Italian Noun Lexicon Fragment

Italian NP structure with gender. Bare arguments restricted (@cite{chierchia-1998} [-arg, +pred]). Italian is the star witness for Chierchia's predOnly parameter: nouns denote predicates and require a determiner to be argumental.

Determiner System

@cite{chierchia-1998}

Italian has a richer article paradigm than French, with allomorphy conditioned by gender, number, and phonological context:

• Definite: il/lo/la (sg), i/gli/le (pl)
• Indefinite: un/uno/una (sg only)
• Partitive: del/dello/della (sg mass), dei/degli/delle (pl)

The partitive articles (di + definite article) serve as the obligatory indefinite plural — Italian has no bare plural arguments.

inductive Fragments.Italian.Nouns.Gender : Type

Grammatical gender (Italian has no neuter).

• masc : Gender
• fem : Gender

instance Fragments.Italian.Nouns.instDecidableEqGender : DecidableEq Gender

Equations

• Fragments.Italian.Nouns.instDecidableEqGender x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Fragments.Italian.Nouns.instReprGender : Repr Gender

Equations

• Fragments.Italian.Nouns.instReprGender = { reprPrec := Fragments.Italian.Nouns.instReprGender.repr }

def Fragments.Italian.Nouns.instReprGender.repr : Gender → ℕ → Std.Format

Equations

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def Fragments.Italian.Nouns.instBEqGender.beq : Gender → Gender → Bool

Equations

• Fragments.Italian.Nouns.instBEqGender.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Italian.Nouns.instBEqGender : BEq Gender

Equations

• Fragments.Italian.Nouns.instBEqGender = { beq := Fragments.Italian.Nouns.instBEqGender.beq }

structure Fragments.Italian.Nouns.NounEntry : Type

A lexical entry for an Italian noun.

• formSg : String

  Singular form

• formPl : Option String

  Plural form

• gender : Gender

  Grammatical gender

• countable : Bool

  Is this a count noun?

• proper : Bool

  Is this a proper name?

def Fragments.Italian.Nouns.instReprNounEntry.repr : NounEntry → ℕ → Std.Format

Equations

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instance Fragments.Italian.Nouns.instReprNounEntry : Repr NounEntry

Equations

• Fragments.Italian.Nouns.instReprNounEntry = { reprPrec := Fragments.Italian.Nouns.instReprNounEntry.repr }

instance Fragments.Italian.Nouns.instBEqNounEntry : BEq NounEntry

Equations

• Fragments.Italian.Nouns.instBEqNounEntry = { beq := Fragments.Italian.Nouns.instBEqNounEntry.beq }

def Fragments.Italian.Nouns.instBEqNounEntry.beq : NounEntry → NounEntry → Bool

Equations

• One or more equations did not get rendered due to their size.
• Fragments.Italian.Nouns.instBEqNounEntry.beq x✝¹ x✝ = false

def Fragments.Italian.Nouns.italianMapping : Semantics.Lexical.Noun.Kind.Chierchia1998.NominalMapping

Italian is a [-arg, +pred] language.

Equations

• Fragments.Italian.Nouns.italianMapping = Semantics.Lexical.Noun.Kind.Chierchia1998.NominalMapping.predOnly

def Fragments.Italian.Nouns.italianBlocking : Semantics.Lexical.Noun.Kind.Chierchia1998.BlockingPrinciple

Italian has a rich article system that blocks most bare arguments.

Equations

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inductive Fragments.Italian.Nouns.Determiner : Type

Italian determiners (articles).

• il : Determiner
• lo : Determiner
• la : Determiner
• i : Determiner
• gli : Determiner
• le : Determiner
• un : Determiner
• uno : Determiner
• una : Determiner
• del : Determiner
• dello : Determiner
• della : Determiner
• dei : Determiner
• degli : Determiner
• delle : Determiner

instance Fragments.Italian.Nouns.instDecidableEqDeterminer : DecidableEq Determiner

Equations

• Fragments.Italian.Nouns.instDecidableEqDeterminer x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Italian.Nouns.instReprDeterminer.repr : Determiner → ℕ → Std.Format

Equations

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instance Fragments.Italian.Nouns.instReprDeterminer : Repr Determiner

Equations

• Fragments.Italian.Nouns.instReprDeterminer = { reprPrec := Fragments.Italian.Nouns.instReprDeterminer.repr }

instance Fragments.Italian.Nouns.instBEqDeterminer : BEq Determiner

Equations

• Fragments.Italian.Nouns.instBEqDeterminer = { beq := Fragments.Italian.Nouns.instBEqDeterminer.beq }

def Fragments.Italian.Nouns.instBEqDeterminer.beq : Determiner → Determiner → Bool

Equations

• Fragments.Italian.Nouns.instBEqDeterminer.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

structure Fragments.Italian.Nouns.NP : Type

Italian NP structure. Italian NPs require determiners in argument positions.

• noun : NounEntry

  The underlying noun

• number : Number

  Number

• isBare : Bool

  Is this a bare NP (no determiner)?

• determiner : Option Determiner

  The determiner (if not bare)

def Fragments.Italian.Nouns.instReprNP.repr : NP → ℕ → Std.Format

Equations

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instance Fragments.Italian.Nouns.instReprNP : Repr NP

Equations

• Fragments.Italian.Nouns.instReprNP = { reprPrec := Fragments.Italian.Nouns.instReprNP.repr }

def Fragments.Italian.Nouns.instBEqNP.beq : NP → NP → Bool

Equations

• One or more equations did not get rendered due to their size.
• Fragments.Italian.Nouns.instBEqNP.beq x✝¹ x✝ = false

instance Fragments.Italian.Nouns.instBEqNP : BEq NP

Equations

• Fragments.Italian.Nouns.instBEqNP = { beq := Fragments.Italian.Nouns.instBEqNP.beq }

def Fragments.Italian.Nouns.defNP (n : NounEntry) (num : Number := Number.sg) : NP

Create a definite NP (il/lo/la/i/gli/le). Uses il for masculine singular and la for feminine singular (the lo/gli allomorphs are phonologically conditioned and not modeled here).

Equations

• Fragments.Italian.Nouns.defNP n UD.Number.Sing = { noun := n, number := UD.Number.Sing, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.il }
• Fragments.Italian.Nouns.defNP n UD.Number.Sing = { noun := n, number := UD.Number.Sing, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.la }
• Fragments.Italian.Nouns.defNP n UD.Number.Plur = { noun := n, number := UD.Number.Plur, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.i }
• Fragments.Italian.Nouns.defNP n UD.Number.Plur = { noun := n, number := UD.Number.Plur, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.le }
• Fragments.Italian.Nouns.defNP n num✝ = { noun := n, number := num✝, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.i }
• Fragments.Italian.Nouns.defNP n num✝ = { noun := n, number := num✝, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.le }

def Fragments.Italian.Nouns.indefNP (n : NounEntry) : NP

Create an indefinite singular NP (un/una).

Equations

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def Fragments.Italian.Nouns.partNP (n : NounEntry) (num : Number := Number.sg) : NP

Create a partitive NP (del/della for mass, dei/delle for plural).

Equations

• Fragments.Italian.Nouns.partNP n UD.Number.Sing = { noun := n, number := UD.Number.Sing, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.del }
• Fragments.Italian.Nouns.partNP n UD.Number.Sing = { noun := n, number := UD.Number.Sing, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.della }
• Fragments.Italian.Nouns.partNP n UD.Number.Plur = { noun := n, number := UD.Number.Plur, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.dei }
• Fragments.Italian.Nouns.partNP n UD.Number.Plur = { noun := n, number := UD.Number.Plur, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.delle }
• Fragments.Italian.Nouns.partNP n num✝ = { noun := n, number := num✝, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.dei }
• Fragments.Italian.Nouns.partNP n num✝ = { noun := n, number := num✝, isBare := false, determiner := some Fragments.Italian.Nouns.Determiner.delle }

def Fragments.Italian.Nouns.bareNP (n : NounEntry) (num : Number := Number.sg) : NP

Create a bare NP (restricted in Italian).

Equations

• Fragments.Italian.Nouns.bareNP n num = { noun := n, number := num, isBare := true }

def Fragments.Italian.Nouns.libro : NounEntry

Equations

• Fragments.Italian.Nouns.libro = { formSg := "libro", formPl := some "libri", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.ragazzo : NounEntry

Equations

• Fragments.Italian.Nouns.ragazzo = { formSg := "ragazzo", formPl := some "ragazzi", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.uomo : NounEntry

Equations

• Fragments.Italian.Nouns.uomo = { formSg := "uomo", formPl := some "uomini", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.gatto : NounEntry

Equations

• Fragments.Italian.Nouns.gatto = { formSg := "gatto", formPl := some "gatti", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.cane : NounEntry

Equations

• Fragments.Italian.Nouns.cane = { formSg := "cane", formPl := some "cani", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.tavolo : NounEntry

Equations

• Fragments.Italian.Nouns.tavolo = { formSg := "tavolo", formPl := some "tavoli", gender := Fragments.Italian.Nouns.Gender.masc }

def Fragments.Italian.Nouns.ragazza : NounEntry

Equations

• Fragments.Italian.Nouns.ragazza = { formSg := "ragazza", formPl := some "ragazze", gender := Fragments.Italian.Nouns.Gender.fem }

def Fragments.Italian.Nouns.donna : NounEntry

Equations

• Fragments.Italian.Nouns.donna = { formSg := "donna", formPl := some "donne", gender := Fragments.Italian.Nouns.Gender.fem }

def Fragments.Italian.Nouns.casa : NounEntry

Equations

• Fragments.Italian.Nouns.casa = { formSg := "casa", formPl := some "case", gender := Fragments.Italian.Nouns.Gender.fem }

def Fragments.Italian.Nouns.acqua : NounEntry

Equations

• Fragments.Italian.Nouns.acqua = { formSg := "acqua", gender := Fragments.Italian.Nouns.Gender.fem, countable := false }

def Fragments.Italian.Nouns.vino : NounEntry

Equations

• Fragments.Italian.Nouns.vino = { formSg := "vino", gender := Fragments.Italian.Nouns.Gender.masc, countable := false }

def Fragments.Italian.Nouns.pane : NounEntry

Equations

• Fragments.Italian.Nouns.pane = { formSg := "pane", gender := Fragments.Italian.Nouns.Gender.masc, countable := false }

def Fragments.Italian.Nouns.latte : NounEntry

Equations

• Fragments.Italian.Nouns.latte = { formSg := "latte", gender := Fragments.Italian.Nouns.Gender.masc, countable := false }

def Fragments.Italian.Nouns.paolo : NounEntry

Equations

• Fragments.Italian.Nouns.paolo = { formSg := "Paolo", gender := Fragments.Italian.Nouns.Gender.masc, proper := true }

def Fragments.Italian.Nouns.maria : NounEntry

Equations

• Fragments.Italian.Nouns.maria = { formSg := "Maria", gender := Fragments.Italian.Nouns.Gender.fem, proper := true }

def Fragments.Italian.Nouns.allNouns : List NounEntry

Equations

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

def Fragments.Italian.Nouns.lookup (form : String) : Option NounEntry

Equations

• Fragments.Italian.Nouns.lookup form = List.find? (fun (n : Fragments.Italian.Nouns.NounEntry) => n.formSg == form || n.formPl == some form) Fragments.Italian.Nouns.allNouns

def Fragments.Italian.Nouns.barePluralLicensed : Bool

In Italian, bare plurals are NOT generally licensed.

Equations

• Fragments.Italian.Nouns.barePluralLicensed = false

def Fragments.Italian.Nouns.bareSingularLicensed : Bool

In Italian, bare singulars are NOT licensed.

Equations

• Fragments.Italian.Nouns.bareSingularLicensed = false

theorem Fragments.Italian.Nouns.definitePluralDenotesKind : Semantics.Lexical.Noun.Kind.Chierchia1998.canDenoteKind italianMapping true = true

Italian definite plurals denote kinds: derived from predOnly + overt D. Because Italian is [-arg, +pred], D is required for argumenthood. With D present, the noun maps to a kind via ∩.

theorem Fragments.Italian.Nouns.barePluralCannotDenoteKind : Semantics.Lexical.Noun.Kind.Chierchia1998.canDenoteKind italianMapping false = false

Italian bare plurals cannot denote kinds: derived from predOnly + no D. Without D, Italian nouns remain predicates. No covert ∩ is available.

theorem Fragments.Italian.Nouns.barePluralDenotesProperty : Semantics.Lexical.Noun.Kind.Chierchia1998.canDenoteProperty italianMapping = true

Italian bare plurals denote properties: derived from predOnly. All [+pred] languages allow property denotation for nouns.

def Fragments.Italian.Nouns.ilLibro : NP

"il libro" (the book)

Equations

• Fragments.Italian.Nouns.ilLibro = Fragments.Italian.Nouns.defNP Fragments.Italian.Nouns.libro

def Fragments.Italian.Nouns.laRagazza : NP

"la ragazza" (the girl)

Equations

• Fragments.Italian.Nouns.laRagazza = Fragments.Italian.Nouns.defNP Fragments.Italian.Nouns.ragazza

def Fragments.Italian.Nouns.unGatto : NP

"un gatto" (a cat)

Equations

• Fragments.Italian.Nouns.unGatto = Fragments.Italian.Nouns.indefNP Fragments.Italian.Nouns.gatto

def Fragments.Italian.Nouns.delVino : NP

"del vino" (some wine, partitive)

Equations

• Fragments.Italian.Nouns.delVino = Fragments.Italian.Nouns.partNP Fragments.Italian.Nouns.vino

def Fragments.Italian.Nouns.deiLibri : NP

"dei libri" (some books, partitive plural)

Equations

• Fragments.Italian.Nouns.deiLibri = Fragments.Italian.Nouns.partNP Fragments.Italian.Nouns.libro Number.pl