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Linglib.Phenomena.ArgumentStructure.Typology

Cross-Linguistic Typology of Valence and Voice (WALS Chapters 105--111) #

@cite{maslova-nedjalkov-2013} @cite{polinsky-2013} @cite{siewierska-2013} @cite{song-2013} @cite{haspelmath-2013} @cite{nordlinger-2023} @cite{dalrymple-et-al-1998} @cite{siloni-2008} @cite{siloni-2012} @cite{konig-kokutani-2006} @cite{dixon-1972} @cite{ryding-2005} @cite{kimenyi-1980} @cite{galloway-1993}

Typological data on valence-changing and voice constructions, drawn from WALS (World Atlas of Language Structures) chapters 105--111:

This module focuses on Ch 105--109 (ditransitives, reciprocals, passives, antipassives, applicatives). Causative typology (Ch 110--111) is covered in Phenomena.Causation.Typology; only aggregate WALS counts are recorded here for cross-reference.

WALS Ch 106: How reciprocal situations are encoded relative to reflexives.

The four values follow @cite{maslova-nedjalkov-2013}'s classification:

  • noDedicated: "There are no non-iconic reciprocal constructions" — the language lacks a dedicated grammatical reciprocal marker.
  • distinctFromReflexive: "All reciprocal constructions are formally distinct from reflexive constructions" (e.g. English "each other" vs "themselves").
  • mixed: "There are both reflexive and non-reflexive reciprocal constructions" — the language has both a reflexive-identical strategy and a formally distinct one (e.g. German "sich" + "einander"). Common in Europe.
  • identicalToReflexive: "The reciprocal and reflexive constructions are formally identical" (e.g. Imbabura Quechua "-ri", West Greenlandic "-ssin-").
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      Morphosyntactic strategy for encoding reciprocity.

      @cite{nordlinger-2023} summarizes the structural typologies of König & Kokutani (2006), Nedjalkov (2007a), and Evans (2008), which classify reciprocal constructions by the morphosyntactic locus of the reciprocal marking:

      • bipartiteNP: Bipartite quantifier NP — English "each other", Icelandic "hvor...annad" (two independently inflected parts).
      • recipPronoun: Reciprocal pronoun — Russian "drug druga", Hausa "jùnan-mù". Free-standing pronominal form in object position.
      • recipClitic: Reciprocal clitic — French/Czech "se", Wambaya "-ngg-" (RR morpheme in auxiliary). Intermediate between pronoun and affix; functionally verbal (valence-reducing in most cases, though Wambaya retains bivalent syntax via ergative case).
      • verbalAffix: Morphological marking on the verb — Swahili "-ana", Hungarian "-oz-", Chicheŵa "-an-". Derives an intransitive (monovalent) verb from a transitive base.
      • verbalAuxiliary: Reciprocal auxiliary — Warrwa "wanji-" replaces the regular transitive auxiliary.
      • lexical: Inherently reciprocal predicate — English "quarrel", "meet". The symmetric meaning is part of the verb's lexical semantics.
      • compoundVerb: Compound verb — Mandarin "dǎ-lái-dǎ-qù" (beat-come-beat-go = 'beat each other').
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          Whether the strategy marks the NP/argument position (nominal strategy) or the verb/predicate (verbal strategy). König & Kokutani (2006)'s primary typological distinction.

          Clitics are classified as non-nominal: Evans (2008) treats them as intermediate, but their valence behavior is typically verbal — French/Czech "se" reduces valence (monovalent), and even Wambaya "-ngg-" is morphologically bound to the auxiliary.

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            Valency effect of reciprocal construction on the base predicate.

            Maslova (2008) distinguishes "unary" and "binary" reciprocals; @cite{nordlinger-2023} (§3.2) discusses how NP/argument strategies tend to preserve valency while verb-marked strategies tend to reduce it. The correlation is a tendency, not absolute — Malagasy verb-marked reciprocals retain full valency at f-structure (Hurst 2006, 2012).

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                Where reciprocal verbs are formed, per Siloni (2008, 2012).

                @cite{nordlinger-2023} (§3.3) discusses Siloni's distinction:

                • lexical: formed in the lexicon through "bundling" — two thematic roles (agent, patient) merge into a single complex role. Produces verbs with inherently symmetric semantics. Can license discontinuous reciprocal constructions (subject + comitative argument).
                • syntactic: formed in the syntax via an operation that creates the symmetric reading. Cannot license discontinuous reciprocals.

                Key empirical prediction: discontinuous reciprocals ("John kissed with Mary") are possible only with lexically-formed reciprocal verbs.

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                    Can the reciprocal construction appear in discontinuous form (reciprocants split across subject and comitative argument)? @cite{nordlinger-2023} §3.3.

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                      WALS Ch 107: Whether a language has passive constructions.

                      Siewierska defines a passive as having five properties: (i) contrasts with active, (ii) active subject demoted or suppressed, (iii) active object promoted to subject (if personal passive), (iv) pragmatically restricted, (v) special verbal morphology. Includes both personal and impersonal passives, both synthetic (Swahili -w-) and periphrastic (English "be + past participle", Polish zostac + participle).

                      • present: The language has at least one passive construction.
                      • absent: No passive construction (agent demotion achieved by other means: subject omission, impersonal pronoun, 3pl verb form, etc.).
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                          WALS Ch 108: Antipassive construction type.

                          An antipassive is a derived detransitivized construction: the patient-like argument is either suppressed or demoted to an oblique. The term indicates the mirror image of the passive: in the passive the agent is demoted, in the antipassive the patient.

                          • implicitPatient: Patient-like argument left implicit (unexpressed).
                          • obliquePatient: Patient-like argument expressed as oblique complement (e.g. Chukchi instrumental kimitw-e in antipassive vs absolutive kimitw-xn in transitive).
                          • noAntipassive: No antipassive construction.
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                              WALS Ch 108 inset map: Productivity of the antipassive.

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                                  Morphological alignment system (simplified for antipassive correlation).

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                                      WALS Ch 105: How ditransitive verbs (prototypically 'give') encode the recipient (R) and theme (T) arguments relative to the monotransitive patient (P).

                                      • indirectObject: R is treated differently from P (R gets a preposition or dative case: "give the book TO Mary").
                                      • doubleObject: R is treated the same as P (both bare NPs: "give Mary the book").
                                      • secondaryObject: T is treated differently from P (T gets special marking: Ainu, Lakhota).
                                      • mixed: More than one construction type is available.
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                                          WALS Ch 109: Transitivity of the base verb for applicative formation.

                                          • bothBases: Applicatives formed from both transitive and intransitive bases (most common pattern when applicatives exist).
                                          • transitiveOnly: Only from transitive bases.
                                          • intransitiveOnly: Only from intransitive bases (rare: Fijian, Wambaya).
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                                              WALS Ch 109: Semantic role of the applied object.

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                                                  WALS Ch 109: Full applicative type combining base and role. none for languages without applicative constructions.

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                                                        WALS Ch 110: Periphrastic causative type.

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                                                            WALS Ch 111: Nonperiphrastic (morphological/compound) causative type.

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                                                                A cross-linguistic valence/voice profile for a single language.

                                                                Covers WALS Ch 106--109 directly, plus Ch 111 causative morphology for the applicative-causative correlation. Ch 110 (periphrastic causatives) is omitted from profiles since most WALS sources do not report it.

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                                                                        English: reciprocal distinct from reflexive ("each other" vs "themselves"), periphrastic passive ("was kicked"), no antipassive (accusative alignment), no applicative, no productive morphological causative (lexical causatives like "kill" only).

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                                                                          Japanese: reciprocal distinct from reflexive ("otagai" vs "jibun"), passive ("-(r)are-"), no antipassive, no applicative, morphological causative suffix "-(s)ase".

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                                                                            Turkish: reciprocal distinct from reflexive — "birbirine" (reciprocal) is formally distinct from "kendi" (reflexive). WALS Ch 106 codes Turkish as Value 2 (distinct from reflexive). Passive ("-Il"), no antipassive (accusative), no applicative, morphological causative "-dUr".

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                                                                              Swahili: reciprocal distinct ("-ana"), passive ("-w-"), no antipassive, applicative ("-i-" / "-e-" benefactive + locative from both bases), morphological causative ("-ish-" / "-esh-").

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                                                                                Dyirbal (Pama-Nyungan, Australia): reciprocal distinct from reflexive. Reflexive: stem + -riy (@cite{dixon-1972} §4.8.1). Reciprocal: reduplicated stem + -(n)bariy (@cite{dixon-1972} §4.8.2). The reciprocal "functions like an intransitive stem" (monovalent). No passive, dedicated antipassive with oblique patient, ergative alignment, no applicative, morphological causative. NOTE: Dyirbal is NOT in WALS Ch 106 sample (175 languages).

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                                                                                  Chukchi (Chukotko-Kamchatkan, Russia): reciprocal distinct, no passive (inverse system instead), dedicated antipassive "ine-" with oblique patient (instrumental), ergative alignment, no applicative, morphological causative.

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                                                                                    Indonesian: reciprocal distinct from reflexive — "saling" (reciprocal) is formally different from "diri sendiri" (reflexive). WALS Ch 106 codes Indonesian as Value 2 (distinct from reflexive). Passive ("di-"), no antipassive, no applicative, morphological causative.

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                                                                                      French: mixed reciprocal type — both reflexive-identical "se" and distinct "l'un l'autre" ('each other'). WALS Ch 106 codes French as Value 3 (mixed). Periphrastic passive ("être + past participle"), no antipassive, no applicative, compound causative ("faire + INF").

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                                                                                        Russian: mixed reciprocal type — both reflexive-identical "-sja"/"-s'" and distinct "drug druga" ('each other'). WALS Ch 106 codes Russian as Value 3 (mixed), parallel to German ("sich" + "einander"). Passive (synthetic "-sja" + periphrastic), no antipassive, no applicative, morphological causative (zero-derivation, e.g. "lomat'-sja" anticausative).

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                                                                                          Arabic (Modern Standard): reciprocal via Form VI (tafaaʿal-a), formally distinct from Form V reflexive (tafaʿʿal-a): Form VI inserts long -aa- after the first root consonant, Form V doubles the medial consonant (@cite{ryding-2005} Ch 27 §1). Example: taʿaanaq-a 'to embrace one another' (Form VI, reciprocal) vs. takallam-a 'to speak' (Form V, reflexive/mediopassive). Passive via internal vowel change (kutiba), no antipassive, no applicative, morphological causative (Form IV ʾafʿala). NOTE: MSA is NOT in WALS Ch 106 sample; Arabic (Egyptian) is listed as Value 2 (distinct from reflexive).

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                                                                                            Hindi: reciprocal distinct ("ek duusre"), passive ("-aa" / "jaanaa" periphrastic), no antipassive, no applicative, morphological causative ("-aa" / "-vaa").

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                                                                                              West Greenlandic (Eskimo-Aleut): reciprocal-reflexive polysemy ("immi-" for both), passive, antipassive with oblique patient, ergative alignment, no applicative, morphological causative.

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                                                                                                Kinyarwanda (Bantu, Rwanda): reciprocal suffix -an- (e.g., -saban- 'ask each other'), formally distinct from reflexive prefix -ii-/-iiy- (e.g., á-r-íi-reeb-a 'she watches herself') (@cite{kimenyi-1980} §4.2.1, p. 5). Passive -w-, no antipassive, applicative -ir-/-er- (benefactive + other from both bases), morphological causative. NOTE: Kinyarwanda is NOT in WALS Ch 106 sample.

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                                                                                                  Lango (Nilotic, Uganda): reciprocal identical to reflexive. WALS Ch 106 codes Lango as Value 4 (identical to reflexive). Passive absent, antipassive with oblique patient (accusative alignment — one of the accusative-language antipassives), no applicative, morphological causative.

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                                                                                                    Chamorro (Austronesian, Guam): reciprocal distinct, passive present, antipassive with oblique patient (accusative alignment), applicative (benefactive + other, both bases), morphological causative.

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                                                                                                      Halkomelem (Salishan, Canada): reciprocal suffix -təl (e.g., ʔiyá·təl 'fight', yéyətəl 'make friends'), formally distinct from reflexive suffixes -lá·mət 'oneself' and -(ə)θət 'oneself, itself' (@cite{galloway-1993} §6.1.3, §11.2.1.14–15). Passive present, antipassive with oblique patient, ergative alignment, applicative (benefactive + other, both bases), morphological causative. NOTE: Halkomelem is NOT in WALS Ch 106 sample.

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                                                                                                        Modern Greek: mixed reciprocal type — both nonactive voice morphology (identical to reflexive) and distinct reciprocal constructions. WALS Ch 106 codes Modern Greek as Value 3 (mixed). Passive present ("periphrastic with nonactive morphology"), no antipassive, no applicative, NEITHER morphological nor compound causative (relies on periphrastic causative).

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                                                                                                          German: mixed reciprocal type ("sich" reflexive/reciprocal + "einander" distinct reciprocal), passive (werden + participle), no antipassive, no applicative, morphological causative (zero-derivation).

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                                                                                                            Finnish: reciprocal distinct from reflexive ("toisiaan" ≠ "itsensä"), impersonal "passive" (present — the Fragment's finnishPassive has semantic content but does not project a syntactic agent), no antipassive, accusative alignment, no applicative, morphological causative -tta- / -ttä-.

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                                                                                                                For each profile whose language IS in WALS Ch 106, prove its reciprocal type matches the WALS data. This eliminates transcription errors by construction: if the profile disagrees with WALS, the theorem fails.

                                                                                                                Per-language grounding: WALS 105A ditransitive type for profile languages. Every profile language appears in the 378-language F105A dataset.

                                                                                                                Per-language grounding: profile applicative types that match WALS 109A. Languages whose profiles disagree with WALS (Dyirbal, Indonesian, West Greenlandic, Lango, Chamorro) are omitted -- their profile values are based on other sources or use a different classification.

                                                                                                                Per-language grounding: WALS 109B applied-object roles for profile languages without applicatives. For these languages, F109B records .noApplicative, and our converter returns none.

                                                                                                                Finnish impersonal "passive" has semantic content (existential closure over agent) — derived from the Fragment's voice head.

                                                                                                                Finnish impersonal "passive" does NOT project a syntactic agent — derived from the Fragment's voice head.

                                                                                                                WALS Ch 107: 162 out of 373 languages have passives (43.4%). Although a minority, passives are widespread enough that most language families include at least some passive-bearing members.

                                                                                                                In the WALS Ch 108 data, antipassives occur in both accusative and ergative languages, but the correlation with ergativity is strong. @cite{polinsky-2013}: more languages have oblique-patient antipassives than implicit-patient antipassives, and the majority have no antipassive.

                                                                                                                In our sample: every ergative language has an antipassive, but not all accusative languages do.

                                                                                                                theorem Phenomena.ArgumentStructure.Typology.most_accusative_lack_antipassive :
                                                                                                                have accusatives := List.filter (fun (p : ValenceProfile) => p.alignment == AlignmentType.accusative) allProfiles; have withoutAP := List.filter (fun (p : ValenceProfile) => !p.antipassive.hasAntipassive) accusatives; withoutAP.length > accusatives.length - withoutAP.length

                                                                                                                In our sample: most accusative languages lack an antipassive.

                                                                                                                WALS Ch 111: The morphological causative type is found in 278 out of 310 languages (254 morphological-only + 24 both), i.e. ~90%. Only 23 languages use neither morphological nor compound causatives. This dwarfs periphrastic causatives in frequency.

                                                                                                                In our sample, all but two languages have a morphological or compound causative (Modern Greek has neither; French has compound only).

                                                                                                                WALS Ch 109 observes that "The main generalization seems to be that applicatives are commonly found in those languages that have little or no case marking of noun phrases and that have sufficiently rich verbal morphology." Since morphological causatives also require rich verbal morphology, we expect a correlation.

                                                                                                                In our sample: every language with an applicative also has a morphological causative.

                                                                                                                WALS Ch 111: Among languages with morphological causatives, suffixation is by far the most common pattern. @cite{song-2013} lists examples: Japanese "-(s)ase", Turkish "-dUr", Swahili "-ish-" / "-esh-". Prefixes (Abkhaz "r-"), infixes (Lepcha "-y-"), and circumfixes (Georgian "a-...-ineb") exist but are rare. This parallels Greenberg's Universal 27: suffixing is generally preferred over prefixing.

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                                                                                                                        Suffixing dominates: most morphological causative examples are suffixes.

                                                                                                                        WALS Ch 106 notes a clear areal pattern: Value 1 (no non-iconic reciprocal constructions) is concentrated in Oceania, Southeast Asia, and parts of Africa. Every Eurasian language in the sample has at least one productive grammatical reciprocal construction (Value 2, 3, or 4).

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                                                                                                                          Every Eurasian language in our sample has a productive grammatical reciprocal construction (i.e., none are Value 1).

                                                                                                                          Languages without passives tend to have other detransitivizing strategies. In our sample, both passive-absent languages with ergative alignment have antipassives.

                                                                                                                          Applicatives and antipassives are dual voice operations: applicatives increase valence (adding an applied object), antipassives decrease it (demoting the patient). Some languages have both -- in our sample, Chamorro and Halkomelem combine applicatives with antipassives, demonstrating that a single language can productively use both valence-increasing and valence-decreasing operations.

                                                                                                                          Languages with antipassives classified by alignment, from WALS Ch 108 Table 1. This is the key empirical evidence for the antipassive-ergativity debate (@cite{silverstein-1976}).

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                                                                                                                                Accusative languages with antipassives (17 in WALS Table 1). These are the key counterexamples to the strong claim that antipassives are limited to ergative languages.

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                                                                                                                                  Ergative languages with antipassives (30 in WALS Table 1).

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                                                                                                                                    theorem Phenomena.ArgumentStructure.Typology.applicatives_only_in_bantu_and_austronesian :
                                                                                                                                    have withApplicative := List.filter (fun (p : ValenceProfile) => p.applicative.hasApplicative) allProfiles; (withApplicative.all fun (p : ValenceProfile) => p.iso == "swa" || p.iso == "kin" || p.iso == "cha" || p.iso == "hur") = true

                                                                                                                                    WALS Ch 109 notes applicatives cluster in three areas: Bantu Africa, Western Pacific (Austronesian), and North/Meso-America (Salish, Mayan, Uto-Aztecan). The dearth in Eurasia correlates with rich case marking: languages with case can use oblique cases instead of applicatives.

                                                                                                                                    In our sample, only Bantu and Austronesian languages have applicatives.

                                                                                                                                    Count of languages with each passive value.

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                                                                                                                                      Count of languages with each antipassive value.

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                                                                                                                                        Count of languages with applicatives in sample.

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                                                                                                                                          @cite{nordlinger-2023} reports that of the 175 languages in @cite{maslova-nedjalkov-2013}'s sample, polysemous reflexive/reciprocal constructions are present in 60 (34%). In WALS terms, polysemy corresponds to Values 3 (mixed) and 4 (identical to reflexive).

                                                                                                                                          Extended reciprocal profile for a single language.

                                                                                                                                          Captures the morphosyntactic strategy, valency effect, and discontinuity licensing from @cite{nordlinger-2023}'s review, going beyond the WALS 4-way reflexive-reciprocal classification.

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                                                                                                                                                  English: bipartite NP "each other" (bivalent, distinct from reflexive). Also has lexical reciprocals ("quarrel", "meet") as secondary strategy. @cite{nordlinger-2023} ex. 1b, 7, 24; ex. 44 (all 6 reciprocity types).

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                                                                                                                                                    Russian: reciprocal pronoun "drug druga" (bivalent, distinct) plus reflexive-identical verbal postfix "-sja"/"-s'" (monovalent, identical). Unlike French "se" (a separable clitic), Russian "-sja" is a bound suffix — classified as .verbalAffix per Evans (2008). @cite{nordlinger-2023} ex. 9, 31.

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                                                                                                                                                      Swahili: verbal affix "-ana" (monovalent, distinct from reflexive "-ji-"). Can form discontinuous reciprocals with comitative "na" (Hurst 2012; @cite{nordlinger-2023} ex. 12, 37, 40). Lexically formed per Siloni's analysis.

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                                                                                                                                                        Hungarian: verbal affix "-oz-" (monovalent, distinct). Can form discontinuous reciprocals with comitative "-val"/"-vel" (Dimitriadis 2008; @cite{nordlinger-2023} ex. 19, 30, 38). Lexically formed per Siloni's analysis.

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                                                                                                                                                          French: reflexive clitic "se" (monovalent, identical to reflexive) plus distinct "l'un l'autre" (bivalent, bipartite NP). "se" reciprocals are syntactically formed per Siloni (2008) and CANNOT form discontinuous reciprocals (@cite{nordlinger-2023} ex. 39). @cite{nordlinger-2023} ex. 28, 35, 39, 47. "se" is a clitic, not an affix — @cite{nordlinger-2023} p. 83: "the clitics se in French and Czech."

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                                                                                                                                                            Greek (Modern): nonactive voice morphology (monovalent, identical to reflexive in form) plus distinct constructions. CAN form discontinuous reciprocals with "me" (= 'with'): "O Giannis filithike me ti Maria" (@cite{nordlinger-2023} ex. 27b, 36). Lexically formed per Siloni's analysis.

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                                                                                                                                                              German: reflexive pronoun "sich" (bivalent — fills object position, identical to reflexive) plus distinct reciprocal pronoun "einander" (bivalent, single-word pronoun). Both strategies preserve transitivity because the reciprocal form occupies the object slot. @cite{nordlinger-2023} via WALS Ch 106.

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                                                                                                                                                                Mandarin: compound verb strategy "dǎ-lái-dǎ-qù" (beat-come-beat-go = 'beat each other'). Distinct from reflexive. @cite{nordlinger-2023} ex. 13 (citing König & Kokutani 2006).

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                                                                                                                                                                  Wambaya: reciprocal clitic "-ngg-" (RR morpheme in auxiliary). Identical to reflexive. @cite{nordlinger-2023} ex. 11 (citing Nordlinger 1998, p. 142).

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                                                                                                                                                                    Icelandic: bipartite NP "hvor...annad" with independent case inflection on each part. Bivalent — retains full transitivity. @cite{nordlinger-2023} ex. 17 (citing Hurst & Nordlinger 2021).

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                                                                                                                                                                      Chicheŵa: verbal affix "-an-" (monovalent). @cite{nordlinger-2023} ex. 20 (citing Dalrymple et al. 1994).

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                                                                                                                                                                        Czech: reflexive clitic "se" (monovalent, identical to reflexive). Syntactically formed per Siloni — cannot form discontinuous reciprocals. @cite{nordlinger-2023} ex. 29; Siloni (2008). "se" is a clitic — @cite{nordlinger-2023} p. 83.

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                                                                                                                                                                            @cite{nordlinger-2023} (§3.2): NP/argument strategies tend to preserve valency (bivalent), while verb-marking strategies tend to reduce valency (monovalent). Nedjalkov (2007a) links this to the morphosyntactic type: morphological markers "reduce the valency of the underlying verb by deleting the direct or indirect object."

                                                                                                                                                                            In our sample: all nominal-strategy profiles are bivalent.

                                                                                                                                                                            Verbal affixes (Swahili "-ana", Hungarian "-oz-", Greek nonactive, Chicheŵa "-an-") are uniformly monovalent in our sample.

                                                                                                                                                                            Converse of nominal_strategy_bivalent: monovalent reciprocal strategies are never nominal (NP/argument). This captures Nedjalkov (2007a, p. 21): morphological reciprocal markers "reduce the valency of the underlying verb." @cite{nordlinger-2023} §3.2.

                                                                                                                                                                            Clitics (French/Czech "se") are also monovalent — the clitic absorbs the object argument. Wambaya "-ngg-" is the exception: bivalent despite being a clitic (ergative case preserves transitivity). @cite{nordlinger-2023} §3.2; Evans et al. (2007).

                                                                                                                                                                            Siloni (2008, 2012) predicts: discontinuous reciprocals (subject + comitative "with"-phrase) are possible only when the reciprocal verb is lexically formed, not syntactically formed.

                                                                                                                                                                            Lexically formed: Greek, Swahili, Hungarian — CAN be discontinuous. Syntactically formed: French, Czech — CANNOT be discontinuous.

                                                                                                                                                                            This is verified in our sample: every profile with a formation locus matches Siloni's prediction.

                                                                                                                                                                            For languages with both a ValenceProfile and a RecipProfile, the reflexive-reciprocal classification must agree.

                                                                                                                                                                            Semantic type of reciprocal relation.

                                                                                                                                                                            @cite{nordlinger-2023} (§4) summarizes the semantic typology from Dalrymple et al. (1998) and Evans et al. (2011), distinguishing six types of mutual relation that reciprocal constructions can encode:

                                                                                                                                                                            • strong: every participant reciprocates with every other ("The members of this family love one another.")
                                                                                                                                                                            • pairwise: participants are paired off ("The people at the dinner party were married to one another.")
                                                                                                                                                                            • chain: sequential, each with the next ("The graduating students followed one another up onto the stage.")
                                                                                                                                                                            • radial: one central participant reciprocates with all others ("The teacher and her pupils intimidated one another.")
                                                                                                                                                                            • melee: widespread but not exhaustive reciprocation ("The drunks in the pub were punching one another.")
                                                                                                                                                                            • ring: circular chain, last links back to first ("The children chased each other round in a ring.")
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                                                                                                                                                                                Whether a reciprocity type requires every participant to be involved in at least one reciprocal pair. Radial IS participant-exhaustive — the center reciprocates with each peripheral — but is not pair-exhaustive (peripherals do not reciprocate with each other). Melee is the only type where some participants may be uninvolved.

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                                                                                                                                                                                  Whether a reciprocity type is symmetric: within each active pair, if A acts on B then B acts on A. Chain and ring are directional (A follows B does not entail B follows A). Radial IS symmetric — the teacher intimidates each pupil AND each pupil intimidates the teacher — it just doesn't cover all pairs.

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                                                                                                                                                                                    Strong, pairwise, and radial are the three symmetric AND participant-exhaustive reciprocity types. Among these, only strong is also pair-exhaustive (every possible pair reciprocates).

                                                                                                                                                                                    Chain and ring are non-symmetric (directional) — they model sequential actions where A acts on B but B does not act on A. The difference: ring links the last element back to the first, chain does not.

                                                                                                                                                                                    Melee is the only non-exhaustive type — some group members may not participate at all.

                                                                                                                                                                                    English "each other" can express all six reciprocity types (Evans et al. 2011b, p. 8; @cite{nordlinger-2023} ex. 44). This is an empirical observation about English, not a structural property — some languages restrict which types their reciprocal construction can express.

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                                                                                                                                                                                      Swahili reciprocal suffix "-an-" as a MorphRule.

                                                                                                                                                                                      Realizes valence reduction: transitive → intransitive. The reciprocal suffix removes the object argument, making the verb monovalent (the participants are encoded in a plural subject).

                                                                                                                                                                                      Example: "pend-" (love) → "pend-an-" (love each other) @cite{nordlinger-2023} ex. 40 (citing Dimitriadis 2004).

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                                                                                                                                                                                        Extended readings of reciprocal markers beyond core reciprocal meaning.

                                                                                                                                                                                        @cite{nordlinger-2023} (§4.2) notes that reciprocal markers are often polysemous, expressing related but non-reciprocal meanings. These extended uses include collective, sociative, and iterative readings, in addition to the reflexive overlap captured by WALS Ch 106.

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                                                                                                                                                                                            Polysemy pattern: which extended readings a language's reciprocal marker(s) can express.

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                                                                                                                                                                                                French "se": reciprocal + reflexive + collective. "Les enfants se sont rassemblés" (collective, no mutual action).

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                                                                                                                                                                                                  Wambaya "-ngg-" (RR): reciprocal + reflexive (identical forms).

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                                                                                                                                                                                                    English reciprocal forms ("each other", "one another") are formally distinct from reflexive forms ("themselves", etc.) — derived from the Fragment's pronoun entries rather than stipulated in the profile.