Sen (2015): Latin /l/ Allophony as Positional Underspecification [Sen15]

Latin /l/ has clear ([l]) and dark ([ɫ]) realisations whose distribution [Sen15] ch. 2 analyses as positional underspecification of the feature [back]. The chosen formal analysis (§2.4, eq. 23) settles on an equipollent specification in which all three positional /l/ allophones share a tongue-body-displacement feature [+high] while differing on [back]: coda /l/ is [+high, +back] (dark), geminate /ll/ is [+high, −back] (clear), and onset /l/ is [+high, Ø back] — left unspecified for [back] and inheriting a surface value from the following vowel by categorical spreading (cf. [Kea88], with the categorical-vs-gradient distinction discussed under Implementation notes).

This file derives the three positional /l/ allophones from the Latin Fragment's single /l/ phoneme via Segment.setFeature, implements the inheritance mechanism as categorical feature spreading through Segment.fillFromContext (with the spreading theorem surfaceL_inherits_back and worked surface theorems for onset /l/ before each Latin short vowel), and proves the categorical context-invariance of coda /l/ and geminate /ll/, illustrating that fillFromContext is feature-filling rather than feature-overwriting.

Main definitions

• lWithDorsal — the Fragment's /l/ with [+high] added (Sen's dorsal articulation, shared by all three positional allophones).
• lOnset — onset /l/: [+high, Ø back].
• lCoda — coda /l/: [+high, +back] (dark).
• lGeminate — geminate /ll/: [+high, −back] (clear).
• surfaceL — feature spreading applied to onset /l/.
• surfaceCoda, surfaceGem — spreading applied to the already- specified coda and geminate values (no-op for [back]).

Main results

• surfaceL_inherits_back — onset /l/ takes its surface [back] value from the following segment.
• surfaceL_before_{i,e,o,u} — concrete realisations from the Fragment's four primary short vowels: clear before front vowels, dark before back vowels.
• surfaceL_before_a — Fragment/Sen divergence on /a/: the Fragment encodes /a/ as [Ø back] (Hayes 2009 convention), so the categorical model leaves onset /l/ at [Ø back]; Sen groups /a/ as a darkening context for onset /l/.
• surfaceCoda_*, surfaceGem_* — coda and geminate /l/ stay at their underlying [back] value regardless of context.

Implementation notes

The Latin Fragment exposes a single /l/ phoneme. The three positional allophones are derived here by Segment.setFeature on Latin.Phonology.l, with the dorsal [+high] articulation that distinguishes /l/'s phonetic profile factored into lWithDorsal. Sen's analysis treats this dorsal raising as common to all three /l/ allophones — only [back] distinguishes them at the underlying level.

The spreading theorems use Segment.fillFromContext rather than the overwriting Segment.setFeature: the operation is filling, which preserves the existing value of [back] on coda and geminate /l/ even when they are followed by a vowel with a conflicting [back] specification. The surfaceCoda_* and surfaceGem_* theorems witness this behaviour end-to-end.

Categorical vs. gradient layer. This file formalises Sen's categorical phonological analysis (eq. 19/23): the ternary [back] underspecification, and the prediction that an unspecified target inherits the immediately following specified value. Sen's full account adds a gradient phonetic interpolation layer (§2.4-2.5, Fig. 2.3) in which surface darkness varies along a gradient scale running from darkest (coda) through onset /l/ before /a o u/, then /e/, then /e:/, to clearest (onset before /i/ and geminate /ll/); in particular, onset /l/ before /e/ is "dark" in Sen's gradient picture while the categorical model formalised here has /l/ inherit /e/'s [−back] and surface "clear". On p. 41 Sen explicitly rejects synchronic categorical feature spreading as the actuating mechanism, on the grounds that it would over-predict identical effects in identical-feature contexts; the substrate's fillFromContext is exactly such a categorical operation — Keating's schema (2) case (b) ([Kea88] p. 287), in which the target acquires a feature value from its neighbour, rather than her case (c) gradient phonetic interpolation in which the target stays unspecified and the phonetics builds a continuous trajectory through it. The categorical underspecification claim is captured faithfully; the gradient phonetic implementation, which is what Keating's own term interpolation picks out, is out of scope.

Fragment-vs-Sen divergence on /a/. The Latin Fragment leaves /a/ unspecified for [back] (following [Hay09]'s convention that low vowels carry no primary [back] value), so the categorical fillFromContext leaves onset /l/ before /a/ at [Ø back]. Sen instead groups /a/ with /o u/ as a darkening context for onset /l/ (§2.3.1, Fig. 2.2), which would require either encoding /a/ as [+back] in Latin or modelling Keating's propagation across the underspecified intermediate. surfaceL_before_a records what the categorical model and the Fragment's vowel inventory predict, not Sen's empirical claim.

Diachronic content out of scope. [Sen15] also develops a diachronic account (the historical loss of geminate /l/, inverse compensatory lengthening, the prehistory of clear/dark /l/ split); this study formalises only the synchronic underspecification analysis of ch. 2. The parallel analysis for /r/ (vowel reduction before TR clusters) in ch. 4 is also deferred.

Todo

• Multi-segment interpolation across consonant + vowel sequences, once Segment.fillFromContextTier lands in the Underspec substrate.
• The parallel reduction analysis for /r/ (Sen ch. 4).

Positional /l/ values

The Fragment's l lacks a [high] specification. Sen 2015 ch. 2 analyses all three positional allophones as bearing [+high] (the dorsal articulation that distinguishes /l/ from a pure alveolar). The three allophones diverge on [back] alone: coda [+back], geminate [−back], onset [Ø back].

def Sen2015.lWithDorsal : Phonology.Segment

The Fragment's /l/ extended with the dorsal [+high] specification common to all three positional allophones.

Equations

• Sen2015.lWithDorsal = Latin.Phonology.l.setFeature Phonology.Feature.high true

def Sen2015.lOnset : Phonology.Segment

Onset /l/: [+high] with [back] left unspecified for Keating-style interpolation from the following vowel.

Equations

• Sen2015.lOnset = Sen2015.lWithDorsal

def Sen2015.lCoda : Phonology.Segment

Coda /l/ (dark [ɫ]): [+high, +back].

Equations

• Sen2015.lCoda = Sen2015.lWithDorsal.setFeature Phonology.Feature.back true

def Sen2015.lGeminate : Phonology.Segment

Geminate /ll/ (clear [l]): [+high, −back].

Equations

• Sen2015.lGeminate = Sen2015.lWithDorsal.setFeature Phonology.Feature.back false

Underlying specification status

theorem Sen2015.lOnset_unspecified_back : lOnset.Unspecified Phonology.Feature.back

Onset /l/ is unspecified for [back]: the Keating interpolation target.

theorem Sen2015.lCoda_back : lCoda.HasValue Phonology.Feature.back true

Coda /l/ is [+back] underlyingly (dark).

theorem Sen2015.lGeminate_front : lGeminate.HasValue Phonology.Feature.back false

Geminate /l/ is [−back] underlyingly (clear).

theorem Sen2015.all_lAllophones_high : lOnset.HasValue Phonology.Feature.high true ∧ lCoda.HasValue Phonology.Feature.high true ∧ lGeminate.HasValue Phonology.Feature.high true

All three positional /l/ allophones are [+high] (Sen's dorsal articulation).

Keating interpolation on onset /l/

Onset /l/ inherits its surface [back] value from the following segment. The general theorem surfaceL_inherits_back exhibits the mechanism; the per-vowel theorems below are concrete instances.

def Sen2015.surfaceL (ctx : Phonology.Segment) : Phonology.Segment

Surface form of onset /l/ before a context segment, via Keating interpolation on [back].

Equations

• Sen2015.surfaceL ctx = Sen2015.lOnset.fillFromContext Phonology.Feature.back ctx

theorem Sen2015.surfaceL_inherits_back (ctx : Phonology.Segment) : surfaceL ctx Phonology.Feature.back = ctx Phonology.Feature.back

The key theorem: onset /l/'s surface [back] equals the following segment's [back] value, by fillFromContext applied to an unspecified target.

theorem Sen2015.surfaceL_before_i : (surfaceL Latin.Phonology.i).HasValue Phonology.Feature.back false

Onset /l/ before /i/ surfaces clear ([−back]): /i/ is [−back].

theorem Sen2015.surfaceL_before_e : (surfaceL Latin.Phonology.e).HasValue Phonology.Feature.back false

Onset /l/ before /e/ inherits /e/'s [−back] in the categorical model, predicting clear /l/. Sen's gradient phonetic analysis (Fig. 2.2, p. 33) treats this context as "Dark" — relatively dark, dark enough to colour a preceding vowel — a distinction the categorical layer formalised here does not capture.

theorem Sen2015.surfaceL_before_o : (surfaceL Latin.Phonology.o).HasValue Phonology.Feature.back true

Onset /l/ before /o/ surfaces dark ([+back]): /o/ is [+back].

theorem Sen2015.surfaceL_before_u : (surfaceL Latin.Phonology.u).HasValue Phonology.Feature.back true

Onset /l/ before /u/ surfaces dark ([+back]): /u/ is [+back].

theorem Sen2015.surfaceL_before_a : (surfaceL Latin.Phonology.a).Unspecified Phonology.Feature.back

Fragment-vs-Sen divergence on /a/: the Latin Fragment encodes /a/ as [Ø back] (Hayes 2009 convention for low vowels), so the categorical fillFromContext leaves onset /l/ before /a/ at [Ø back]. Sen instead groups /a/ with /o u/ as a darkening context for onset /l/; this theorem records what the Fragment's vowel inventory and the categorical model predict, not Sen's empirical claim.

Context-invariance of categorically-specified /l/

Coda /l/ and geminate /l/ have [back] specified underlyingly, so fillFromContext is a no-op for them: they retain their categorical [back] value regardless of the following segment.

def Sen2015.surfaceCoda (ctx : Phonology.Segment) : Phonology.Segment

Surface form of coda /l/ in some right context.

Equations

• Sen2015.surfaceCoda ctx = Sen2015.lCoda.fillFromContext Phonology.Feature.back ctx

def Sen2015.surfaceGem (ctx : Phonology.Segment) : Phonology.Segment

Surface form of geminate /l/ in some right context.

Equations

• Sen2015.surfaceGem ctx = Sen2015.lGeminate.fillFromContext Phonology.Feature.back ctx

theorem Sen2015.surfaceCoda_invariant (ctx : Phonology.Segment) : (surfaceCoda ctx).HasValue Phonology.Feature.back true

Coda /l/ stays [+back] for any context, by fillFromContext applied to an already-specified target.

theorem Sen2015.surfaceGem_invariant (ctx : Phonology.Segment) : (surfaceGem ctx).HasValue Phonology.Feature.back false

Geminate /l/ stays [−back] for any context.

theorem Sen2015.surfaceCoda_before_i : (surfaceCoda Latin.Phonology.i).HasValue Phonology.Feature.back true

Concrete witness: coda /l/ followed by the front vowel /i/ stays dark, contrasting with surfaceL_before_i where onset /l/ surfaces clear.

theorem Sen2015.surfaceGem_before_o : (surfaceGem Latin.Phonology.o).HasValue Phonology.Feature.back false

Concrete witness: geminate /l/ followed by the back vowel /o/ stays clear, contrasting with surfaceL_before_o where onset /l/ surfaces dark.

Cross-feature preservation

The interpolation modifies only [back]; the dorsal [+high] specification and every other feature on onset /l/ pass through unchanged.

theorem Sen2015.surfaceL_high (ctx : Phonology.Segment) : (surfaceL ctx).HasValue Phonology.Feature.high true

Onset /l/'s [+high] dorsal articulation survives interpolation.