MaxEnt Gradient Variation #
@cite{goldwater-johnson-2003}
Predicates for reasoning about gradient phonological variation in Maximum Entropy Harmonic Grammar. Since exp is monotone, the harmony ordering directly determines the probability ordering:
H(a) > H(b) ⟺ P(a) > P(b)
This makes moreProbable a computable, decidable proxy for
probability comparison without requiring real-number arithmetic.
@[reducible]
def
Theories.Phonology.HarmonicGrammar.moreProbable
{C : Type}
(constraints : List (WeightedConstraint C))
(a b : C)
:
One candidate is more probable than another under a MaxEnt grammar when its harmony score is strictly higher.
Justified by monotonicity of exp: exp(H(a)) > exp(H(b)) ⟺ H(a) > H(b),
so harmony ordering = probability ordering.
Equations
- Theories.Phonology.HarmonicGrammar.moreProbable constraints a b = (Theories.Phonology.HarmonicGrammar.harmonyScore constraints a > Theories.Phonology.HarmonicGrammar.harmonyScore constraints b)