Partee (1987): Type-Shifting and the Copula

@cite{partee-1987}

Partee's §5 argues that English be subcategorizes for an e argument and an ⟨e,t⟩ argument, meaning "apply predicate." The BE type-shifting functor applies to the post-copular NP to convert its GQ meaning (⟨⟨e,t⟩,t⟩) into a predicative one (⟨e,t⟩):

BE = λQ.λx. Q(λy. y = x) : ⟨⟨e,t⟩,t⟩ → ⟨e,t⟩

The copula's combined effect is thus BE(⟦NP⟧)(⟦subject⟧). "John is a teacher" composes as BE(⟦a teacher⟧)(⟦John⟧) = teacher'(john').

This connects compositional semantics (Theory) to cross-linguistic copula typology (Data): languages vary in whether BE is lexicalized (verbal copula), covert (zero copula), or expressed through other strategies.

Predictions

• Zero copula possible → BE available as a covert type-shift.
• Verbal adjectives → adjectives are already type ⟨e,t⟩ (predicates), so no BE needed for adjectival predication.
• Nom/loc split → different predication types lexicalize different type-shifting operations.

@[reducible, inline]

abbrev Phenomena.Copulas.Studies.Partee1987.be_sem (m : Semantics.Montague.Model) : m.interpTy Semantics.Montague.Ty.ett → m.interpTy Semantics.Montague.Ty.et

⟦be⟧ = BE (Partee §5): the copula IS the type-shifting functor. Takes a GQ (⟨⟨e,t⟩,t⟩) and returns a predicate (⟨e,t⟩).

Equations

• Phenomena.Copulas.Studies.Partee1987.be_sem m = Semantics.Composition.TypeShifting.BE

theorem Phenomena.Copulas.Studies.Partee1987.be_transparent {m : Semantics.Montague.Model} (j : m.interpTy Semantics.Montague.Ty.e) : be_sem m (Semantics.Composition.TypeShifting.lift j) = Semantics.Composition.TypeShifting.ident j

The copula is semantically transparent for proper names. "John is a teacher" with ⟦John⟧ = lift(j): BE(lift(j)) = ident(j) = λx. [j = x].

def Phenomena.Copulas.Studies.Partee1987.requiresLexicalBE (p : Typology.CopulaProfile) : Bool

A language requires overt lexicalization of BE when zero copula is impossible for nominal predication.

Equations

• Phenomena.Copulas.Studies.Partee1987.requiresLexicalBE p = (p.zeroCopula == Phenomena.Copulas.Typology.ZeroCopulaStatus.impossible)

def Phenomena.Copulas.Studies.Partee1987.adjRequiresBE (p : Typology.CopulaProfile) : Bool

A language needs BE specifically for adjectival predication when adjectives are non-verbal (categorially distinct from verbs). If adjectives are verbal, they are already type ⟨e,t⟩ and can predicate directly via FA — no type-shift needed.

Equations

• Phenomena.Copulas.Studies.Partee1987.adjRequiresBE p = (p.predAdj == Phenomena.Copulas.Typology.PredAdjStrategy.nonVerbal)

def Phenomena.Copulas.Studies.Partee1987.beIsFullyCovert (p : Typology.CopulaProfile) : Bool

A language has fully covert access to BE when zero copula is widespread (not just restricted to certain tense/person contexts).

Equations

• Phenomena.Copulas.Studies.Partee1987.beIsFullyCovert p = (p.zeroCopula == Phenomena.Copulas.Typology.ZeroCopulaStatus.widespread)

theorem Phenomena.Copulas.Studies.Partee1987.english_requires_be : requiresLexicalBE Typology.english = true

theorem Phenomena.Copulas.Studies.Partee1987.english_adj_needs_be : adjRequiresBE Typology.english = true

theorem Phenomena.Copulas.Studies.Partee1987.mandarin_adj_no_be : adjRequiresBE Typology.mandarin = false

theorem Phenomena.Copulas.Studies.Partee1987.russian_partial_zero : requiresLexicalBE Typology.russian = false

theorem Phenomena.Copulas.Studies.Partee1987.russian_not_fully_covert : beIsFullyCovert Typology.russian = false

theorem Phenomena.Copulas.Studies.Partee1987.tagalog_fully_covert : beIsFullyCovert Typology.tagalog = true

theorem Phenomena.Copulas.Studies.Partee1987.arabic_partial_zero : requiresLexicalBE Typology.arabic = false

theorem Phenomena.Copulas.Studies.Partee1987.japanese_mixed_adj : adjRequiresBE Typology.japanese = false

theorem Phenomena.Copulas.Studies.Partee1987.korean_adj_no_be : adjRequiresBE Typology.korean = false

theorem Phenomena.Copulas.Studies.Partee1987.korean_nom_requires_be : requiresLexicalBE Typology.korean = true

theorem Phenomena.Copulas.Studies.Partee1987.spanish_nom_loc_split : (Typology.spanish.nomLoc == Typology.NomLocStrategy.different) = true

theorem Phenomena.Copulas.Studies.Partee1987.english_no_split : (Typology.english.nomLoc == Typology.NomLocStrategy.identical) = true

theorem Phenomena.Copulas.Studies.Partee1987.verbal_adj_implies_no_be : ((List.filter (fun (x : Typology.CopulaProfile) => x.predAdj == Typology.PredAdjStrategy.verbal) Typology.allLanguages).all fun (p : Typology.CopulaProfile) => !adjRequiresBE p) = true

Every language with verbal adjective encoding allows adjectival predication without BE — adjectives are already type ⟨e,t⟩.

Verbal adj. languages in sample: Mandarin, Korean, Turkish, Swahili, Tagalog, Yoruba, Thai.

theorem Phenomena.Copulas.Studies.Partee1987.zero_copula_implies_covert_be : ((List.filter (fun (x : Typology.CopulaProfile) => x.zeroCopula == Typology.ZeroCopulaStatus.widespread) Typology.allLanguages).all fun (p : Typology.CopulaProfile) => !requiresLexicalBE p) = true

Languages with widespread zero copula never require lexical BE — the type-shift is freely available without lexicalization.

Widespread zero-copula languages in sample: Swahili, Tagalog, Yoruba.

theorem Phenomena.Copulas.Studies.Partee1987.majority_nom_loc_different : (List.filter (fun (x : Typology.CopulaProfile) => x.nomLoc == Typology.NomLocStrategy.different) Typology.allLanguages).length > (List.filter (fun (x : Typology.CopulaProfile) => x.nomLoc == Typology.NomLocStrategy.identical) Typology.allLanguages).length

The majority of languages in the sample differentiate nominal and locational predication strategies. This supports the view that different predication types involve distinct type-shifting operations.