Longobardi (2001): A Unified Parametric Theory of Bare Nouns and Proper Names

@cite{longobardi-2001}

Natural Language Semantics 9: 335--369.

Core Thesis

Crosslinguistic variation in bare noun (BN) semantics and proper name (PN) syntax reduces to two DP-internal parameters: whether D has 'strong' referential features (strongD), and whether N-raising crosses adjectives transparently (transparentAlpha). The paper establishes:

1. Romance BNs are always indefinites — quantificational variables (existentially or generically bound), never kind-denoting constants.
2. English BNs are ambiguous — they can be referential (kind names, in the spirit of @cite{carlson-1977}) OR quantificational (indefinite variables, like Romance BNs).
3. Two types of genericity (supporting @cite{gerstner-krifka-1987}):
   • Indefinite/quantificational generics: variables bound by GEN
   • Definite/referential generics: kind-denoting constants (via D)
4. Typological generalization: PN syntax (N-to-D raising) and BN semantics (kind reference) are parametrically linked — object-referring nouns may occur without phonetically filled D iff kind-referring nouns can.

Connection to Existing Theory

Longobardi's ArgumentType distinction (referential vs quantificational) cross-cuts @cite{chierchia-1998}'s Nominal Mapping Parameter:

• Chierchia's NMP captures which denotation types are available
• Longobardi's parameters capture why the denotation types vary, grounding the variation in DP-internal syntax (N-to-D raising)

The DPParameter structure unifies Chierchia's three-way typology into a 2×2 parametric space that also predicts PN syntax.

inductive Longobardi2001.ArgumentType : Type

The semantic type of a nominal argument.

@cite{longobardi-2001} §2: All nominal arguments denote entities from Carlson's ontology (objects and kinds). They divide into two types:

• Referential: constants — denote directly through the lexical referring potential of the head noun. Proper names and kind names. Rigid designators with widest scope (@cite{kripke-1980}).
• Quantificational: variables — denote via a variable bound by a (possibly covert) operator, with the noun's kind-naming meaning serving as predicative restrictor. Overt indefinites and Romance BNs.

• referential : ArgumentType

  Constants: denote directly via lexical reference (proper names, kind names). No variable, no operator binding.

• quantificational : ArgumentType

  Variables: denote via a variable bound by Ex or Gen. The noun's kind-naming meaning provides the restrictor.

@[implicit_reducible]

instance Longobardi2001.instDecidableEqArgumentType : DecidableEq ArgumentType

Equations

• Longobardi2001.instDecidableEqArgumentType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Longobardi2001.instReprArgumentType : Repr ArgumentType

Equations

• Longobardi2001.instReprArgumentType = { reprPrec := Longobardi2001.instReprArgumentType.repr }

def Longobardi2001.instReprArgumentType.repr : ArgumentType → ℕ → Std.Format

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structure Longobardi2001.DPParameter : Type

The DP-internal parametric system from @cite{longobardi-2001} table (61).

Two binary parameters on the nominal projection:

• strongD: Whether D has 'strong' referential features requiring visible association with referential items. In Romance, D is strong: referential nouns must be introduced by a phonetically filled D (either by N-to-D raising for PNs or by an expletive article). In English/Germanic, D is weak: referential readings are available without overt D.

• transparentAlpha: Whether the α constituent (between D and N) is transparent to N-raising. In Romance, α is transparent: N can raise across adjectives to D. In English/Germanic, α is opaque: N cannot raise past adjectives. This is visible from adjective position: Romance has postnominal adjectives (N raises past them), English has prenominal adjectives (N stays in situ).

Note: transparentAlpha affects only DP-internal syntax (adjective position, N-raising), not BN semantics directly. BN semantics is determined by strongD alone. The two parameters are independent but co-vary in the unmarked cases (Romance: both +; English: both −). Greek (§9.5) shows they can be set independently (+strong, −transparent).

• strongD : Bool

  D has strong referential features (Romance +, English −)

• transparentAlpha : Bool

  α is transparent to N-raising (Romance +, English −)

def Longobardi2001.instDecidableEqDPParameter.decEq (x✝ x✝¹ : DPParameter) : Decidable (x✝ = x✝¹)

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@[implicit_reducible]

instance Longobardi2001.instDecidableEqDPParameter : DecidableEq DPParameter

Equations

• Longobardi2001.instDecidableEqDPParameter = Longobardi2001.instDecidableEqDPParameter.decEq

@[implicit_reducible]

instance Longobardi2001.instReprDPParameter : Repr DPParameter

Equations

• Longobardi2001.instReprDPParameter = { reprPrec := Longobardi2001.instReprDPParameter.repr }

def Longobardi2001.instReprDPParameter.repr : DPParameter → ℕ → Std.Format

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def Longobardi2001.romance : DPParameter

Romance (Italian, French, Spanish): strong D, transparent α.

Equations

• Longobardi2001.romance = { strongD := true, transparentAlpha := true }

def Longobardi2001.english : DPParameter

English (Germanic): weak D, opaque α.

Equations

• Longobardi2001.english = { strongD := false, transparentAlpha := false }

def Longobardi2001.greek : DPParameter

Greek: strong D, opaque α — the intermediate case. BNs pattern like Romance (quantificational only). PNs require overt definite article (cannot raise to D through opaque α, and D is strong so must be overtly filled).

Equations

• Longobardi2001.greek = { strongD := true, transparentAlpha := false }

def Longobardi2001.celtic : DPParameter

Celtic (speculative): weak D, transparent α — the other intermediate. @cite{longobardi-2001} fn. 35: "The other intermediate pair of values ('weak' D and transparent α) is likely to be instantiated by Celtic languages and is irrelevant to the present reasoning." Included for completeness of the 2×2 table; not empirically developed in the paper.

Equations

• Longobardi2001.celtic = { strongD := false, transparentAlpha := true }

def Longobardi2001.bnCanBeReferential (dp : DPParameter) : Bool

Whether bare nouns can be referential (kind-denoting constants) in a given language's parametric setting.

@cite{longobardi-2001} (44): English BNs can be referential (kind names) because D is weak — referential status doesn't require overt D. Romance BNs are always quantificational because D is strong — referential status requires overt D (only definite plurals achieve it).

The derivation: BN referentiality requires that a kind-naming meaning can reach D without overt material. With weak D, no overt association needed. With strong D, the noun would need to raise to D (N-to-D) or an expletive article is needed — but BNs by definition lack both.

Note: this depends only on strongD, not transparentAlpha. The α parameter affects whether N can raise to D (relevant for PNs), but BN referentiality is about whether D requires overt filling at all.

Equations

• Longobardi2001.bnCanBeReferential dp = !dp.strongD

def Longobardi2001.bnAlwaysQuantificational (dp : DPParameter) : Bool

Whether bare nouns are always quantificational (indefinites).

Equations

• Longobardi2001.bnAlwaysQuantificational dp = dp.strongD

def Longobardi2001.bnArgumentTypes (dp : DPParameter) : List ArgumentType

Available argument types for BNs in a language.

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inductive Longobardi2001.GenericType : Type

Generic reading type, following @cite{gerstner-krifka-1987} as adopted by @cite{longobardi-2001}.

The paper shows that 'genericity' is an epiphenomenon covering two structurally distinct interpretive strategies.

• indefiniteGeneric : GenericType

  Quantificational generalization over objects of a kind. The nominal is an indefinite (variable) bound by GEN. Available in characterizing environments only. Romance BNs, overt indefinites (both Romance and English).

• definiteGeneric : GenericType

  Kind denotation — the nominal is a referential expression (a kind name, like a proper name). Available in all environments. Only through overtly definite DPs in Romance (definite generics), or through bare plurals in English (which can be kind names).

@[implicit_reducible]

instance Longobardi2001.instDecidableEqGenericType : DecidableEq GenericType

Equations

• Longobardi2001.instDecidableEqGenericType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Longobardi2001.instReprGenericType : Repr GenericType

Equations

• Longobardi2001.instReprGenericType = { reprPrec := Longobardi2001.instReprGenericType.repr }

def Longobardi2001.instReprGenericType.repr : GenericType → ℕ → Std.Format

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def Longobardi2001.bnGenericTypes (dp : DPParameter) : List GenericType

Which generic types are available for bare nouns in a language.

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def Longobardi2001.pnRequiresOvertD (dp : DPParameter) : Bool

Whether proper names require overt D (an article or N-to-D raising).

@cite{longobardi-2001} (52): In some languages (Romance), argument PNs must undergo N-to-D raising or appear with an expletive article. In others (English), they need neither.

This is derived from strongD: if D must be overtly associated with referential items, PNs (prototypical referential items) need overt D. If D is weak, PNs can occur bare.

Equations

• Longobardi2001.pnRequiresOvertD dp = dp.strongD

def Longobardi2001.pnRequiresArticle (dp : DPParameter) : Bool

Whether proper names require an overt article specifically (as opposed to satisfying strong D by N-to-D raising).

@cite{longobardi-2001} §9.5: In Romance (strong D, transparent α), PNs can satisfy strong D by N-raising across the transparent α constituent. In Greek (strong D, opaque α), N cannot raise past α, so PNs MUST appear with an overt definite article. This is the paper's key prediction confirmed by (65): all Greek object-referring arguments require an overt determiner.

This is the only prediction that uses transparentAlpha directly, making the 2×2 parametric table genuinely non-redundant.

Equations

• Longobardi2001.pnRequiresArticle dp = (dp.strongD && !dp.transparentAlpha)

theorem Longobardi2001.pn_article_romance_vs_greek : pnRequiresArticle romance = false ∧ pnRequiresArticle greek = true ∧ pnRequiresArticle english = false ∧ pnRequiresArticle celtic = false

Romance PNs can N-raise to D (transparent α), so they don't need an article. Greek PNs cannot raise (opaque α), so they do.

theorem Longobardi2001.typological_generalization (dp : DPParameter) : (!pnRequiresOvertD dp) = bnCanBeReferential dp

Typological generalization (56) from @cite{longobardi-2001}: Object-referring nouns may occur without a phonetically filled D iff kind-referring nouns may.

Both PN syntax (bare PNs allowed?) and BN semantics (kind reference without overt D?) are controlled by the same parameter: strongD. When D is weak, both bare PNs and referential BNs are licensed. When D is strong, neither is.

inductive Longobardi2001.NominalClass : Type

The four nominal types considered by @cite{longobardi-2001}.

The paper's key empirical observation (p.355, table) is that three of these four pattern identically (as quantificational indefinites), while English BNs are the outlier — they can also be referential.

| Romance overt indef | Romance BN | ← same (quantificational) | English overt indef | English BN | ← English BN is different

• romanceOvertIndef : NominalClass
• romanceBN : NominalClass
• englishOvertIndef : NominalClass
• englishBN : NominalClass

@[implicit_reducible]

instance Longobardi2001.instDecidableEqNominalClass : DecidableEq NominalClass

Equations

• Longobardi2001.instDecidableEqNominalClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Longobardi2001.instReprNominalClass : Repr NominalClass

Equations

• Longobardi2001.instReprNominalClass = { reprPrec := Longobardi2001.instReprNominalClass.repr }

def Longobardi2001.instReprNominalClass.repr : NominalClass → ℕ → Std.Format

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def Longobardi2001.nominalClassReferential : NominalClass → Bool

Whether a nominal class can be referential (kind-denoting).

@cite{longobardi-2001} (5): Three of four nominal types are purely quantificational. Only English BNs have the additional referential (kind-denoting) reading.

Equations

• Longobardi2001.nominalClassReferential Longobardi2001.NominalClass.romanceOvertIndef = false
• Longobardi2001.nominalClassReferential Longobardi2001.NominalClass.romanceBN = false
• Longobardi2001.nominalClassReferential Longobardi2001.NominalClass.englishOvertIndef = false
• Longobardi2001.nominalClassReferential Longobardi2001.NominalClass.englishBN = true

theorem Longobardi2001.gen5a_romance_bn_eq_indef : nominalClassReferential NominalClass.romanceBN = nominalClassReferential NominalClass.romanceOvertIndef

Generalization (5a): Italian BNs = Italian overt indefinites in distribution of Ex/Gen readings.

theorem Longobardi2001.gen5b_romance_bn_ne_english_bn : nominalClassReferential NominalClass.romanceBN ≠ nominalClassReferential NominalClass.englishBN

Generalization (5b): Italian BNs ≠ English BNs.

theorem Longobardi2001.natural_class : ([NominalClass.romanceOvertIndef, NominalClass.romanceBN, NominalClass.englishOvertIndef].all fun (nc : NominalClass) => !nominalClassReferential nc) = true ∧ nominalClassReferential NominalClass.englishBN = true

The natural class: three of four types are quantificational only. English BNs are the outlier.

structure Longobardi2001.ItalianBNDatum : Type

Italian BN reading datum.

@cite{longobardi-2001} §3--7: Italian BNs distribute their readings identically to overt indefinites (generalization (5a)).

• sentence : String
• gloss : String
• exOK : Bool

  Available readings: Ex, Gen, or both

• genOK : Bool
• kLevelPred : Bool

  Kind-level predicate (K-level)?

• notes : String

@[implicit_reducible]

instance Longobardi2001.instReprItalianBNDatum : Repr ItalianBNDatum

Equations

• Longobardi2001.instReprItalianBNDatum = { reprPrec := Longobardi2001.instReprItalianBNDatum.repr }

def Longobardi2001.instReprItalianBNDatum.repr : ItalianBNDatum → ℕ → Std.Format

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def Longobardi2001.elephantsEpisodic : ItalianBNDatum

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def Longobardi2001.elephantsHabitual : ItalianBNDatum

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def Longobardi2001.elephantsAdverb : ItalianBNDatum

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def Longobardi2001.watchdogsEfficient : ItalianBNDatum

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def Longobardi2001.statesProsperous : ItalianBNDatum

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def Longobardi2001.watchdogsHairy : ItalianBNDatum

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def Longobardi2001.elephantsExtinct : ItalianBNDatum

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def Longobardi2001.elephantsGrowLarger : ItalianBNDatum

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def Longobardi2001.excludedOldLadies : ItalianBNDatum

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def Longobardi2001.loveOranges : ItalianBNDatum

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def Longobardi2001.italianBNData : List ItalianBNDatum

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structure Longobardi2001.ItalianDefGenericDatum : Type

Italian definite generics can appear in ALL environments where Italian BNs cannot — including with K-level predicates and in episodic contexts with generic readings. @cite{longobardi-2001} examples (34)--(37).

• sentence : String
• gloss : String
• genOK : Bool
• notes : String

@[implicit_reducible]

instance Longobardi2001.instReprItalianDefGenericDatum : Repr ItalianDefGenericDatum

Equations

• Longobardi2001.instReprItalianDefGenericDatum = { reprPrec := Longobardi2001.instReprItalianDefGenericDatum.repr }

def Longobardi2001.instReprItalianDefGenericDatum.repr : ItalianDefGenericDatum → ℕ → Std.Format

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def Longobardi2001.defElephantsCuriosity : ItalianDefGenericDatum

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def Longobardi2001.defElephantsExtinct : ItalianDefGenericDatum

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def Longobardi2001.defElephantsGrow : ItalianDefGenericDatum

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def Longobardi2001.defElephantsSoCalled : ItalianDefGenericDatum

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def Longobardi2001.italianDefGenericData : List ItalianDefGenericDatum

Equations

• Longobardi2001.italianDefGenericData = [Longobardi2001.defElephantsCuriosity, Longobardi2001.defElephantsExtinct, Longobardi2001.defElephantsGrow, Longobardi2001.defElephantsSoCalled]

structure Longobardi2001.AnaphoricBindingDatum : Type

@cite{longobardi-2001} §5: The anaphoric binding test distinguishes referential from quantificational BNs.

English (22): "Cats think very highly of themselves." → Ambiguous: 'themselves' refers to the species (kind anaphora, non-distributive) OR to each individual cat (distributive).

Italian (24): "Gatti di grandi dimensioni hanno un'alta opinione di se stessi." → Distributive only: each big cat thinks highly of itself. The species reading is unavailable because Italian BNs cannot denote kinds (quantificational variables lack kind reference).

The kind-anaphora reading requires referential (kind-denoting) status. Only English BNs, which can be referential, provide it.

• sentence : String
• gloss : String
• language : String
• speciesReadingOK : Bool

  Species (kind anaphora, non-distributive) reading available?

• distributiveReadingOK : Bool

  Distributive (each individual) reading available?

• notes : String

def Longobardi2001.instReprAnaphoricBindingDatum.repr : AnaphoricBindingDatum → ℕ → Std.Format

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@[implicit_reducible]

instance Longobardi2001.instReprAnaphoricBindingDatum : Repr AnaphoricBindingDatum

Equations

• Longobardi2001.instReprAnaphoricBindingDatum = { reprPrec := Longobardi2001.instReprAnaphoricBindingDatum.repr }

def Longobardi2001.englishCatsThemselves : AnaphoricBindingDatum

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def Longobardi2001.italianCatsThemselves : AnaphoricBindingDatum

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def Longobardi2001.anaphoricData : List AnaphoricBindingDatum

Equations

• Longobardi2001.anaphoricData = [Longobardi2001.englishCatsThemselves, Longobardi2001.italianCatsThemselves]

theorem Longobardi2001.anaphoric_binding_from_referentiality : bnCanBeReferential english = true ∧ englishCatsThemselves.speciesReadingOK = true ∧ bnCanBeReferential romance = false ∧ italianCatsThemselves.speciesReadingOK = false

The anaphoric binding test aligns with bnCanBeReferential: kind anaphora requires referential status.

structure Longobardi2001.ContrastDatum : Type

@cite{longobardi-2001} §§4,9.1: English BNs can be generic with predicates where Italian BNs cannot — episodic S-level, K-level, and stative I-level predicates. The contrast arises because English BNs can be referential (kind names), while Italian BNs cannot. The six contrast environments are summarized in §9.3.

• predType : String
• italianBNgeneric : Bool
• englishBNgeneric : Bool
• notes : String

@[implicit_reducible]

instance Longobardi2001.instReprContrastDatum : Repr ContrastDatum

Equations

• Longobardi2001.instReprContrastDatum = { reprPrec := Longobardi2001.instReprContrastDatum.repr }

def Longobardi2001.instReprContrastDatum.repr : ContrastDatum → ℕ → Std.Format

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def Longobardi2001.contrastEpisodic : ContrastDatum

Equations

• Longobardi2001.contrastEpisodic = { predType := "episodic S-level", italianBNgeneric := false, englishBNgeneric := true, notes := "Italian Ex only; English Ex/Gen" }

def Longobardi2001.contrastKLevel : ContrastDatum

Equations

• Longobardi2001.contrastKLevel = { predType := "K-level", italianBNgeneric := false, englishBNgeneric := true, notes := "Italian *; English Gen (kind name)" }

def Longobardi2001.contrastStativeILevel : ContrastDatum

Equations

• Longobardi2001.contrastStativeILevel = { predType := "stative (class B) I-level", italianBNgeneric := false, englishBNgeneric := true, notes := "Italian ?; English Gen" }

def Longobardi2001.contrastHabitualSLevel : ContrastDatum

Equations

• Longobardi2001.contrastHabitualSLevel = { predType := "habitual S-level", italianBNgeneric := true, englishBNgeneric := true, notes := "Both: Gen available (characterizing environment)" }

def Longobardi2001.contrastData : List ContrastDatum

Equations

• Longobardi2001.contrastData = [Longobardi2001.contrastEpisodic, Longobardi2001.contrastKLevel, Longobardi2001.contrastStativeILevel, Longobardi2001.contrastHabitualSLevel]

structure Longobardi2001.GreekDatum : Type

@cite{longobardi-2001} §9.5: Greek has strong D + opaque α. This predicts:

• BNs are quantificational only (like Romance) → no K-level predicates
• PNs require overt definite article (strong D + opaque α blocks both N-raising and bare referential D)

Greek examples (62)-(65) confirm both predictions.

• sentence : String
• gloss : String
• grammatical : Bool

  Is the sentence grammatical (under any reading)?

• kindReadingOK : Bool

  Is a kind/generic reading available?

• notes : String

@[implicit_reducible]

instance Longobardi2001.instReprGreekDatum : Repr GreekDatum

Equations

• Longobardi2001.instReprGreekDatum = { reprPrec := Longobardi2001.instReprGreekDatum.repr }

def Longobardi2001.instReprGreekDatum.repr : GreekDatum → ℕ → Std.Format

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def Longobardi2001.greekBNExtinct : GreekDatum

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def Longobardi2001.greekBNEpisodic : GreekDatum

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def Longobardi2001.greekDefPlExtinct : GreekDatum

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def Longobardi2001.greekPNRequiresArticle : GreekDatum

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def Longobardi2001.greekData : List GreekDatum

Equations

• Longobardi2001.greekData = [Longobardi2001.greekBNExtinct, Longobardi2001.greekBNEpisodic, Longobardi2001.greekDefPlExtinct, Longobardi2001.greekPNRequiresArticle]

theorem Longobardi2001.greek_confirms_strong_d : bnCanBeReferential greek = false ∧ pnRequiresOvertD greek = true ∧ bnCanBeReferential greek = bnCanBeReferential romance

Greek confirms the strongD prediction: BN kind reference is blocked, and PNs require overt D — same as Romance for both.

def Longobardi2001.toNominalMapping (dp : DPParameter) : Semantics.Kinds.NMP.NominalMapping

Map Longobardi's DPParameter to Chierchia's NominalMapping.

Only strongD determines the mapping; transparentAlpha is irrelevant because it controls DP-internal word order (adjective position), not the argument/predicate denotation types available to nouns.

• Strong D → nouns are predicates (need D for argumenthood) → predOnly
• Weak D → nouns can be arguments without D → argAndPred

argOnly (Chinese) is not addressed by Longobardi's parameters — it would require a separate parameter for classifier systems.

Equations

• Longobardi2001.toNominalMapping dp = if dp.strongD = true then Semantics.Kinds.NMP.NominalMapping.predOnly else Semantics.Kinds.NMP.NominalMapping.argAndPred

theorem Longobardi2001.romance_is_predOnly : toNominalMapping romance = Semantics.Kinds.NMP.NominalMapping.predOnly

Romance parameters yield Chierchia's predOnly.

theorem Longobardi2001.english_is_argAndPred : toNominalMapping english = Semantics.Kinds.NMP.NominalMapping.argAndPred

English parameters yield Chierchia's argAndPred.

theorem Longobardi2001.greek_is_predOnly : toNominalMapping greek = Semantics.Kinds.NMP.NominalMapping.predOnly

Greek parameters yield predOnly (same as Romance for BN semantics).

theorem Longobardi2001.english_bn_can_denote_kind : Semantics.Kinds.NMP.CanDenoteKind (toNominalMapping english) False

English BNs can denote kinds (without overt D). Derived: weak D → argAndPred → CanDenoteKind holds without D.

theorem Longobardi2001.italian_bn_cannot_denote_kind : ¬Semantics.Kinds.NMP.CanDenoteKind (toNominalMapping romance) False

Italian BNs cannot denote kinds (without overt D). Derived: strong D → predOnly → CanDenoteKind fails without D.

theorem Longobardi2001.italian_defpl_can_denote_kind : Semantics.Kinds.NMP.CanDenoteKind (toNominalMapping romance) True

Italian definite plurals can denote kinds (with overt D). Even in a predOnly language, overt D restores kind denotation.

theorem Longobardi2001.greek_bn_cannot_denote_kind : ¬Semantics.Kinds.NMP.CanDenoteKind (toNominalMapping greek) False

Greek BNs cannot denote kinds. Same as Romance: strong D → predOnly → no kind without D.

theorem Longobardi2001.english_bn_referential_is_carlson : ArgumentType.referential ∈ bnArgumentTypes english

@cite{longobardi-2001} (43) recovers @cite{carlson-1977}'s original insight: English generic BNs (outside characterizing environments) are kind-referential expressions — proper names of kinds.

Carlson analyzed ALL bare plural readings as kind-denoting. Longobardi refines this: English BNs are AMBIGUOUS between kind-referential (Carlson's analysis) and quantificational (like Romance BNs). The referential reading is the one that behaves like proper names — rigid, scopeless, opaque-only.

When a BN is referential, its semantics is @cite{carlson-1977}'s barePluralTranslation: λP.P{k}.

theorem Longobardi2001.romance_bn_never_referential : ArgumentType.referential ∉ bnArgumentTypes romance

Romance BNs are never referential — contra Carlson's universal claim but consistent with his observations about English specifically.

theorem Longobardi2001.referential_bn_semantics (Entity : Type) (k : Entity) (P : Entity → Bool) : Semantics.Kinds.SortedOntology.barePluralTranslation k P = P k

Referential BNs denote kinds via @cite{carlson-1977}'s λP.P{k}.

The bare plural "dogs" denotes the kind d; applying any predicate P just evaluates P at d — no quantificational structure. This is what makes referential BNs scopeless and opaque-only: proper names don't take scope.

theorem Longobardi2001.kind_level_via_carlson (Entity : Type) (k : Entity) (P : Entity → Bool) : Semantics.Kinds.SortedOntology.genericDerivation k P = P k

Kind-level predicates apply directly to a referential BN via @cite{carlson-1977}'s genericDerivation. This is why English BNs (which can be referential) appear with kind-level predicates ("Dogs are extinct") while Italian BNs (always quantificational) cannot.

theorem Longobardi2001.existential_via_carlson (Entity : Type) (R : Semantics.Kinds.SortedOntology.RealizationRel Entity) (k : Entity) (P : Entity → Bool) : Semantics.Kinds.SortedOntology.existentialDerivation R k P = Semantics.Kinds.SortedOntology.stageLevelPred Entity R P k

Existential readings of referential BNs arise via @cite{carlson-1977}'s existentialDerivation: the predicate introduces ∃ over stages, not the NP.

"Dogs are in the yard" = ∃y[R(y,d) ∧ in-yard'(y)]

The existential is part of the predicate semantics, which is why it always takes narrowest scope.

theorem Longobardi2001.romance_matches_italian_fragment : toNominalMapping romance = Fragments.Italian.Nouns.italianMapping

Longobardi's romance parameters correctly predict the Italian fragment's independently-declared mapping parameter.

theorem Longobardi2001.english_matches_english_fragment : toNominalMapping english = Fragments.English.Nouns.englishMapping

Longobardi's english parameters correctly predict the English fragment's independently-declared mapping parameter.

theorem Longobardi2001.greek_matches_greek_fragment : toNominalMapping greek = Fragments.Greek.StandardModern.Nouns.greekMapping

Longobardi's greek parameters correctly predict the Greek fragment's independently-declared mapping parameter.

theorem Longobardi2001.all_fragment_mappings : toNominalMapping romance = Fragments.Italian.Nouns.italianMapping ∧ toNominalMapping english = Fragments.English.Nouns.englishMapping ∧ toNominalMapping greek = Fragments.Greek.StandardModern.Nouns.greekMapping

All three fragment bridges together: DPParameter predicts the independently-stipulated NominalMapping in each fragment.

The derivation chain is:

DPParameter (Longobardi syntax) → toNominalMapping → NominalMapping

and each fragment independently declares the same NominalMapping, so the bridge theorems verify the prediction.

theorem Longobardi2001.italian_bare_restriction_from_strong_d : bnAlwaysQuantificational romance = true ∧ Fragments.Italian.Nouns.barePluralLicensed = false ∧ Fragments.Italian.Nouns.bareSingularLicensed = false

Longobardi's analysis explains WHY Italian bare plurals are not licensed: strong D means BNs are always quantificational variables, and these variables need licensing (characterizing environments for Gen, VP-internal position for Ex). General bare argument use is restricted because BNs cannot function as referential (kind) names.

theorem Longobardi2001.english_bare_plurals_licensed : bnCanBeReferential english = true ∧ Fragments.English.Nouns.barePluralLicensed = true

English bare plurals are licensed (weak D allows referential BNs).

theorem Longobardi2001.greek_bare_restriction_from_strong_d : bnAlwaysQuantificational greek = true ∧ Fragments.Greek.StandardModern.Nouns.barePluralLicensed = false

Greek bare plurals are not licensed (same as Italian: strong D).

theorem Longobardi2001.kind_reference_predictions : bnCanBeReferential english = true ∧ bnCanBeReferential romance = false ∧ Semantics.Kinds.NMP.CanDenoteKind (toNominalMapping romance) True

Longobardi's theory predicts the Italian vs English BP denotation data in KindReference.lean.

English BPs: kind denotation available (weak D → referential OK) Italian bare plurals: kind denotation unavailable (strong D) Italian definite plurals: kind denotation available (overt D fills D)

theorem Longobardi2001.parametric_table : bnCanBeReferential romance = false ∧ pnRequiresOvertD romance = true ∧ pnRequiresArticle romance = false ∧ bnCanBeReferential english = true ∧ pnRequiresOvertD english = false ∧ pnRequiresArticle english = false ∧ bnCanBeReferential greek = false ∧ pnRequiresOvertD greek = true ∧ pnRequiresArticle greek = true ∧ bnCanBeReferential celtic = true ∧ pnRequiresOvertD celtic = false ∧ pnRequiresArticle celtic = false

Full parametric table (61) from @cite{longobardi-2001} with derived properties.

Language	Strong D	Transp. α	BN ref.	PN needs D	PN needs art.
Romance	+	+	no	yes	no
English	−	−	yes	no	no
Greek	+	−	no	yes	yes
Celtic	−	+	yes	no	no

The "PN needs article" column is the only prediction that uses transparentAlpha directly, making the 2×2 table non-redundant.

theorem Longobardi2001.four_language_types : romance ≠ english ∧ romance ≠ greek ∧ romance ≠ celtic ∧ english ≠ greek ∧ english ≠ celtic ∧ greek ≠ celtic

The 2×2 table has four distinct parameter combinations.

inductive Longobardi2001.BNEnvironment : Type

@cite{longobardi-2001} (45)-(46): The two mapping systems.

English BNs have two sources of Ex/Gen ambiguity:

1. Referential → Gen (in all environments, kind-level)
2. Quantificational → Gen (characterizing) / Ex (S-level)

Romance BNs have only one source:

1. Quantificational → Gen (characterizing) / Ex (S-level)

• characterizing : BNEnvironment

  Characterizing: habitual aspect, Q-adverb, I-level pred

• episodic : BNEnvironment

  Episodic: S-level predicate with non-habitual aspect

• kindLevel : BNEnvironment

  Kind-level: predicate applies to kinds (extinct, widespread)

@[implicit_reducible]

instance Longobardi2001.instDecidableEqBNEnvironment : DecidableEq BNEnvironment

Equations

• Longobardi2001.instDecidableEqBNEnvironment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Longobardi2001.instReprBNEnvironment : Repr BNEnvironment

Equations

• Longobardi2001.instReprBNEnvironment = { reprPrec := Longobardi2001.instReprBNEnvironment.repr }

def Longobardi2001.instReprBNEnvironment.repr : BNEnvironment → ℕ → Std.Format

Equations

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

def Longobardi2001.bnGenericAvailable (dp : DPParameter) (env : BNEnvironment) : Bool

Whether a generic reading is available for a BN in a given environment.

Equations

• Longobardi2001.bnGenericAvailable dp Longobardi2001.BNEnvironment.characterizing = true
• Longobardi2001.bnGenericAvailable dp Longobardi2001.BNEnvironment.episodic = Longobardi2001.bnCanBeReferential dp
• Longobardi2001.bnGenericAvailable dp Longobardi2001.BNEnvironment.kindLevel = Longobardi2001.bnCanBeReferential dp

theorem Longobardi2001.english_bn_generic_everywhere (env : BNEnvironment) : bnGenericAvailable english env = true

English BNs are generic in all environments.

theorem Longobardi2001.romance_bn_generic_characterizing_only : bnGenericAvailable romance BNEnvironment.characterizing = true ∧ bnGenericAvailable romance BNEnvironment.episodic = false ∧ bnGenericAvailable romance BNEnvironment.kindLevel = false

Romance BNs are generic only in characterizing environments.

theorem Longobardi2001.contrast_environments (env : BNEnvironment) : bnGenericAvailable english env ≠ bnGenericAvailable romance env → env = BNEnvironment.episodic ∨ env = BNEnvironment.kindLevel

The environments where English and Italian BNs contrast are exactly those requiring referential (kind) denotation.

def Longobardi2001.predicateLevelToEnvironment : Semantics.Kinds.SortedOntology.PredicateLevel → BNEnvironment

Maps @cite{carlson-1977}'s PredicateLevel to Longobardi's BNEnvironment for the purpose of determining whether referential (kind) denotation is needed.

• Individual-level predicates (properties) create characterizing environments where quantificational Gen suffices
• Stage-level predicates (states) in episodic aspect create environments where only referential BNs get generic readings

Equations

• Longobardi2001.predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.individualLevel = Longobardi2001.BNEnvironment.characterizing
• Longobardi2001.predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.stageLevel = Longobardi2001.BNEnvironment.episodic

theorem Longobardi2001.ilp_yields_characterizing : predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.individualLevel = BNEnvironment.characterizing

Individual-level predicates yield characterizing environments where both English and Italian BNs get generic readings.

theorem Longobardi2001.slp_episodic_needs_referential : bnGenericAvailable english (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.stageLevel) = true ∧ bnGenericAvailable romance (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.stageLevel) = false

Stage-level predicates in episodic aspect yield environments where only referential BNs (English) get generic readings. Italian BNs are stuck with the existential reading.

theorem Longobardi2001.carlson_longobardi_integration : bnGenericAvailable english (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.individualLevel) = true ∧ bnGenericAvailable romance (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.individualLevel) = true ∧ bnGenericAvailable english (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.stageLevel) = true ∧ bnGenericAvailable romance (predicateLevelToEnvironment Semantics.Kinds.SortedOntology.PredicateLevel.stageLevel) = false

The full chain: @cite{carlson-1977}'s PredicateLevel determines BNEnvironment, which together with @cite{longobardi-2001}'s DPParameter determines whether a generic reading is available.

PredicateLevel	Environment	English BN Gen	Italian BN Gen
individualLevel	characterizing	yes	yes
stageLevel	episodic	yes	no
(kind-level pred)	kindLevel	yes	no

The Italian/English contrast arises only in non-characterizing environments — exactly where @cite{carlson-1977}'s referential kind-denotation is needed.