Palmieri (2024): Lexical and Grammatical Reciprocity

This file formalizes the second chapter of [palmieri-2024], on lexical reciprocity in Romance. Against the language-level parameter of [siloni-2012], on which Romance forms its reciprocals in the syntax, verbs fall into three classes by the entries they carry: reciprocal intransitives with a lexical reciprocal entry only, plain transitives with a transitive entry only, and verbs like 'hug' with both, whose reciprocal reading requires se in most environments but emerges without it in language-specific ones, Brazilian Portuguese finite clauses, analytic causatives everywhere, and Spanish and Catalan absolute participials (VerbClass.formations, SeOmissible). The columns of Table 2.1 follow from the entries: a class combines with se iff it has a transitive entry and expresses reciprocity by itself iff it has a lexical one (table21, romance_not_monolithic). The readings follow too: with se the transitive entry contributes the grammatical reciprocal and reflexive readings and the lexical entry its pseudo-reciprocal reading, so a class-3 se-clause is three-ways ambiguous, and without se only the lexical entry contributes, so the grammatical readings disappear and the pseudo-reciprocal reading survives exactly for the classes with a lexical entry (grammatical_needs_se, pseudo_without_se_iff). A Romance lexical reciprocal is a verb with some construction in which a reciprocal interpretation emerges without se, the chapter's definition (44), which is having a lexical entry, in every language (lexicalReciprocalIn_iff). Grammatical reciprocity is plain in the sense of [winter-2018] for any relation, x and y kissed each other being x kissed y and y kissed x (50) (eachOther_plainReciprocity), whereas the collective predicate of a lexical entry is not so constrained, 'divorce' and 'kiss' failing one direction each (53), (54). The reciprocal 'with'-construction tracks the lexical entry, the generalization of [kemmer-1993], including non-symmetric members and the si-retaining Italian cases that refine the French-based restriction of [siloni-2012] (withConstruction_iff_lexical).

Implementation notes

The entries are primitive and the class tables derived. The per-language inventories of lexical reciprocals come from the Romance Fragments, and one theorem from the fourth chapter's Swahili data records that lexical reciprocity need not be derivational. The Swahili chapters and the questionnaires are not otherwise formalized.

References

• [palmieri-2024]
• [siloni-2012]
• [winter-2018]
• [kemmer-1993]

The verb classes and their entries (Table 2.1)

inductive Palmieri2024.VerbClass : Type

The three classes of Romance verbs: 'chat', with no transitive entry (31); 'describe', unambiguously transitive (32); and 'hug', transitive with a lexical reciprocal entry besides (34), (38), (40), (42).

• reciprocalIntransitive : VerbClass
• plainTransitive : VerbClass
• reciprocalTransitive : VerbClass

@[instance_reducible]

instance Palmieri2024.instDecidableEqVerbClass : DecidableEq VerbClass

Equations

• Palmieri2024.instDecidableEqVerbClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Palmieri2024.VerbClass.formations : VerbClass → List Reciprocal.Formation

The entries a class carries, the two-entry proposal: a lexical reciprocal entry, a transitive entry fed by the grammatical se strategy, or both.

Equations

• Palmieri2024.VerbClass.reciprocalIntransitive.formations = [Reciprocal.Formation.lexical]
• Palmieri2024.VerbClass.plainTransitive.formations = [Reciprocal.Formation.syntactic]
• Palmieri2024.VerbClass.reciprocalTransitive.formations = [Reciprocal.Formation.lexical, Reciprocal.Formation.syntactic]

def Palmieri2024.VerbClass.CombinesWithSe (c : VerbClass) : Prop

The first column of Table 2.1: a class combines with se iff it has a transitive entry.

Equations

• c.CombinesWithSe = (Reciprocal.Formation.syntactic ∈ c.formations)

def Palmieri2024.VerbClass.ReciprocityByItself (c : VerbClass) : Prop

The second column of Table 2.1: a class expresses reciprocity by itself iff it has a lexical entry.

Equations

• c.ReciprocityByItself = (Reciprocal.Formation.lexical ∈ c.formations)

@[instance_reducible]

instance Palmieri2024.instDecidablePredVerbClassCombinesWithSe : DecidablePred VerbClass.CombinesWithSe

Equations

• Palmieri2024.instDecidablePredVerbClassCombinesWithSe c = Palmieri2024.instDecidablePredVerbClassCombinesWithSe._aux_1 c

@[instance_reducible]

instance Palmieri2024.instDecidablePredVerbClassReciprocityByItself : DecidablePred VerbClass.ReciprocityByItself

Equations

• Palmieri2024.instDecidablePredVerbClassReciprocityByItself c = Palmieri2024.instDecidablePredVerbClassReciprocityByItself._aux_1 c

theorem Palmieri2024.table21 : (¬VerbClass.reciprocalIntransitive.CombinesWithSe ∧ VerbClass.reciprocalIntransitive.ReciprocityByItself) ∧ (VerbClass.plainTransitive.CombinesWithSe ∧ ¬VerbClass.plainTransitive.ReciprocityByItself) ∧ VerbClass.reciprocalTransitive.CombinesWithSe ∧ VerbClass.reciprocalTransitive.ReciprocityByItself

Table 2.1 as printed: the intransitives express reciprocity by themselves and reject se, the plain transitives the reverse, and the third class both.

theorem Palmieri2024.romance_not_monolithic : VerbClass.reciprocalTransitive.ReciprocityByItself ∧ Siloni2012.italian.formation = Reciprocal.Formation.syntactic

The divergence from [siloni-2012]: Italian carries lexical reciprocal entries, class 3 abbracciare 'hug' (40), though the language-level parameter classifies it as syntax-set.

theorem Palmieri2024.abbracciare_grounds_divergence : "abbracciare" ∈ List.map Verb.form Italian.Reciprocals.lexicalReciprocals

The witness grounded in the Italian Fragment: abbracciare carries a lexical reciprocal entry alongside its homophonous transitive alternate.

The se-less environments (Table 2.2)

inductive Palmieri2024.Language : Type

The four Romance languages of the chapter.

• brazilianPortuguese : Language
• italian : Language
• spanish : Language
• catalan : Language

@[instance_reducible]

instance Palmieri2024.instDecidableEqLanguage : DecidableEq Language

Equations

• Palmieri2024.instDecidableEqLanguage x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

inductive Palmieri2024.Environment : Type

The constructions in which a class-3 verb may express reciprocity without se (§3): finite clauses (34), analytic causatives (38), (40), and absolute participials (42).

• finiteClause : Environment
• analyticCausative : Environment
• absoluteParticipial : Environment

@[instance_reducible]

instance Palmieri2024.instDecidableEqEnvironment : DecidableEq Environment

Equations

• Palmieri2024.instDecidableEqEnvironment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Palmieri2024.SeOmissible : Language → Environment → Prop

Table 2.2: whether the language lets a class-3 verb receive a reciprocal interpretation without se in the environment.

Equations

• Palmieri2024.SeOmissible Palmieri2024.Language.brazilianPortuguese Palmieri2024.Environment.absoluteParticipial = False
• Palmieri2024.SeOmissible Palmieri2024.Language.brazilianPortuguese x✝ = True
• Palmieri2024.SeOmissible Palmieri2024.Language.italian Palmieri2024.Environment.analyticCausative = True
• Palmieri2024.SeOmissible Palmieri2024.Language.italian x✝ = False
• Palmieri2024.SeOmissible Palmieri2024.Language.spanish Palmieri2024.Environment.finiteClause = False
• Palmieri2024.SeOmissible Palmieri2024.Language.spanish x✝ = True
• Palmieri2024.SeOmissible Palmieri2024.Language.catalan Palmieri2024.Environment.finiteClause = False
• Palmieri2024.SeOmissible Palmieri2024.Language.catalan x✝ = True

@[instance_reducible]

instance Palmieri2024.instDecidableSeOmissible (l : Language) (e : Environment) : Decidable (SeOmissible l e)

Equations

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

theorem Palmieri2024.every_language_diagnosable (l : Language) : SeOmissible l Environment.analyticCausative

Analytic causatives are the pan-Romance diagnostic: every language omits se there.

def Palmieri2024.inventory : Language → List Verb

Per-language inventories of lexical reciprocals, from the Fragments.

Equations

• Palmieri2024.inventory Palmieri2024.Language.brazilianPortuguese = BrazilianPortuguese.Reciprocals.lexicalReciprocals
• Palmieri2024.inventory Palmieri2024.Language.italian = Italian.Reciprocals.lexicalReciprocals
• Palmieri2024.inventory Palmieri2024.Language.spanish = Spanish.Reciprocals.lexicalReciprocals
• Palmieri2024.inventory Palmieri2024.Language.catalan = Catalan.Reciprocals.lexicalReciprocals

Readings with and without se (§4.3)

inductive Palmieri2024.SeReading : Type

The readings of a plural-subject clause: the pseudo-reciprocal reading of a lexical entry, a single collective event, and the grammatical reciprocal and reflexive readings of a transitive entry under se.

• pseudoReciprocal : SeReading
• grammaticalReciprocal : SeReading
• grammaticalReflexive : SeReading

@[instance_reducible]

instance Palmieri2024.instDecidableEqSeReading : DecidableEq SeReading

Equations

• Palmieri2024.instDecidableEqSeReading x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Palmieri2024.Formation.readingsWithSe : Reciprocal.Formation → List SeReading

The readings an entry contributes under se: the lexical entry its pseudo-reciprocal reading, the transitive entry the two grammatical readings (55), (56a), (57a).

Equations

• Palmieri2024.Formation.readingsWithSe Reciprocal.Formation.lexical = [Palmieri2024.SeReading.pseudoReciprocal]
• Palmieri2024.Formation.readingsWithSe Reciprocal.Formation.syntactic = [Palmieri2024.SeReading.grammaticalReciprocal, Palmieri2024.SeReading.grammaticalReflexive]

def Palmieri2024.Formation.readingsWithoutSe : Reciprocal.Formation → List SeReading

The readings an entry contributes without se: only the lexical entry contributes (56b), (57b).

Equations

• Palmieri2024.Formation.readingsWithoutSe Reciprocal.Formation.lexical = [Palmieri2024.SeReading.pseudoReciprocal]
• Palmieri2024.Formation.readingsWithoutSe Reciprocal.Formation.syntactic = []

def Palmieri2024.VerbClass.readingsWithSe (c : VerbClass) : List SeReading

The readings of a se-clause of the class, when the class combines with se at all.

Equations

• c.readingsWithSe = if c.CombinesWithSe then List.flatMap Palmieri2024.Formation.readingsWithSe c.formations else []

def Palmieri2024.VerbClass.readingsWithoutSe (c : VerbClass) : List SeReading

The readings of a se-less clause of the class.

Equations

• c.readingsWithoutSe = List.flatMap Palmieri2024.Formation.readingsWithoutSe c.formations

theorem Palmieri2024.class3_three_ways : VerbClass.reciprocalTransitive.readingsWithSe = [SeReading.pseudoReciprocal, SeReading.grammaticalReciprocal, SeReading.grammaticalReflexive]

A class-3 se-clause is three-ways ambiguous (56a), (57a).

theorem Palmieri2024.grammatical_needs_se (c : VerbClass) : SeReading.grammaticalReciprocal ∉ c.readingsWithoutSe ∧ SeReading.grammaticalReflexive ∉ c.readingsWithoutSe

Without se no grammatical reading survives, for any class: the reflexive and the accumulated-events reciprocal readings need the grammatical strategy.

theorem Palmieri2024.pseudo_without_se_iff (c : VerbClass) : SeReading.pseudoReciprocal ∈ c.readingsWithoutSe ↔ c.ReciprocityByItself

The pseudo-reciprocal reading survives without se exactly for the classes with a lexical entry.

def Palmieri2024.LexicalReciprocalIn (l : Language) (c : VerbClass) : Prop

Definition (44): a class is a lexical reciprocal in a language iff some construction of that language lets a reciprocal interpretation emerge without se.

Equations

• Palmieri2024.LexicalReciprocalIn l c = ∃ (e : Palmieri2024.Environment), Palmieri2024.SeOmissible l e ∧ Palmieri2024.SeReading.pseudoReciprocal ∈ c.readingsWithoutSe

theorem Palmieri2024.lexicalReciprocalIn_iff (l : Language) (c : VerbClass) : LexicalReciprocalIn l c ↔ c.ReciprocityByItself

Lexical reciprocity in the sense of (44) is having a lexical entry, in every language.

Pseudo-reciprocity against plain reciprocity (§4.3)

def Palmieri2024.eachOther {A : Type u_1} (R : A → A → Prop) : Finset A → Prop

Grammatical reciprocity over a set of participants, each other: the relation holds between every two distinct members.

Equations

• Palmieri2024.eachOther R s = ∀ x ∈ s, ∀ y ∈ s, x ≠ y → R x y

theorem Palmieri2024.eachOther_plainReciprocity {A : Type u_1} [DecidableEq A] (R : A → A → Prop) : Winter2018.PlainReciprocity (eachOther R) R

(50): grammatical reciprocity is plain in the sense of [winter-2018] for every relation, symmetric or not: x and y kissed each other iff x kissed y and y kissed x.

theorem Palmieri2024.exists_collective_not_plain (R : Bool → Bool → Prop) : ∃ (P : Finset Bool → Prop), ¬Winter2018.PlainReciprocity P R

A lexical entry's collective predicate is not so constrained: for any relation some collective predicate fails plain reciprocity for it, the room in which 'divorce' fails the collective-to-unidirectional direction (53) and 'kiss' the converse (54).

The reciprocal 'with'-construction (§4.4)

def Palmieri2024.VerbClass.AllowsWithConstruction : VerbClass → Prop

Whether the class allows the reciprocal 'with'-construction, the observation of §4.4: both classes with a lexical entry do, including non-symmetric members, consultarsi con, lasciarsi con (59), and the attested baciarsi con, abbracciarsi con (60), and the plain transitives do not, ringraziarsi con (61). Italian retains si in the construction, unlike French.

Equations

• Palmieri2024.VerbClass.plainTransitive.AllowsWithConstruction = False
• x✝.AllowsWithConstruction = True

theorem Palmieri2024.withConstruction_iff_lexical (c : VerbClass) : c.AllowsWithConstruction ↔ c.ReciprocityByItself

The generalization of [kemmer-1993] over the class system: the 'with'-construction is available exactly where a lexical entry is.

Swahili (fourth chapter)

theorem Palmieri2024.jibizana_no_binary_base : "jibizana" ∈ List.map Verb.form Swahili.Reciprocals.lexicalReciprocals ∧ ∀ p ∈ Swahili.Reciprocals.derivedFrom, p.1.form ≠ "jibizana"

Swahili lexical reciprocals may lack a binary base altogether: jibizana 'discuss' is in the reciprocal inventory but in no derivational pair, so lexical reciprocity is not always derivational, the Bantu analogue of the Romance intransitive class.