Documentation

Studies.Haspelmath2001

Haspelmath (2001): The European linguistic area: Standard Average European #

This file formalizes the argument of [Has01] that the core European languages form a linguistic area: a structural feature is a Europeanism when the great majority of the core languages have it while the geographically adjacent languages, the eastern Indo-European languages and the majority of the world's languages lack it, §1, and twelve such features are mapped in §2. Language is the sample of Maps 107.1–107.13 and isogloss the languages each map places inside the feature's line, the two gradient features being derived from the figures the maps print: Bossong's inversion ratios (experiencerRatio, Map 107.4) and the percentages of anticausative pairs (anticausativePercent, Map 107.6). IsEuropeanism states criteria (i)–(iii) over the map sample and WorldMinority criterion (iv) over the world-wide surveys the chapter cites.

clusterScore is the cluster map of §4, the number of the nine selected features a language has: nucleus_eq derives the Charlemagne nucleus, French and German with all nine; eight_eq and seven_eq the next two layers; and area_eq the area of at least five features that stands out from the remaining languages. The criteria hold on the map data with two exceptions the chapter itself flags, majorityOfCore_iff: negative indefinites without verbal negation and strict subject agreement are not majority features of the core, and Armenian carries the relative-pronoun strategy on Map 107.2, easternIELack_iff.

Implementation notes #

The feature values are read from the maps of the scanned chapter, and the readings are checked against the layer counts §4 states: the cluster map's isopleths reproduce exactly. "The great majority" of criterion (i) is read as a majority, and "lack" in (ii) as fewer than half, relative to the languages a feature's map covers. Map 107.5 places Hungarian inside the participial-passive line although §2.5 says Hungarian has no passive; the map is followed, as the cluster count of five for Hungarian requires. Maps 107.4, 107.6 and 107.9 cover different samples (Bossong's, the 1993 verb-pair survey's and Stassen's), so criteria are evaluated per map.

TODO #

References #

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inductive Haspelmath2001.Language :
Type

The languages of Maps 107.1–107.13, by the abbreviations of §6, with the languages of Bossong's sample (Map 107.4) and Stassen's (Map 107.9) that the base map lacks.

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    @[instance_reducible]
    instance Haspelmath2001.instDecidableEqLanguage :
    DecidableEq Language
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    @[instance_reducible]
    instance Haspelmath2001.instFintypeLanguage :
    Fintype Language
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    @[instance_reducible]
    instance Haspelmath2001.instReprLanguage :
    Repr Language
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    def Haspelmath2001.instReprLanguage.repr :
    Language → ℕ → Std.Format
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      inductive Haspelmath2001.Family :
      Type

      The genealogical groups §1 reasons with: the branches of the core, the neighbours of criterion (ii), and the eastern Indo-European branch of criterion (iii) present on the maps.

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        @[instance_reducible]
        instance Haspelmath2001.instDecidableEqFamily :
        DecidableEq Family
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        @[instance_reducible]
        instance Haspelmath2001.instReprFamily :
        Repr Family
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        def Haspelmath2001.instReprFamily.repr :
        Family → ℕ → Std.Format
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          def Haspelmath2001.Language.family :
          Language → Family
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            def Haspelmath2001.Family.IsCore :
            Family → Prop

            The core European languages of §1: Romance, Germanic, Balto-Slavic, the Balkan languages, and the westernmost Finno-Ugrian languages.

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              def Haspelmath2001.Family.IsAdjacent :
              Family → Prop

              The geographically adjacent languages of criterion (ii).

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                The twelve features of §2 #

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                inductive Haspelmath2001.Feature :
                Type

                The Europeanisms of §2.1–§2.12.

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                  @[instance_reducible]
                  instance Haspelmath2001.instDecidableEqFeature :
                  DecidableEq Feature
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                  @[instance_reducible]
                  instance Haspelmath2001.instFintypeFeature :
                  Fintype Feature
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                  @[instance_reducible]
                  instance Haspelmath2001.instReprFeature :
                  Repr Feature
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                  def Haspelmath2001.instReprFeature.repr :
                  Feature → ℕ → Std.Format
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                    def Haspelmath2001.baseMap :
                    Finset Language

                    The languages of the base map shared by Maps 107.1–3, 107.5, 107.7–8 and 107.10–13.

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                      def Haspelmath2001.experiencerRatio :
                      Language → Option ℕ

                      Bossong's ratio of inverting to generalizing experiential predicates, in hundredths, as Map 107.4 prints it.

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                        def Haspelmath2001.anticausativePercent :
                        Language → Option ℕ

                        The percentage of anticausative inchoative–causative pairs, as Map 107.6 prints it.

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                          def Haspelmath2001.mapped :
                          Feature → Finset Language

                          The languages a feature's map covers.

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                            def Haspelmath2001.isogloss :
                            Feature → Finset Language

                            The languages inside a feature's isogloss: the SAE value. Map 107.4 draws the line at Bossong's ratio 0.8, predominant generalization below it, and Map 107.6 at 70% of anticausative pairs.

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                              The criteria of §1 #

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                              def Haspelmath2001.core (f : Feature) :
                              Finset Language

                              The core languages a feature's map covers.

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                                def Haspelmath2001.adjacent (f : Feature) :
                                Finset Language

                                The adjacent languages a feature's map covers.

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                                  def Haspelmath2001.MajorityOfCore (f : Feature) :
                                  Prop

                                  Criterion (i): the great majority of the core European languages have the feature, read as a majority of the core languages on the map.

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                                    def Haspelmath2001.AdjacentLack (f : Feature) :
                                    Prop

                                    Criterion (ii): the adjacent languages lack the feature, read as fewer than half of the adjacent languages on the map.

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                                      def Haspelmath2001.EasternIELack (f : Feature) :
                                      Prop

                                      Criterion (iii): the eastern Indo-European languages lack the feature; Armenian is the one on the maps.

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                                        def Haspelmath2001.worldSurvey :
                                        Feature → Option (ℕ × ℕ)

                                        The world-wide surveys the chapter cites for criterion (iv), as the number of languages with the feature out of the sample: Dryer's languages with both articles, the participle-plus- auxiliary passives of the 1990 survey, Kahrel's V + NI negation patterns, and Siewierska's strict-agreement languages.

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                                          def Haspelmath2001.WorldMinority (f : Feature) :
                                          Prop

                                          Criterion (iv): the feature is not found in the majority of the world's languages.

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                                            @[instance_reducible]
                                            instance Haspelmath2001.instDecidableMajorityOfCore (f : Feature) :
                                            Decidable (MajorityOfCore f)
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                                            @[instance_reducible]
                                            instance Haspelmath2001.instDecidableAdjacentLack (f : Feature) :
                                            Decidable (AdjacentLack f)
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                                            @[instance_reducible]
                                            instance Haspelmath2001.instDecidableEasternIELack (f : Feature) :
                                            Decidable (EasternIELack f)
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                                            @[instance_reducible]
                                            instance Haspelmath2001.instDecidableWorldMinority (f : Feature) :
                                            Decidable (WorldMinority f)
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                                            structure Haspelmath2001.IsEuropeanism (f : Feature) :
                                            Prop

                                            A Europeanism: criteria (i)–(iii) on the map and (iv) on the surveys.

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                                              theorem Haspelmath2001.majorityOfCore_iff (f : Feature) :
                                              MajorityOfCore f ↔ f ≠ Feature.negativeIndefinitesWithoutVerbalNegation ∧ f ≠ Feature.strictAgreement

                                              Criterion (i) holds of every feature except the two the chapter describes as narrow: the V + NI negation of French and Germanic, §2.8, and strict agreement, "characteristic of a few European languages", §2.11.

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                                              theorem Haspelmath2001.adjacentLack (f : Feature) :
                                              AdjacentLack f

                                              Criterion (ii) holds of every feature.

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                                              theorem Haspelmath2001.easternIELack_iff (f : Feature) :
                                              EasternIELack f ↔ f ≠ Feature.relativePronouns

                                              Criterion (iii) holds of every feature except the relative-pronoun strategy, which Map 107.2 extends to Armenian.

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                                              theorem Haspelmath2001.worldMinority (f : Feature) :
                                              WorldMinority f

                                              Every survey the chapter cites puts the feature in a minority of the world's languages.

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                                              theorem Haspelmath2001.havePerfect_isEuropeanism :
                                              IsEuropeanism Feature.havePerfect

                                              The 'have'-perfect meets all four criteria on the chapter's data.

                                              The cluster map of §4 #

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                                              def Haspelmath2001.clusterFeatures :
                                              Finset Feature

                                              The nine features Map 107.13 combines, those with complete information.

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                                                def Haspelmath2001.clusterScore (l : Language) :
                                                ℕ

                                                The number of the nine features a language has: the isopleth of Map 107.13.

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                                                  theorem Haspelmath2001.nucleus_eq :
                                                  {x ∈ baseMap | clusterScore x = 9} = {Language.french, Language.german}

                                                  The nucleus, French and German, shows the SAE value in all nine features: the Charlemagne Sprachbund.

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                                                  theorem Haspelmath2001.eight_eq :
                                                  {x ∈ baseMap | clusterScore x = 8} = {Language.dutch, Language.spanish, Language.portuguese, Language.sardinian, Language.italian, Language.albanian}

                                                  The next layer, Dutch, the other Romance languages and Albanian, shows eight.

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                                                  theorem Haspelmath2001.seven_eq :
                                                  {x ∈ baseMap | clusterScore x = 7} = {Language.english, Language.greek, Language.romanian}

                                                  The next layer, English, Greek and Romanian, shows seven.

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                                                  theorem Haspelmath2001.area_eq :
                                                  {x ∈ baseMap | 5 ≤ clusterScore x} = {Language.french, Language.german, Language.dutch, Language.spanish, Language.portuguese, Language.sardinian, Language.italian, Language.albanian, Language.english, Language.greek, Language.romanian, Language.icelandic, Language.norwegian, Language.swedish, Language.czech, Language.russian, Language.polish, Language.latvian, Language.lithuanian, Language.ukrainian, Language.serboCroatian, Language.slovene, Language.hungarian, Language.bulgarian}

                                                  The area with at least five features: the nucleus, the two layers, and the Scandinavian, Slavic, Baltic and Hungarian languages inside the outer isopleth.

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                                                  theorem Haspelmath2001.outside_le_four (l : Language) :
                                                  l ∈ baseMap → clusterScore l < 5 → clusterScore l ≤ 4

                                                  The remaining languages of the base map have at most four of the nine features.