PhonologicalFeature
plain-language theorem explainer
The inductive definition enumerates five phonological feature classes for the Recognition Science treatment of language acquisition. Researchers modeling the critical period via J-cost on plasticity ratios would cite this enumeration to fix the feature count at five. The definition lists the constructors explicitly and derives Fintype, DecidableEq, and related type classes in one step.
Claim. The type of phonological features is the inductive type whose constructors are vowel, consonant, tone, stress, and prosody, equipped with decidable equality, representation, boolean equality, and finite type structure.
background
The Language Acquisition Critical Period from J-Cost module models Lenneberg's critical period through the J-cost J(r) applied to the synaptic plasticity ratio r. Peak childhood plasticity gives r = 1 and J(r) = 0; entry into the J(phi) band raises acquisition difficulty, while r < 1/phi renders near-native fluency impossible. The module fixes configDim D = 5, so that each of the five feature classes is independently subject to the same threshold.
proof idea
The declaration is an inductive definition that introduces the five constructors and attaches the deriving clause for DecidableEq, Repr, BEq, and Fintype. No tactics or lemmas are invoked; the Fintype instance is generated automatically from the finite list of constructors.
why it matters
This definition supplies the concrete feature set required by the LanguageAcquisitionCert structure, which records both the cardinality five and the critical period threshold via CanonicalCert. It thereby connects the config-dimension count to the J-cost acquisition model and aligns with the parallel five-feature enumeration in PhonologicalFeaturesFromConfigDim. The construction touches the open mapping from individual features to specific J(phi) thresholds.
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