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Linglib.Phenomena.Phonotactics.Studies.HayesWilson2008

@cite{hayes-wilson-2008}: A Maximum Entropy Model of Phonotactics #

@cite{hayes-wilson-2008}

@cite{hayes-wilson-2008} propose that phonotactic well-formedness is probability: a MaxEnt grammar assigns each surface form a score h(x) = Σ wⱼ · Cⱼ(x), and well-formedness is P(x) = exp(−h(x)) / Z.

Hayes & Wilson's "score" is the negation of harmonyScore: h(x) = −harmonyScore(x), so P(x) ∝ exp(harmonyScore(x)). Higher harmony = higher probability = better well-formedness. This is exactly softmax(harmonyScoreR, 1) on a finite candidate set.

Key contribution: ganging #

The central empirical prediction distinguishing MaxEnt from OT is ganging: two individually weak constraints can jointly override a stronger one. This is impossible with OT's strict ranking, which corresponds to exponentially separated weights (OTLimit.lean).

The Ganging definition and anti-ganging theorems live in OTLimit.lean alongside ExponentiallySeparated, since they are two sides of the same coin.

English onset data #

We encode a subset of the learned grammar (Table (4)) and verify that the model assigns higher harmony (= higher MaxEnt probability via exp_lt_exp) to attested onsets than to unattested ones (§2).

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@[reducible, inline]
abbrev Phenomena.Phonotactics.Studies.HayesWilson2008.Onset :
Type

An English onset: a list of consonants preceding the nucleus.

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    def Phenomena.Phonotactics.Studies.HayesWilson2008.c1_star_son_dors :
    Theories.Phonology.HarmonicGrammar.WeightedConstraint Onset

    Constraint #1 from Table (4): *[+sonorant, +dorsal]. Weight 5.64.

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      def Phenomena.Phonotactics.Studies.HayesWilson2008.c4_star_blank_cont :
      Theories.Phonology.HarmonicGrammar.WeightedConstraint Onset

      Constraint #4 from Table (4): *[ ][+continuant]. Weight 5.17.

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        def Phenomena.Phonotactics.Studies.HayesWilson2008.c5_star_blank_voice :
        Theories.Phonology.HarmonicGrammar.WeightedConstraint Onset

        Constraint #5 from Table (4): *[ ][+voice, −sonorant]. Weight 5.37.

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          def Phenomena.Phonotactics.Studies.HayesWilson2008.c6_star_son_blank :
          Theories.Phonology.HarmonicGrammar.WeightedConstraint Onset

          Constraint #6 from Table (4): *[+sonorant][ ]. Weight 6.66.

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            def Phenomena.Phonotactics.Studies.HayesWilson2008.onsetGrammar :
            List (Theories.Phonology.HarmonicGrammar.WeightedConstraint Onset)

            The subset grammar: 4 constraints from Table (4).

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.k_harmony :
              Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.k] = 0

              Attested onset [k]: harmony = 0 (no violations).

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.ŋ_harmony :
              Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.ŋ] = -(564 / 100)

              Unattested onset *[ŋ]: harmony = −5.64 (violates *[+son,+dors]).

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.rk_harmony :
              Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.r, Fragments.English.Phonology.k] = -(666 / 100)

              Unattested onset *[rk]: harmony = −6.66 (violates *[+son][ ]).

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.attested_higher_harmony_k_ŋ :
              Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.ŋ] < Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.k]

              Attested [k] has higher harmony than unattested *[ŋ].

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.attested_higher_harmony_br_rk :
              Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.r, Fragments.English.Phonology.k] < Theories.Phonology.HarmonicGrammar.harmonyScore onsetGrammar [Fragments.English.Phonology.b, Fragments.English.Phonology.r]

              Attested [br] has higher harmony than unattested *[rk].

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.maxent_prob_k_gt_ŋ :
              Real.exp (Theories.Phonology.HarmonicGrammar.harmonyScoreR onsetGrammar [Fragments.English.Phonology.ŋ]) < Real.exp (Theories.Phonology.HarmonicGrammar.harmonyScoreR onsetGrammar [Fragments.English.Phonology.k])

              MaxEnt probability ordering: higher harmony ⟹ higher exp(harmonyScore) ⟹ higher MaxEnt probability.

              Applies exp_lt_exp (Mathlib) to harmonyScoreR (HarmonicGrammar.Basic).

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              theorem Phenomena.Phonotactics.Studies.HayesWilson2008.gradient_prob_ŋ_gt_rk :
              Real.exp (Theories.Phonology.HarmonicGrammar.harmonyScoreR onsetGrammar [Fragments.English.Phonology.r, Fragments.English.Phonology.k]) < Real.exp (Theories.Phonology.HarmonicGrammar.harmonyScoreR onsetGrammar [Fragments.English.Phonology.ŋ])

              Gradient well-formedness: among unattested forms, *[ŋ] has higher MaxEnt probability than *[rk]. Uses exp_lt_exp.