Graded Constraints in English Word Forms: Theory and Data James L. McClelland and Brent C. Vander Wyk Graded Constraint Theory Agrees with classical OT that there are violable constraints. Also consistent with natural phonology and the thinking of many others now emphasizing graded constraints (Boursma, Hayes and Wilson, Burzio, Harris, Hammond ) Does not insist on strict ranking, allowing constraints to combine to determine the overall goodness of forms. What can and cannot occur is determined by the cumulative weight of the constraints. Weights can be such that strict ranking effects occur, but there can also be graded effects: Forms that violate a constraint can just be less common than forms that do not. Forms that violate different constraints can be about equally good, if the constraints that each violates have about the same weight. Why Care? GCT accounts for data showing there are graded patterns in: language structure language judgments the time it takes to speak Even if you only care about what does and does not occur: GCT can lead to a simpler theory. Overview Unit of analysis, corpus, and evidence of graded constraints. Tenets of Graded Constraint Theory Non-parametric and parametric corpus analysis Rating experiments Production duration experiment Unit of Analysis: The Rhyme Type Rhyme Type = Vowel Type (V or VV) + Following Consonants Vt:bat, pet, mit VVt: bait, mite, shout VVks:hoax, coax Corpus Pronunciations of Monomorphemic Monosyllabic entries in the CELEX lemma corpus, when used in stressed contexts: This is the Book Excludes all forms that even hint at morphological complexity, including: wealth, first Uses Received Pronunciation so no /r/ in coda (fahm not farm). Measure: Observed per-vowel occurrence rate The number of different lemmas of each rhyme type divided by the number of vowels of the given type (5 for short vowels, 10 for long vowels). There are 113 words with the Vt rhyme type, so its rate is: 113/5 = 22.6 Analysis focuses on the number of lemmas, regardless of each lemmas frequency. Phonologically identical lemmas count twice, e.g. bat. t d V VV p b k g V VV V Data Suggests Graded Constraints Against: -Voiced consonants - Long vowels -Non-coronals Evidence of Graded Constraints Effect of coda embellishments In every case, the embellishment reduces the number of word forms containing the indicated coda. Some go below threshold. V Effect of coda embellishments (contd) Same thing happens here more cases below threshold because of the added constraint. VV Hard and Soft Constraints The Template (fill slots from left to right): Hard constraints: Bare short vowels do not occur in stressed monosyllables Nasals share place w/ following Cs; Obstruents must agree in voicing No geminates allowed (e.g., *tt). Soft Constraints: Added segments of any type X Long vowels [long]/V Voiced obstruents [voi]/O Non-coronal articulations [-cor]/O Non-alv place for coronal fricatives [-alv]/F[cor] Summary of constraints: Keep it short, simple, coronal, and unvoiced. Partial Ordering Law For forms i and i: If i violates a proper superset of the constraints violated by i, then i should occur less frequently than i, or neither should occur at all. Definitions: Base form, immediate descendent: An immediate descendent i of a base form i violates the same constraints as i plus one additional constraint. Partial Ordering Graph for legal rhymes containing at least one stop and at most two consonants Overall Partial Ordering Results 20 violations out of 363 base/immediate descendent pairs involving at most two coda consonants; only 13 of the violations were statistically significant. The few three-consonant codas are always rarer than any of the base forms of which they are immediate descendents. - E.g. Vkst < Vks, Vkt, Vst. The constraint against adding segments, X is very robust: one violation: - V < V k (sing / sink) The constraint against voiced obstruents, VO is also quite robust: - There are just two violations: Vlt