Phenomena.Copulas.Studies.Stassen2013

@cite{stassen-2013} @cite{hengeveld-1992} @cite{pustet-2003}

Cross-linguistic copula and predication analysis anchored on @cite{stassen-2013}'s four WALS chapters (117 predicative possession, 118 predicative adjectives, 119 nominal-vs-locational predication, 120 zero copula). The 20-language CopulaProfile sample tests the cross- chapter implications Stassen draws (e.g. nonverbal nominal predication correlates with zero copula availability) plus areal patterns (Western European cluster, East Asian verbal-adjective cluster, Semitic restricted-zero pattern).

Stassen's central observation

Predication is not uniform across predicate types: many languages use fundamentally different strategies for adjectival ("The book is red"), nominal ("She is a doctor"), and locational ("The cat is on the mat") predication. The copula, where it exists, is best understood as a family of strategies deployed differently across predicate types, not a single phenomenon.

Contents

• §1. The 20-language CopulaProfile sample (5 IE, 2 Semitic, 2 East Asian, etc.).
• §2. Sample-level distribution counts.
• §3. Sample-grounded cross-chapter generalisations: Stassen's implication (nonverbal noun → zero copula), copula-required-tends-identical, verbal-adj-tends-nomloc-split.
• §4. Areal-cluster theorems (Western European, East Asian, Semitic).
• §5. CopulaType distribution.

Out of scope

The substrate types (PredAdjStrategy, CopulaProfile, WALS converters, corpus-only theorems) live in Linglib/Typology/Copulas.lean. Partee's compositional BE type-shift bridge to copula typology is in Phenomena/Copulas/Studies/Partee1987.lean.

def Phenomena.Copulas.Studies.Stassen2013.english : Typology.Copulas.CopulaProfile

English (Indo-European, Germanic). Adjectives non-verbal (require be), nominal predication uses verbal copula be, same copula for nominal and locational, no zero copula.

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def Phenomena.Copulas.Studies.Stassen2013.french : Typology.Copulas.CopulaProfile

French (Indo-European, Romance). Le livre est rouge; Elle est medecin.

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def Phenomena.Copulas.Studies.Stassen2013.german : Typology.Copulas.CopulaProfile

German (Indo-European, Germanic). Das Buch ist rot; Sie ist Arztin.

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def Phenomena.Copulas.Studies.Stassen2013.spanish : Typology.Copulas.CopulaProfile

Spanish (Indo-European, Romance). DIFFERENT copulas: ser (nominal/ permanent) vs estar (locational/temporary).

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def Phenomena.Copulas.Studies.Stassen2013.russian : Typology.Copulas.CopulaProfile

Russian (Indo-European, Slavic). Zero copula in present (Ona vrach); byt' in past. RESTRICTED zero: present only.

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def Phenomena.Copulas.Studies.Stassen2013.arabic : Typology.Copulas.CopulaProfile

Arabic (Standard) (Afro-Asiatic, Semitic). Present-tense zero copula (hiya tabiba); kaana for past.

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def Phenomena.Copulas.Studies.Stassen2013.hebrew : Typology.Copulas.CopulaProfile

Hebrew (Afro-Asiatic, Semitic). Pronominal copula hu/hi/hem/hen in present; haya for past.

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def Phenomena.Copulas.Studies.Stassen2013.hungarian : Typology.Copulas.CopulaProfile

Hungarian (Uralic). Zero copula in 3rd person present (O orvos), van in other persons/tenses.

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def Phenomena.Copulas.Studies.Stassen2013.japanese : Typology.Copulas.CopulaProfile

Japanese (Japonic). MIXED adjectives (i-adjectives verbal, na-adjectives need da); nominal predication uses da/desu.

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def Phenomena.Copulas.Studies.Stassen2013.korean : Typology.Copulas.CopulaProfile

Korean (Koreanic). Verbal adjectives (ppalgah-da); nominal predication via copula -i-da.

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def Phenomena.Copulas.Studies.Stassen2013.mandarin : Typology.Copulas.CopulaProfile

Mandarin Chinese (Sino-Tibetan). Verbal adjectives (shu hong); nominal predication via shi; locational via zai.

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def Phenomena.Copulas.Studies.Stassen2013.turkish : Typology.Copulas.CopulaProfile

Turkish (Turkic). Verbal adjectives; copular suffix -dIr for nominals (often dropped in 3rd person present).

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def Phenomena.Copulas.Studies.Stassen2013.swahili : Typology.Copulas.CopulaProfile

Swahili (Niger-Congo, Bantu). Particle ni for affirmative nominal predication; widespread zero copula in many contexts.

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def Phenomena.Copulas.Studies.Stassen2013.hindiUrdu : Typology.Copulas.CopulaProfile

Hindi-Urdu (Indo-European, Indo-Aryan). Copula hona for both nominal and locational; no zero copula.

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def Phenomena.Copulas.Studies.Stassen2013.tagalog : Typology.Copulas.CopulaProfile

Tagalog (Austronesian). Widespread zero copula (doktor siya); ay is a topic marker, not a true copula.

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def Phenomena.Copulas.Studies.Stassen2013.irish : Typology.Copulas.CopulaProfile

Irish (Indo-European, Celtic). Two copulas: is (nominal/identity) vs ta (attributive/locational) — classic split.

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def Phenomena.Copulas.Studies.Stassen2013.finnish : Typology.Copulas.CopulaProfile

Finnish (Uralic). Copula olla for all predication types; no zero copula.

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def Phenomena.Copulas.Studies.Stassen2013.quechua : Typology.Copulas.CopulaProfile

Quechua (Quechuan). Copular suffixes -mi/-n; ka- in past/future.

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def Phenomena.Copulas.Studies.Stassen2013.yoruba : Typology.Copulas.CopulaProfile

Yoruba (Niger-Congo, Atlantic-Congo). Verbal adjectives; widespread zero copula for nominal predication.

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def Phenomena.Copulas.Studies.Stassen2013.thai : Typology.Copulas.CopulaProfile

Thai (Tai-Kadai). Verbal adjectives; verbal copula pen for nominals; yuu for locational.

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def Phenomena.Copulas.Studies.Stassen2013.allLanguages : List Typology.Copulas.CopulaProfile

The 20-language sample.

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def Phenomena.Copulas.Studies.Stassen2013.countBy (langs : List Typology.Copulas.CopulaProfile) (pred : Typology.Copulas.CopulaProfile → Bool) : Nat

Count of languages in a list matching a predicate.

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• Phenomena.Copulas.Studies.Stassen2013.countBy langs pred = (List.filter pred langs).length

theorem Phenomena.Copulas.Studies.Stassen2013.sample_size : allLanguages.length = 20

theorem Phenomena.Copulas.Studies.Stassen2013.sample_verbal_adj_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.hasVerbalAdj) = 7

theorem Phenomena.Copulas.Studies.Stassen2013.sample_mixed_adj_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.predAdj == Typology.Copulas.PredAdjStrategy.mixed) = 1

theorem Phenomena.Copulas.Studies.Stassen2013.sample_nonverbal_adj_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.predAdj == Typology.Copulas.PredAdjStrategy.nonVerbal) = 12

theorem Phenomena.Copulas.Studies.Stassen2013.sample_verbal_noun_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.hasVerbalNounCopula) = 11

theorem Phenomena.Copulas.Studies.Stassen2013.sample_nonverbal_noun_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.predNoun == Typology.Copulas.PredNounStrategy.nonVerbal) = 9

theorem Phenomena.Copulas.Studies.Stassen2013.sample_nomloc_different_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.hasNomLocSplit) = 11

theorem Phenomena.Copulas.Studies.Stassen2013.sample_nomloc_identical_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.nomLoc == Typology.Copulas.NomLocStrategy.identical) = 9

theorem Phenomena.Copulas.Studies.Stassen2013.sample_zero_impossible_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.alwaysRequiresCopula) = 11

theorem Phenomena.Copulas.Studies.Stassen2013.sample_zero_restricted_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.zeroCopula == Typology.Copulas.ZeroCopulaStatus.restricted) = 6

theorem Phenomena.Copulas.Studies.Stassen2013.sample_zero_widespread_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.zeroCopula == Typology.Copulas.ZeroCopulaStatus.widespread) = 3

theorem Phenomena.Copulas.Studies.Stassen2013.stassen_implication_noun_zero : (allLanguages.all fun (p : Typology.Copulas.CopulaProfile) => if (p.predNoun == Typology.Copulas.PredNounStrategy.nonVerbal) = true then p.allowsZeroCopula else true) = true

@cite{stassen-2013}'s implicational universal in the sample: if a language has non-verbal nominal predication, it allows some form of zero copula. Holds without exception in this sample.

theorem Phenomena.Copulas.Studies.Stassen2013.no_zero_implies_verbal_noun : (allLanguages.all fun (p : Typology.Copulas.CopulaProfile) => if (p.zeroCopula == Typology.Copulas.ZeroCopulaStatus.impossible) = true then p.predNoun == Typology.Copulas.PredNounStrategy.verbal else true) = true

Contrapositive of Stassen's implication: if zero copula is impossible, the language uses verbal nominal predication.

theorem Phenomena.Copulas.Studies.Stassen2013.widespread_zero_implies_nonverbal_noun : ((List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.zeroCopula == Typology.Copulas.ZeroCopulaStatus.widespread) allLanguages).all fun (x : Typology.Copulas.CopulaProfile) => x.predNoun == Typology.Copulas.PredNounStrategy.nonVerbal) = true

Cross-chapter: in the sample, languages with widespread zero copula always use non-verbal nominal predication (logically expected: if zero copula is the norm, predication IS non-verbal).

theorem Phenomena.Copulas.Studies.Stassen2013.mixed_adj_implies_verbal_noun : ((List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.predAdj == Typology.Copulas.PredAdjStrategy.mixed) allLanguages).all fun (x : Typology.Copulas.CopulaProfile) => x.predNoun == Typology.Copulas.PredNounStrategy.verbal) = true

In the sample, no language has mixed adjectives AND non-verbal noun predication. Mixed-adjective languages use verbal nominal copulas.

theorem Phenomena.Copulas.Studies.Stassen2013.verbal_adj_nonverbal_noun : (List.filter (fun (p : Typology.Copulas.CopulaProfile) => p.predAdj == Typology.Copulas.PredAdjStrategy.verbal && p.predNoun == Typology.Copulas.PredNounStrategy.nonVerbal) allLanguages).length ≥ 3

Languages with verbal adjectives often pair with non-verbal nouns (the verbal-adjective strategy eliminates the need for a copula with adjectives but does not provide a copula for nouns).

theorem Phenomena.Copulas.Studies.Stassen2013.restricted_zero_has_copula_forms : ((List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.zeroCopula == Typology.Copulas.ZeroCopulaStatus.restricted) allLanguages).all fun (x : Typology.Copulas.CopulaProfile) => decide (x.copulaForms.length > 0)) = true

Languages with restricted zero copula in the sample all have overt past-tense copula forms (Russian, Arabic, Hungarian, Turkish).

theorem Phenomena.Copulas.Studies.Stassen2013.verbal_adj_tends_nomloc_split : have verbalAdj := List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.hasVerbalAdj) allLanguages; have splitNomLoc := List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.hasNomLocSplit) verbalAdj; splitNomLoc.length > verbalAdj.length / 2

Languages with verbal adjectives tend to split nominal and locational predication. Most verbal-adjective sample languages have different nom-loc strategies.

theorem Phenomena.Copulas.Studies.Stassen2013.copula_required_tends_identical : have required := List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.alwaysRequiresCopula) allLanguages; have identical := List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.nomLoc == Typology.Copulas.NomLocStrategy.identical) required; identical.length ≥ required.length / 2

Languages where the copula is always required tend to use the same copula for nominal and locational predication.

def Phenomena.Copulas.Studies.Stassen2013.hasSplitPredication (p : Typology.Copulas.CopulaProfile) : Bool

A split predication language uses different strategies for at least two of: adjectival, nominal, and locational predication.

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theorem Phenomena.Copulas.Studies.Stassen2013.split_predication_common : countBy allLanguages hasSplitPredication ≥ 12

theorem Phenomena.Copulas.Studies.Stassen2013.spanish_irish_clear_split : spanish.hasNomLocSplit = true ∧ irish.hasNomLocSplit = true

Spanish and Irish exemplify the clearest nom-loc splits: both have two distinct copulas that partition predicate types.

theorem Phenomena.Copulas.Studies.Stassen2013.mandarin_three_way_split : (mandarin.predAdj == Typology.Copulas.PredAdjStrategy.verbal) = true ∧ (mandarin.predNoun == Typology.Copulas.PredNounStrategy.verbal) = true ∧ (mandarin.nomLoc == Typology.Copulas.NomLocStrategy.different) = true

Mandarin exemplifies a three-way split: adjectives are verbal (no copula), nouns require shi, locations use zai.

theorem Phenomena.Copulas.Studies.Stassen2013.nomloc_split_languages_have_distinct_forms : ((List.filter (fun (x : Typology.Copulas.CopulaProfile) => x.hasNomLocSplit) allLanguages).all fun (x : Typology.Copulas.CopulaProfile) => decide (x.copulaForms.length ≥ 1)) = true

Languages that split nominal and locational predication have at least one copula form recorded in the profile.

def Phenomena.Copulas.Studies.Stassen2013.westernEuropean : List Typology.Copulas.CopulaProfile

Western European languages (English, French, German) share a common profile: non-verbal adjectives, verbal nominal copula, no zero copula. The "Standard Average European" pattern.

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theorem Phenomena.Copulas.Studies.Stassen2013.western_european_nonverbal_adj : (westernEuropean.all fun (x : Typology.Copulas.CopulaProfile) => x.predAdj == Typology.Copulas.PredAdjStrategy.nonVerbal) = true

theorem Phenomena.Copulas.Studies.Stassen2013.western_european_verbal_noun : (westernEuropean.all fun (x : Typology.Copulas.CopulaProfile) => x.predNoun == Typology.Copulas.PredNounStrategy.verbal) = true

theorem Phenomena.Copulas.Studies.Stassen2013.western_european_no_zero : (westernEuropean.all fun (x : Typology.Copulas.CopulaProfile) => x.alwaysRequiresCopula) = true

def Phenomena.Copulas.Studies.Stassen2013.eastAsian : List Typology.Copulas.CopulaProfile

East and Southeast Asian languages all have verbal or mixed adjectives.

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theorem Phenomena.Copulas.Studies.Stassen2013.east_asian_verbal_or_mixed_adj : (eastAsian.all fun (p : Typology.Copulas.CopulaProfile) => p.predAdj == Typology.Copulas.PredAdjStrategy.verbal || p.predAdj == Typology.Copulas.PredAdjStrategy.mixed) = true

theorem Phenomena.Copulas.Studies.Stassen2013.east_asian_nomloc_split : (eastAsian.all fun (x : Typology.Copulas.CopulaProfile) => x.hasNomLocSplit) = true

def Phenomena.Copulas.Studies.Stassen2013.semitic : List Typology.Copulas.CopulaProfile

Semitic languages (Arabic, Hebrew) share a profile: non-verbal adjectives, non-verbal nominal predication, restricted zero copula (present tense only).

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• Phenomena.Copulas.Studies.Stassen2013.semitic = [Phenomena.Copulas.Studies.Stassen2013.arabic, Phenomena.Copulas.Studies.Stassen2013.hebrew]

theorem Phenomena.Copulas.Studies.Stassen2013.semitic_nonverbal_adj : (semitic.all fun (x : Typology.Copulas.CopulaProfile) => x.predAdj == Typology.Copulas.PredAdjStrategy.nonVerbal) = true

theorem Phenomena.Copulas.Studies.Stassen2013.semitic_nonverbal_noun : (semitic.all fun (x : Typology.Copulas.CopulaProfile) => x.predNoun == Typology.Copulas.PredNounStrategy.nonVerbal) = true

theorem Phenomena.Copulas.Studies.Stassen2013.semitic_restricted_zero : (semitic.all fun (x : Typology.Copulas.CopulaProfile) => x.zeroCopula == Typology.Copulas.ZeroCopulaStatus.restricted) = true

theorem Phenomena.Copulas.Studies.Stassen2013.sample_verbal_copula_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.verbalCopula) = 11

theorem Phenomena.Copulas.Studies.Stassen2013.sample_zero_copula_type_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.zero) = 4

theorem Phenomena.Copulas.Studies.Stassen2013.sample_particle_copula_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.particle) = 4

theorem Phenomena.Copulas.Studies.Stassen2013.sample_pronominal_copula_count : (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.pronominalCopula) = 1

theorem Phenomena.Copulas.Studies.Stassen2013.verbal_copula_most_common : ((countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.verbalCopula) > countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.particle) ∧ ((countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.verbalCopula) > countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.zero) ∧ (countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.verbalCopula) > countBy allLanguages fun (x : Typology.Copulas.CopulaProfile) => x.copulaType == Typology.Copulas.CopulaType.pronominalCopula

Verbal copulas are the most common copula type in the sample.