Reciprocal constructions: morphosyntactic typology

Cross-linguistic vocabulary for reciprocal constructions: the reciprocal-reflexive formal relation (WALS Ch 106, [MN13]), the marking strategy ([Nor23]'s synthesis of [KK06], [Ned07a], and [Eva08]), the valency effect, and the formation locus of reciprocal verbs ([Sil08], [Sil12]).

The exponence primitive is the marker (Marker): form, strategy, and polysemy readings. The WALS Ch 106 value is computed from a language's marker inventory (ofInventory), isNominal projects from the coding site, and the default valency effect derives from the coding-frame operation a strategy realizes (Voice.reciprocalization).

Main definitions

• ReflexiveRelation — reciprocal/reflexive formal relation (WALS Ch 106).
• Strategy + codingSite/isNominal — the morphosyntactic locus.
• Strategy.alternation / defaultValency — the realized coding-frame operation and the valency effect it derives.
• Valency, Formation + Formation.allowsDiscontinuous.
• Reading, Marker, ofInventory — marker inventories and the derived WALS Ch 106 value.

Per-language inventories live in Fragments/{Lang}/Reciprocals.lean; WALS-data grounding lives with the studies that use it (e.g. Studies/Nordlinger2023.lean), not here.

inductive Reciprocal.ReflexiveRelation : Type

WALS Ch 106 relation between reciprocal and reflexive marking ([MN13]).

• noDedicated : ReflexiveRelation

  "There are no non-iconic reciprocal constructions."

• distinctFromReflexive : ReflexiveRelation

  "All reciprocal constructions are formally distinct from reflexive constructions" (English each other vs themselves).

• mixed : ReflexiveRelation

  "There are both reflexive and non-reflexive reciprocal constructions" (German sich + einander).

• identicalToReflexive : ReflexiveRelation

  "The reciprocal and reflexive constructions are formally identical" (Imbabura Quechua -ri-).

@[implicit_reducible]

instance Reciprocal.instDecidableEqReflexiveRelation : DecidableEq ReflexiveRelation

Equations

• Reciprocal.instDecidableEqReflexiveRelation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Reciprocal.instReprReflexiveRelation.repr : ReflexiveRelation → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Reciprocal.instReprReflexiveRelation : Repr ReflexiveRelation

Equations

• Reciprocal.instReprReflexiveRelation = { reprPrec := Reciprocal.instReprReflexiveRelation.repr }

inductive Reciprocal.Strategy : Type

Morphosyntactic strategy for encoding reciprocity ([Nor23] §3.1's compression of [KK06], [Ned07a], and [Eva08]).

• bipartiteNP : Strategy

  Bipartite quantifier NP (English each other, Icelandic hvort annað).

• recipPronoun : Strategy

  Reciprocal pronoun (Hausa jūnan-mù).

• recipClitic : Strategy

  Reciprocal clitic (French se, Wambaya -ngg-).

• verbalAffix : Strategy

  Verbal affix (Swahili -an-, Hungarian -óz-).

• verbalAuxiliary : Strategy

  Reciprocal auxiliary (Warrwa wanji- 'exchange', [Eva08]).

• lexical : Strategy

  Inherently reciprocal predicate (English quarrel, meet).

• compoundVerb : Strategy

  Compound verb (Mandarin dǎ-lái-dǎ-qù, [KK06]).

@[implicit_reducible]

instance Reciprocal.instDecidableEqStrategy : DecidableEq Strategy

Equations

• Reciprocal.instDecidableEqStrategy x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Reciprocal.instReprStrategy : Repr Strategy

Equations

• Reciprocal.instReprStrategy = { reprPrec := Reciprocal.instReprStrategy.repr }

def Reciprocal.instReprStrategy.repr : Strategy → ℕ → Std.Format

Equations

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

inductive Reciprocal.Valency : Type

Valency effect of the reciprocal construction ([Nor23] §3.2).

• bivalent : Valency

  Two overt syntactic argument slots preserved.

• monovalent : Valency

  The reciprocants form a single subject NP.

@[implicit_reducible]

instance Reciprocal.instDecidableEqValency : DecidableEq Valency

Equations

• Reciprocal.instDecidableEqValency x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Reciprocal.instReprValency.repr : Valency → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Reciprocal.instReprValency : Repr Valency

Equations

• Reciprocal.instReprValency = { reprPrec := Reciprocal.instReprValency.repr }

inductive Reciprocal.CodingSite : Type

Coding site of reciprocal marking: argument position, predicate, or fused multipredicate structure.

• argument : CodingSite
• predicate : CodingSite
• multiclausal : CodingSite

@[implicit_reducible]

instance Reciprocal.instDecidableEqCodingSite : DecidableEq CodingSite

Equations

• Reciprocal.instDecidableEqCodingSite x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Reciprocal.instReprCodingSite.repr : CodingSite → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Reciprocal.instReprCodingSite : Repr CodingSite

Equations

• Reciprocal.instReprCodingSite = { reprPrec := Reciprocal.instReprCodingSite.repr }

def Reciprocal.Strategy.codingSite : Strategy → CodingSite

Coding site of each strategy. Clitics sit on the predicate side, following [Sil12] rather than [KK06]'s nominal grouping.

Equations

• Reciprocal.Strategy.bipartiteNP.codingSite = Reciprocal.CodingSite.argument
• Reciprocal.Strategy.recipPronoun.codingSite = Reciprocal.CodingSite.argument
• Reciprocal.Strategy.recipClitic.codingSite = Reciprocal.CodingSite.predicate
• Reciprocal.Strategy.verbalAffix.codingSite = Reciprocal.CodingSite.predicate
• Reciprocal.Strategy.verbalAuxiliary.codingSite = Reciprocal.CodingSite.predicate
• Reciprocal.Strategy.lexical.codingSite = Reciprocal.CodingSite.predicate
• Reciprocal.Strategy.compoundVerb.codingSite = Reciprocal.CodingSite.multiclausal

def Reciprocal.Strategy.isNominal (s : Strategy) : Bool

Whether the strategy marks a (nonsubject) argument position ([Nor23] §3.2).

Equations

• s.isNominal = (s.codingSite == Reciprocal.CodingSite.argument)

def Reciprocal.Strategy.alternation : Strategy → Option Voice.ValencyAlternation

The coding-frame operation a strategy realizes: grammatical verb-marking strategies apply [Cre25]'s denucleativizing reciprocalization.

Equations

• Reciprocal.Strategy.recipClitic.alternation = some Voice.reciprocalization
• Reciprocal.Strategy.verbalAffix.alternation = some Voice.reciprocalization
• Reciprocal.Strategy.verbalAuxiliary.alternation = some Voice.reciprocalization
• Reciprocal.Strategy.compoundVerb.alternation = some Voice.reciprocalization
• Reciprocal.Strategy.bipartiteNP.alternation = none
• Reciprocal.Strategy.recipPronoun.alternation = none
• Reciprocal.Strategy.lexical.alternation = none

def Reciprocal.Strategy.defaultValency (s : Strategy) : Valency

Default valency effect, derived from the realized alternation's derivedTransitive field; a tendency that languages may override (Wambaya, Tonga, Malagasy — [Mas08], [Hur12]).

Equations

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

inductive Reciprocal.Formation : Type

Formation locus of reciprocal verbs: lexical θ-role bundling vs syntactic derivation ([Sil08], [Sil12]; [RS05]'s lex-syn parameter).

• lexical : Formation
• syntactic : Formation

@[implicit_reducible]

instance Reciprocal.instDecidableEqFormation : DecidableEq Formation

Equations

• Reciprocal.instDecidableEqFormation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Reciprocal.instReprFormation : Repr Formation

Equations

• Reciprocal.instReprFormation = { reprPrec := Reciprocal.instReprFormation.repr }

def Reciprocal.instReprFormation.repr : Formation → ℕ → Std.Format

Equations

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

def Reciprocal.Formation.allowsDiscontinuous : Formation → Bool

Whether the formation licenses the discontinuous reciprocal construction — lexical only ([Sil12] §7; verb-level exceptions exist, fn. 32).

Equations

• Reciprocal.Formation.lexical.allowsDiscontinuous = true
• Reciprocal.Formation.syntactic.allowsDiscontinuous = false

Marker inventories

inductive Reciprocal.Reading : Type

Readings a reciprocal marker can carry ([Nor23] §4.2, [Ned07b]).

• reciprocal : Reading
• reflexive : Reading
• collective : Reading
• sociative : Reading
• iterative : Reading

@[implicit_reducible]

instance Reciprocal.instDecidableEqReading : DecidableEq Reading

Equations

• Reciprocal.instDecidableEqReading x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Reciprocal.instReprReading.repr : Reading → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Reciprocal.instReprReading : Repr Reading

Equations

• Reciprocal.instReprReading = { reprPrec := Reciprocal.instReprReading.repr }

structure Reciprocal.Marker : Type

A reciprocal exponent: form, strategy, and the readings it covers.

• form : String

  Surface form (romanization or orthographic).

• script : Option String

  Native-script form, when form is a romanization.

• strategy : Strategy

  Morphosyntactic strategy of the exponent.

• readings : List Reading

  Readings the marker covers.

def Reciprocal.instDecidableEqMarker.decEq (x✝ x✝¹ : Marker) : Decidable (x✝ = x✝¹)

Equations

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

@[implicit_reducible]

instance Reciprocal.instDecidableEqMarker : DecidableEq Marker

Equations

• Reciprocal.instDecidableEqMarker = Reciprocal.instDecidableEqMarker.decEq

@[implicit_reducible]

instance Reciprocal.instReprMarker : Repr Marker

Equations

• Reciprocal.instReprMarker = { reprPrec := Reciprocal.instReprMarker.repr }

def Reciprocal.instReprMarker.repr : Marker → ℕ → Std.Format

Equations

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

def Reciprocal.ofInventory (inv : List Marker) : ReflexiveRelation

WALS Ch 106 value computed from a marker inventory: no reciprocal-capable marker → noDedicated; all also reflexive → identicalToReflexive; none reflexive → distinctFromReflexive; both kinds → mixed.

Equations

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