matrixNegatedComparative : Non2Datum

Maria non è più intelligente di quanto non sia Carlo: the matrix is negated.

Equations

• NapoliNespor1976.matrixNegatedComparative = { profile := Pragmatics.Bias.matrixNegatedProfile, non2Ok := false }

def NapoliNespor1976.equalityComparative : Non2Datum

Equality comparatives (Maria è tanto intelligente quanto è Carlo) demand explicit, precise knowledge of the compared degrees, while non₂ demands inferred, imprecise knowledge.

Equations

• NapoliNespor1976.equalityComparative = { profile := Pragmatics.Bias.preciseProfile, non2Ok := false }

def NapoliNespor1976.precisionComparative : Non2Datum

Explicit degree modifiers (molto più intelligente, due metri più alta) require precise knowledge of the degree gap.

Equations

• NapoliNespor1976.precisionComparative = { profile := Pragmatics.Bias.preciseProfile, non2Ok := false }

def NapoliNespor1976.menoComparative : Non2Datum

Maria è meno intelligente di quanto tu non creda 'Maria is less intelligent than you think': meno-comparatives admit non₂ under the same contextual conditions as più. Negated equality comparatives are semantically close to meno-comparatives yet reject non₂, so the equality restriction cannot reduce to equality linking two similar things (contra [Seu69] and [AP71]); it follows from matrix negation and the precision condition.

Equations

• NapoliNespor1976.menoComparative = { profile := Pragmatics.Bias.licensedProfile, non2Ok := true }

def NapoliNespor1976.chissaSeNon : Non2Datum

Chissà se non vale la pena di comprarlo 'Who knows if it's (not) worth buying it': an indirect question whose negated proposition the speaker presupposes to be contrary to expectation, licensed by the same profile as the comparatives.

Equations

• NapoliNespor1976.chissaSeNon = { profile := Pragmatics.Bias.licensedProfile, non2Ok := true }

def NapoliNespor1976.paradigm : List Non2Datum

The paper's acceptability paradigm.

Equations

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

theorem NapoliNespor1976.paradigm_licenses_iff_non2Ok (d : Non2Datum) : d ∈ paradigm → (d.profile.licenses ↔ d.non2Ok = true)

The licensing predicate reproduces the paper's judgment on every row of the paradigm.

Morphosyntactic diagnostics for underlying negation

Six surface diagnostics witness underlying negation in the comparative clause. Two are forced choices — mood morphology and indefinite specificity. Four are admissibility asymmetries — complementizer che, predicative clitic lo, the weak NPI pur, and neanche-conjunction: the bias-marked alternant is possible only under licensed non₂, while the default (di quanto, clitic-less repetition) remains available throughout. The NPI diagnostics are derived from the Italian Fragment's licensingContexts registry.

inductive NapoliNespor1976.SpecificityProfile : Type

Specificity of indefinites embedded in the than-clause.

• unrestricted : SpecificityProfile

  Both [+specific] and [−specific] readings available.

• nonspecificOnly : SpecificityProfile

  Restricted to [−specific] under the scope of underlying negation.

@[instance_reducible]

instance NapoliNespor1976.instDecidableEqSpecificityProfile : DecidableEq SpecificityProfile

Equations

• NapoliNespor1976.instDecidableEqSpecificityProfile x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance NapoliNespor1976.instReprSpecificityProfile : Repr SpecificityProfile

Equations

• NapoliNespor1976.instReprSpecificityProfile = { reprPrec := NapoliNespor1976.instReprSpecificityProfile.repr }

def NapoliNespor1976.instReprSpecificityProfile.repr : SpecificityProfile → ℕ → Std.Format

Equations

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

inductive NapoliNespor1976.ComplementizerChoice : Type

The Italian comparative complementizers.

• diQuanto : ComplementizerChoice

  The default than-complementizer.

• che : ComplementizerChoice

  The alternant admissible only under non₂.

@[instance_reducible]

instance NapoliNespor1976.instDecidableEqComplementizerChoice : DecidableEq ComplementizerChoice

Equations

• NapoliNespor1976.instDecidableEqComplementizerChoice x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance NapoliNespor1976.instReprComplementizerChoice : Repr ComplementizerChoice

Equations

• NapoliNespor1976.instReprComplementizerChoice = { reprPrec := NapoliNespor1976.instReprComplementizerChoice.repr }

def NapoliNespor1976.instReprComplementizerChoice.repr : ComplementizerChoice → ℕ → Std.Format

Equations

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

inductive NapoliNespor1976.CliticPresence : Type

Presence of the predicative clitic lo substituting for a repeated predicate adjective in the than-clause.

• present : CliticPresence
• absent : CliticPresence

@[instance_reducible]

instance NapoliNespor1976.instDecidableEqCliticPresence : DecidableEq CliticPresence

Equations

• NapoliNespor1976.instDecidableEqCliticPresence x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def NapoliNespor1976.instReprCliticPresence.repr : CliticPresence → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance NapoliNespor1976.instReprCliticPresence : Repr CliticPresence

Equations

• NapoliNespor1976.instReprCliticPresence = { reprPrec := NapoliNespor1976.instReprCliticPresence.repr }

def NapoliNespor1976.predictedMood (p : Pragmatics.Bias.BiasLicensingProfile) : Mood.Grammatical

Mood of the than-clause: subjunctive exactly when non₂ is underlyingly present, indicative otherwise (lexical mood control by credere etc. is abstracted away). Surface subjunctive without non is derived by the paper's optional deletion of an underlying non₂.

Equations

• NapoliNespor1976.predictedMood p = if p.licenses then Mood.Grammatical.subjunctive else Mood.Grammatical.indicative

def NapoliNespor1976.predictedSpecificity (p : Pragmatics.Bias.BiasLicensingProfile) : SpecificityProfile

Embedded indefinites are restricted to [−specific] under licensed non₂ and unrestricted otherwise.

Equations

• NapoliNespor1976.predictedSpecificity p = if p.licenses then NapoliNespor1976.SpecificityProfile.nonspecificOnly else NapoliNespor1976.SpecificityProfile.unrestricted

def NapoliNespor1976.complementizerAdmissible (p : Pragmatics.Bias.BiasLicensingProfile) : ComplementizerChoice → Prop

Complementizer admissibility: di quanto occurs in comparatives with and without non₂; che only with it.

Equations

• NapoliNespor1976.complementizerAdmissible p NapoliNespor1976.ComplementizerChoice.diQuanto = True
• NapoliNespor1976.complementizerAdmissible p NapoliNespor1976.ComplementizerChoice.che = p.licenses

def NapoliNespor1976.cliticAdmissible (p : Pragmatics.Bias.BiasLicensingProfile) : CliticPresence → Prop

Clitic admissibility: clitic-less comparatives are always available; lo is possible only under non₂, and optional there.

Equations

• NapoliNespor1976.cliticAdmissible p NapoliNespor1976.CliticPresence.present = p.licenses
• NapoliNespor1976.cliticAdmissible p NapoliNespor1976.CliticPresence.absent = True

def NapoliNespor1976.neancheConjunctionAdmissible (p : Pragmatics.Bias.BiasLicensingProfile) : Prop

Neanche-conjunction ('and not even …') is admissible iff its host clause is negated at some underlying level — in a comparative, iff non₂ is licensed. The negation requirement is the Fragment registry fact that neanche lists .negation among its licensing contexts.

Equations

• NapoliNespor1976.neancheConjunctionAdmissible p = (p.licenses ∧ Polarity.LicensingContext.negation ∈ Italian.PolarityItems.neanche.licensingContexts)

theorem NapoliNespor1976.predictedMood_eq_subjunctive_iff (p : Pragmatics.Bias.BiasLicensingProfile) : predictedMood p = Mood.Grammatical.subjunctive ↔ p.licenses

The mood diagnostic tracks the licensing predicate: the than-clause is subjunctive exactly on licensed profiles.

theorem NapoliNespor1976.predictedSpecificity_eq_nonspecificOnly_iff (p : Pragmatics.Bias.BiasLicensingProfile) : predictedSpecificity p = SpecificityProfile.nonspecificOnly ↔ p.licenses

The specificity diagnostic tracks the licensing predicate.

theorem NapoliNespor1976.neanche_conjunction_with_non2 : neancheConjunctionAdmissible Pragmatics.Bias.licensedProfile

Neanche-conjunction is admissible under licensed non₂; the second conjunct is the Fragment's registry datum.

The pur / affatto contrast

The weak NPI pur is licensed in non₂-comparatives; the weak NPI affatto is blocked, because affatto requires precise knowledge of the contradicted belief — incompatible with the imprecise/inferred licensing condition (a footnote observation of [NN76]). The contrast is witnessed at the lexical layer: pur.licensingContexts lists the clausal-comparative slot .clausalComparative while affatto's does not, so the predictions below are derived from the Fragment registry.

def NapoliNespor1976.weakNPIAdmissible (p : Pragmatics.Bias.BiasLicensingProfile) (npi : Polarity.Item) : Prop

A weak NPI is admissible in a bias-conditioned comparative iff its registry lists the clausal-comparative slot (surface phrasal comparatives are not NPI environments) and the profile licenses non₂.

Equations

• NapoliNespor1976.weakNPIAdmissible p npi = (p.licenses ∧ Polarity.LicensingContext.clausalComparative ∈ npi.licensingContexts)

theorem NapoliNespor1976.pur_admissible_with_non2 : weakNPIAdmissible Pragmatics.Bias.licensedProfile Italian.PolarityItems.pur

Pur is admissible wherever non₂ is licensed; the registry conjunct is the Fragment's pur_licensed_in_comparative.

theorem NapoliNespor1976.affatto_blocked_in_non2 (p : Pragmatics.Bias.BiasLicensingProfile) : ¬weakNPIAdmissible p Italian.PolarityItems.affatto

Affatto is inadmissible in non₂-comparatives whatever the bias profile: the block is registered in the lexical entry itself.