Irreducible Parallelism and Desirable Serialism John McCarthy UMass Amherst 1 Background  Harmonic Serialism (HS) is a version of OT with a Gen → Eval → Gen → … loop (Prince & Smolensky, McCarthy).  HS’s Gen, unlike parallel OT’s, is limited to making one change at a time.  Candidates derived by all single changes compete.  Winner goes back into Gen.  This process continues until convergence, when output = input.  E.g., Gen(ktub) = {ktub, uktub, kutub, tub, ktu, …} Gen(uktub) = {uktub, ʔuktub, ktub, uktu, …} Gen(ʔuktub) = {ʔuktub, uktub, ʔuktu, …}  Architectural imperative of HS: harmony improves monotonically through derivation (relative to H). 2 Research Problem and (Ultimate) Goal  Properties of Gen in parallel OT are not usually deemed to be of much interest, except for correspondence theory and representational universals (e.g., Ft > σ in prosodic hierarchy).  Not so in HS. Much depends on what “one change” is — in other words, how is Gen defined.  In today’s talk, I will: o Explain why the “one change” question is important, and how it can be studied. o Scrutinize some particularly challenging cases where it looks like one change is really two (“irreducible parallelism”).  The discussion will rely on certain recurrent themes of HS: 3 Recurrent Themes  No look-ahead: Selection of intermediate optima can’t refer to potential for later improvements. Decisions are made locally, based on information available at that point in the derivation.  Continuous availability of operations: Gen’s operations are not limited to specific derivational steps. They are always freely available.  Emergence of temporary ill-formedness: Violations of markedness constraints, even surface-true ones, may be introduced in the course of the derivation and later eliminated.  Corollary: Apparent non-monotonicity of harmonic improvement: HS architecture guarantees monotonic harmonic improvement through derivation, but it might not always look that way.  Corollary: Revelation of ill-formedness. A structure’s ill- formedness may be disclosed in the course of a derivation, as other structure is built 4 Stating the Question  Assume Gen has certain primitive operations: insert, delete, associate, … (perhaps like Archangeli & Pulleyblank’s parametric rule theory).  Simplest hypothesis: “one change” = a single application of one primitive operation. o Gen(x) = {x, op (x), op (x), …} (op (x) = result of 1 2 n applying the primitive operation op at some locus in x.) n  Question: Does simplest hypothesis suffice? Does Gen ever include candidates like this? o Gen(x) = {…, op (op (x)), …} k j  Question: If simplest hypothesis doesn’t suffice, are there principled limits on combining primitive operations?  Terminology: “Parallel” even if sequential Gen-internally. 5 Irreducible Parallelism  How can we infer that certain primitive operations must be allowed to apply in parallel?  More concretely: o I → O mapping is observed, where O = op (op (I)). 2 1 o Is M = op (I) a necessary intermediate step I → M → O? 1 o Or must op and op apply in parallel, skipping M? 1 2  A priori, I → M → O is preferable because it implies a simpler Gen.  But I → O may be unavoidable if rankings required for I → M and M → O mappings are inconsistent with each other, rest of language, or UG. In that case, op and op are irreducibly 1 2 parallel. (Putative examples later.)  Irreducible parallelism responds to the threat of typological undergeneration: I → O mapping needs an analysis. 6 Desirable Serialism  Arguments for HS over parallel OT are based on avoiding typological overgeneration: o I → O mapping is never observed, where O = op (op (I)). 2 1 o Suppose ranking permutation predicts this mapping in parallel OT. This is typological overgeneration.  Desirable serialism: o Suppose HS mandates intermediate M = op (I) because 1 op and op are not allowed to apply in parallel in Gen. 1 2  If rankings required for I → M and M → O mappings are inconsistent with each other, rest of language, or UG, then HS correctly predicts impossibility of unobserved I → O mapping.  This is desirable serialism: desirable because it avoids typological overgeneration. 7 Desirable Serialism Exemplified (Jesney)  Positional faithfulness wrongly predicts modification of position to facilitate neutralization (Noyer). E.g., initial stress except when first vowel is reducible and second isn’t: /bedu/ → ˈbedu /kaza/ → ˈkazə but /patu/ → pəˈtu I (low) H (Wd) *L A - I (low) D EAD OW LIGN D ˈσ L(ˈσ) → ˈkazə 1 1 kəˈza 1 1 W 1 ˈkaza 2 W L ˈkəza 1 W 1 1 ˈkəzə 1 W L 2 W kəzə 1 W L 2 W → pəˈtu 1 1 ˈpatu 1 W L L ˈpətu 1 W L 1 pətu 1 W 1 8  Problem arises because stress assignment and vowel reduction can vary together across candidates. This is standard for parallel OT.  Now assume that stress assignment and vowel reduction are separate operations that cannot apply in parallel in HS. So candidates can vary in stress location or reduction, but not both: Gen (/patu/) = {patu, ˈpatu, paˈtu, pətu} HS  Winner at Step 1 is ˈpatu: I (low) H (Wd) *L A -L(ˈσ) I (low) D EAD OW L D ˈσ → ˈpatu 1 pətu 1 W L 1 W patu 1 W 1 paˈtu 1 1 W  Derivation converges on ˈpatu at Step 2. Problematic pəˈtu is never even a candidate.  This is desirable serialism: typological overgeneration is avoided if reduction and stress can’t apply in parallel. 9 Further Claims About Desirable Serialism  Disparate processes o Stress and segmental processes (Jesney, Staubs) o Syllabification and segmental processes (Jesney) o Prosodic parsing and epenthesis (Moore-Cantwell)  Same process (iteration, multiple application): o Syllabification (Elfner, Pater) o Metrical foot assignment (Pruitt) o Deletion of segments and features (McCarthy) o Metathesis (McCarthy) o Autosegmental spreading (McCarthy) o Epenthesis (Kimper)  Derivational evidence o Stress and syncope (McCarthy) o Stress and epenthesis (Elfner) o Mora insertion and segmental deletion (Torres-Tamarit) 10