PhonologicalFeature
The inductive type enumerates the five phonological feature axes place, manner, voicing, nasality and roundness that arise for configDim equal to 5. Researchers applying Recognition Science to language acquisition cite this enumeration to fix the SPE feature matrix for phoneme inventories. The declaration is a direct inductive definition that derives decidable equality and finite type structure.
claimLet $F$ be the finite set of phonological features $F = $ {place, manner, voicing, nasality, roundness}, equipped with decidable equality and Fintype structure, with cardinality 5.
background
In the Recognition Science linguistics module, configDim is the dimension of the configuration space; here it is specialized to D = 5 to generate the canonical phonological axes. The module states that these five axes (place of articulation, manner of articulation, voicing, nasality, roundness) span the SPE (Chomsky-Halle) feature matrix that produces every attested phoneme inventory. Lean status is zero sorry and zero axiom.
proof idea
The declaration is an inductive definition that introduces exactly five constructors, one for each feature axis. It automatically derives the instances DecidableEq, Repr, BEq and Fintype, which together establish that the type is finite with cardinality five.
why it matters in Recognition Science
This definition supplies the concrete feature set used by PhonologicalFeatureCert and the theorem phonologicalFeature_count, both of which assert Fintype.card = 5. It feeds LanguageAcquisitionCert in the sibling module, where feature_count equals 5 and critical_period_threshold is a CanonicalCert. The enumeration aligns with the configDim = 5 specialization and supports the claim that language acquisition thresholds derive from J-cost; it touches the open question of how configDim = 5 emerges from the T0-T8 forcing chain.
scope and limits
- Does not derive the choice of these five axes from J-uniqueness or the phi-ladder.
- Does not address cross-linguistic variation or alternative feature systems.
- Does not connect the features to spatial dimension D = 3 or the eight-tick octave.
- Does not map the features onto physical constants such as alpha or G.
formal statement (Lean)
18inductive PhonologicalFeature where
19 | place
20 | manner
21 | voicing
22 | nasality
23 | roundness
24 deriving DecidableEq, Repr, BEq, Fintype
25