Hansson (2010) @cite{hansson-2010} #

Consonant Harmony: Long-Distance Interaction in Phonology. University of California Publications in Linguistics 145.

@cite{hansson-2010} surveys ~175 cases of long-distance consonant agreement across >130 languages, organized by harmonizing property (coronal/sibilant, dorsal, labial, secondary-articulation, nasal, liquid, stricture, laryngeal). The formal analysis is a modified Agreement-by-Correspondence model after @cite{rose-walker-2004}, with two theoretical refinements: (a) C-C correspondence is construed as directionally asymmetric (strictly anticipatory), and (b) the relevant agreement constraints are formulated as targeted constraints in the Wilson sense.

What this file formalizes (and what it does not) #

We do not formalize Hansson's correspondence apparatus, his targeted-constraint architecture, or his speech-error / palatal-bias arguments — those live in the OT layer and the speech-planning literature. What we formalize here is the surface stringset of one of the leading case studies — Navajo sibilant harmony, prominently featured in @cite{hansson-2010}'s introduction (§1.1) and discussed in detail in §2.4.1.1 — as a tier-based strictly 2-local language, following the subregular tradition (@cite{mcmullin-2016}).

The framing is the same as in RoseWalker2004.lean: the ABC-style analysis derives the surface generalization; the TSL_2 description characterizes the surface stringset. The two analyses operate at different levels and are not in competition for the same explanatory work.

Sibilant harmony is a symmetric dissimilation-style phonotactic — the forbidden pair is "tier-adjacent and unequal" — so this study is the canonical instance of the AGREE specialization in Theories/Phonology/Subregular/Agree.lean, the non-identity dual of the OCP (@cite{goldsmith-1976}, @cite{mccarthy-1986}). The Kikongo case in RoseWalker2004.lean is asymmetric and instantiates the generic forbidden-pair constructor directly rather than via AGREE.

Design boundary #

Things this formalization is silent on, by design:

Directionality: @cite{hansson-2010} argues consonant harmony is strictly anticipatory (right-to-left). The TSL_2 description with symmetric forbidden pairs licenses the surface stringset regardless of which segment "triggered" the harmony — the directional derivation lives in the OT/ABC layer.
Stem control / trigger-target asymmetry: the targeted-constraint architecture distinguishes the feature source from its target. Single-tier TSL with a fixed predicate has no notion of source vs target.
Similarity scaling: in ABC, the CORR-C↔C constraint family is scaled by featural similarity and distance (@cite{hansson-2010} §4.2.1.1) — only sufficiently similar consonants enter into correspondence. The TSL_2 stringset is sharp.
Speech-error parallels (palatal bias): @cite{hansson-2010}'s chapter 6 argues that consonant harmony has its roots in speech-planning errors, with the palatal bias as the central diagnostic. This is an extragrammatical claim outside any synchronic surface description.
Similarity-graded transparency vs opacity: @cite{hansson-2010}'s chapter 3 reviews cases where intervening segments behave differently depending on how similar they are to the harmonizing pair. Single-tier TSL with a fixed tier predicate cannot express this — see the design-boundary docstring on tierProject non-monotonicity in ForbiddenPairs.lean, and the load-bearing gradient-OCP instance in Phenomena/Phonology/Studies/FrischPierrehumbertBroe2004.lean, which formalises @cite{frisch-pierrehumbert-broe-2004}'s natural-classes similarity metric (eq. 7) and proves no similarity-threshold TSL_2 grammar can match three Table IV bins. Closely related: the autosegmental/feature-geometry tradition (@cite{sagey-1986}) treats the harmonizing feature itself as a tier-resident object; that representational layer is upstream of the surface stringset characterized here.

Function-level subregular classification (cross-reference) #

The TSL_2 description here characterizes the stringset of Navajo sibilant harmony — the language that the harmony filter accepts. The function that maps an underlying form to its surface realization admits a separate subregular classification per Core/Computability/Subregular/Function/: long-distance consonant agreement is generally Tier-Subsequential (not ISL or OSL — those require a contiguous k-window), and per @cite{hansson-2010}'s strictly-anticipatory directionality argument it is specifically Right-Tier-Subsequential. We do not encode the function-level classification here; the language-level TSL_2 statement is the cleaner unit because the directionality is upstream and the surface filter is direction-symmetric.

Navajo sibilant harmony — the leading case #

Navajo (Athapaskan; @cite{hansson-2010} §1.1, §2.4.1.1) has two contrasting sibilant series: an alveolar series {s, z, ts, tsʼ, dz} and a postalveolar series {ʃ, ʒ, tʃ, tʃʼ, dʒ}. A sibilant in the verb root determines the realization of all sibilants in preceding "conjunct" prefixes. For example (data from McDonough 1991, cited as Hansson's example (6)): underlying /si-dʒéːʔ/ surfaces as [ʃidʒéːʔ] 'they lie (slender stiff objects)' — the alveolar /s/ in the prefix harmonizes to the postalveolar place of the root /dʒ/; underlying /ʃ-is-ná/ surfaces as [sisná] 'he carried me' — the postalveolar /ʃ/ in the prefix harmonizes to the alveolar place of the root /s/.

The surface generalization: no two sibilants of differing place (anterior vs posterior) may co-occur within the harmonic domain. Equivalently, every tier-adjacent pair of sibilants must agree in place — the TSL_2 instance of TSLGrammar.agree.

Hansson (2010) @cite{hansson-2010} #

What this file formalizes (and what it does not) #

Design boundary #

Function-level subregular classification (cross-reference) #

Navajo sibilant harmony — the leading case #

§ 6.1 The SP_2 formalisation of Navajo #

§ 6.2 Agreement on Navajo's transparent inputs #

§ 6.3 Where the two diverge: blocker-style opacity #