Albright & Hayes (2003): Rules vs. analogy in English past tenses #

@cite{albright-hayes-2003} @cite{berko-1958} @cite{albright-hayes-2002} @cite{mikheev-1997} @cite{pinker-prince-1988} @cite{bybee-moder-1983}

A computational/experimental study of how speakers form past tenses for novel English verbs (wug verbs). The paper's central architectural claim is that morphological knowledge is best modelled as multiple stochastic rules — each with a structural description, a scope, a hit count, and an adjusted-confidence score — and that this model fits human wug-test data better than either a purely analogical model or a single-default-rule dual-mechanism model.

Architectural commitments #

Three positions are at stake:

Single-default-rule dual-mechanism: regular pasts are derived by a single, context-free rule; only irregular pasts are sensitive to phonological context. Predicts that novel-word ratings of regular pasts are invariant in the phonological context of the stem.
Pure analogy (e.g. GCM-style): all generalisation flows from variegated similarity to existing lexemes. No structured rules; the influence of a model form on a novel form can ride on any feature.
Multiple stochastic rules (this paper): the lexicon supplies many rules per change, each restricted to a structurally-defined context. A novel form's past-tense rating depends on the adjusted confidence of the most accurate rule whose structural description it satisfies. Predicts both regular and irregular ratings vary with phonological context — specifically, with island-of-reliability membership.

Empirical core: islands of reliability for both regulars and irregulars #

A&H's central empirical contribution is that wug ratings of regular past tenses also show context sensitivity, contrary to the single-default-rule prediction. The 4-way Core stimulus design crosses island-of-reliability (IOR) status for regulars × IOR for irregulars, and the published rating data show:

ratings F(1, 78) = 27.23, P < 0.0001 main effect of islandhood
production-probability F(1, 78) = 14.05, P < 0.001 main effect of islandhood

with no significant interaction. Both regulars and irregulars are sensitive to IOR membership.

What this file formalises #

This is the second consumer of Paradigms/WugTest.lean (the first is @cite{breiss-katsuda-kawahara-2026}). It supplies:

The 4-way IOR Core wug stem set (example 14 in the paper);
A StochasticRule type with scope/hits/rawConfidence;
A note on Mikheev (1997) lower-confidence-limit adjustment, kept as an abstract specification rather than a numerical implementation;
An AHWugCell type that participates in the WugTest contract via HasAttestation;
A local typeclass HasIORForRegular (binary IOR factor — the WugTest HasFrequency analogue for the discrete IOR dimension);
Two paradigm-level predicates NovelRegularsShowIORGradient and NovelRegularsInvariantInIOR;
A structural discriminator novelRegularsGradient_inconsistent_with_invariance;
A concrete A&H step-function model that satisfies the gradient and hence rules out the single-default-rule prediction by structural impossibility.

Out of scope #

Per CLAUDE.md "do not encode conclusions as definitions": we do not formalise the numerical correlation tables (r = 0.745 etc.) as Lean theorems with rfl proofs. The numbers are reported in prose and the paper-side citation. We formalise the qualitative prediction-shape contrasts that the empirical correlations support.

We also do not implement the @cite{mikheev-1997} lower-confidence-limit interval. The discriminator below depends only on rawConfidence and on the qualitative shape of the prediction (gradient on novel cells across IOR membership), not on the adjustment formula. We expose adjustedConfidence as a placeholder definition equal to rawConfidence so that downstream code can reference the API name; wiring this to a real Wilson interval (or the @cite{albright-hayes-2002} MGL implementation) is deferred.

Albright & Hayes (2003): Rules vs. analogy in English past tenses #

Architectural commitments #

Empirical core: islands of reliability for both regulars and irregulars #

What this file formalises #

Out of scope #

Named cells of Table 3, retained as abbrevs so that #

Sample stems from each cell of Table 3 (example 14) #

Named cells of Table 3, retained as `abbrev`s so that #