Documentation

Linglib.Theories.Sociolinguistics.SCM

Stereotype Content Model #

@cite{fiske-cuddy-glick-2007}

The SCM property space: 6 properties organized as 3 bipolar dimensions (competence, warmth, solidarity). The SocialDimension type (axis labels) and SCMProperty type (pole endpoints) live here rather than in Core/SocialMeaning.lean because they are specific to the SCM theoretical framework.

Types #

Key results #

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inductive Sociolinguistics.SCM.SCMProperty :
Type

The 6 property endpoints of the SCM: two poles for each of the three dimensions.

These are the values that a persona can take — a persona selects one pole from each dimension (e.g., competent + warm + solidary).

Instances For
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    instance Sociolinguistics.SCM.instDecidableEqSCMProperty :
    DecidableEq SCMProperty
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    instance Sociolinguistics.SCM.instBEqSCMProperty :
    BEq SCMProperty
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    def Sociolinguistics.SCM.instBEqSCMProperty.beq :
    SCMProperty → SCMProperty → Bool
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      def Sociolinguistics.SCM.instReprSCMProperty.repr :
      SCMProperty → ℕ → Std.Format
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      • One or more equations did not get rendered due to their size.
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        instance Sociolinguistics.SCM.instReprSCMProperty :
        Repr SCMProperty
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        instance Sociolinguistics.SCM.instFintypeSCMProperty :
        Fintype SCMProperty
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        • One or more equations did not get rendered due to their size.
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        inductive Sociolinguistics.SCM.SocialDimension :
        Type

        Social-meaning dimensions, grounded in @cite{fiske-cuddy-glick-xu-2002} @cite{fiske-cuddy-glick-2007}'s universal dimensions of social cognition.

        • competence: precision, intelligence, reliability, education — Fiske et al.'s competence dimension; BSB2022's "Status" PCA factor (articulate, intelligent, confident, trustworthy)
        • warmth: friendliness, spontaneity, casualness, approachability — Fiske et al.'s warmth dimension; BSB2022's "Solidarity" PCA factor (friendly, cool, laid-back, likeable)
        • antiSolidarity: pedantic, uptight — the negative pole of warmth, factored out as an independent PCA component in BSB2022 because pedantic/uptight load separately from the positive warmth scales
        Instances For
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          instance Sociolinguistics.SCM.instDecidableEqSocialDimension :
          DecidableEq SocialDimension
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          instance Sociolinguistics.SCM.instBEqSocialDimension :
          BEq SocialDimension
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          def Sociolinguistics.SCM.instBEqSocialDimension.beq :
          SocialDimension → SocialDimension → Bool
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            def Sociolinguistics.SCM.instReprSocialDimension.repr :
            SocialDimension → ℕ → Std.Format
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              instance Sociolinguistics.SCM.instReprSocialDimension :
              Repr SocialDimension
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              instance Sociolinguistics.SCM.instFintypeSocialDimension :
              Fintype SocialDimension
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              def Sociolinguistics.SCM.SCMProperty.dimension :
              SCMProperty → SocialDimension

              Which dimension a pole belongs to.

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                def Sociolinguistics.SCM.SCMProperty.isPositive :
                SCMProperty → Bool

                Whether a pole is the positive end of its dimension.

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                  def Sociolinguistics.SCM.scmIncompatible :
                  SCMProperty → SCMProperty → Bool

                  Two SCM properties are incompatible iff they are opposite poles of the same dimension: competent/incompetent, warm/cold, solidary/antiSolidary.

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                    theorem Sociolinguistics.SCM.scm_incomp_symm (p q : SCMProperty) (h : scmIncompatible p q = true) :
                    scmIncompatible q p = true
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                    theorem Sociolinguistics.SCM.scm_incomp_irrefl (p : SCMProperty) :
                    scmIncompatible p p = false
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                    def Sociolinguistics.SCM.scmSpace :
                    PropertySpace

                    The SCM property space: 6 properties with 3 incompatibility pairs (opposite poles of each dimension).

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                      theorem Sociolinguistics.SCM.scm_persona_count :
                      scmSpace.allPersonaeSets.card = 8

                      The SCM has exactly 8 personae (2^3 from 3 binary dimensions).

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                      theorem Sociolinguistics.SCM.incomp_same_dimension (p q : SCMProperty) (h : scmIncompatible p q = true) :
                      p.dimension = q.dimension

                      Incompatible properties are always on the same dimension.

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                      theorem Sociolinguistics.SCM.incomp_opposite_polarity (p q : SCMProperty) (h : scmIncompatible p q = true) :
                      p.isPositive ≠ q.isPositive

                      Incompatible properties always have opposite polarity.