Element Theory — vowels, glides, and gutturals as elemental bundles #

@cite{kaye-lowenstamm-vergnaud-1985} @cite{backley-2011} @cite{kaye-lowenstamm-1984} @cite{backley-nasukawa-2010}

Element Theory (ET) builds segments from a small inventory of privative primes called elements. Three resonance elements suffice for the vowel/glide system:

|I| — palatality (front quality); surfaces as [i] in a nucleus, as [j] elsewhere (onset/coda/offglide).
|U| — labiality (rounding); surfaces as [u] in a nucleus, as [w] elsewhere.
|A| — aperture (lowness/openness); surfaces as [a]/[ʌ] in a nucleus, and — per @cite{angoujard-1995} and @cite{faust-lampitelli-2026} — as the resonance element of gutturals when associated to a C-slot. Two further elements, |ʔ| (occlusion, glottal closure) and |h| (noise, frication), specify the consonantal "stop" or "fricative" character of laryngeals/pharyngeals/uvulars.

Following @cite{backley-2011} ch. 2, each element in a segment may be the head (most prominent contributor) or an operator (modifier). The contrast between [ʌ] and [a] in the paper (eq. 21) is precisely a headedness contrast: [ʌ] = bare |A|, [a] = headed |A|. The contrast between pharyngeals (ħ, ʕ) and laryngeals/uvulars (ʔ, h, χ, ʁ) is analogously a headedness contrast on the |A| element (eq. 20).

ET as a FeatureBundle instance, not a parallel framework #

Per the design of Theories/Phonology/Featural/Bundle.lean, FeatureBundle F V is parametric over feature index F and value type V. ET is the instantiation F := Element, V := Headedness:

none at element e means absent from this segment.
some .bare at element e means present as operator.
some .headed at element e means present as head.

Lionnet's Subtonal feature bundle in Theories/Phonology/Autosegmental/RegisterTier.lean is the binary-feature instantiation F := Subtonal, V := Bool. Hayes-style binary features in Theories/Phonology/Featural/Features.lean are the instantiation F := Feature, V := Bool (after a thin Segment wrapper).

The shared OCP-merger operation lives at the tier level (Phonology.Tier.ocpCollapse in OCPMerger.lean) and works uniformly for all three instantiations. The framework-divergence between Hayes binary, Lionnet subtonal, and ET privative-with-head lives at the segment representation level — different (F, V) choices commit to different theories of what makes two segments "the same".

Scope #

This file provides the substrate. Per CLAUDE.md fragment-schema discipline, ET decompositions of specific languages (Tigrinya gutturals, Tigre vowels) are paper-specific projections and live in study files (e.g. Phenomena/Phonology/Studies/FaustLampitelli2026.lean), not in fragment files.

The full Backley 2011 inventory adds tonal elements |H| and |L| (omitted here — they belong with Phonology.Autosegmental.RegisterTier's TRN substrate when needed). Charm (@cite{kaye-lowenstamm-vergnaud-1985}) is omitted following @cite{backley-2011}'s textbook synthesis, which abandoned charm in favour of headedness as the prominence-encoding device.