Roberts/HT 2013 Week 7


Stratal Optimality Theory

The problem reviewed

Classic OT is structurally incapable of modelling opaque interactions between phonological generalisations, and opaque interactions are attested.

Example: the interaction between Diphthong Raising and [t]-Flapping in Canadian English:

Canadian Diphthong Raising: a historical development of Pre-Fortis Clipping. Diphthongs in the fortis context have higher on-glides: write → [ɹəɪt].
[t]-Flapping: the coronal stops /t/ and /d/ are realized as [ɾ] when between vowels in a syllable that is not foot-initial (roughly).
Raising counterbleeds [t]-flapping: writer is realised as [ɹəɪɾɚɹ], with both rules applying, despite the fact that the environment for Raising is no longer visible on the surface.

A related issue

A matter every theory of phonology has to address is the morphology-phonology interface. We often find that the sound of a word depends on its internal structure.


The stress pattern of an English word depends on the class of its affixes, if any: hélp, hélp-less and hélp-less-ness (with class II affixes) all have initial stress, but stress shifts in n[ˈeɪ]tion, n[ˈæ]tion-al and nation-[ˈæ]l-ity (class I affixes; note that the vowel quality changes in national).
Canadian Raising is also an example; it does not occur when a Class II morpheme boundary intervenes: Eiffel is pronounced [əɪfəl], but eye-ful is pronounced [ɑɪfəl].

It is common for opaque interactions between phonological generalisations to be coincident with complex morphological structure in the words that exemplify them. Practitioners of Stratal Optimality Theory like me believe that this is no accident.

Stratal Optimality Theory

Stratal OT (Bermúdez-Otero 1999, Kiparsky 2000) imports the mechanism for dealing with the morphology-phonology interface from Lexical Phonology and Morphology into Optimality Theory (in fact, Kiparsky’s original name for it was LPM-OT).

Lexical Phonology deals with morphological effects by incorporating the notion of domain. Each domain in LPM has its own co-phonology, with its own set of ordered rewrite rules.


For each domain in Stratal OT, there is a separate Optimality-Theoretic co-phonology, with its own constraint ranking. Therefore, there are two (and only two!) intermediate representations between UR and SR.

Raising and Flapping: once more with counterbleeding

Stem-level constraint ranking:

Input: /ɹɑɪt/ Clip­Diph Clear­Diph Ident-V
a. ɹɑɪt *! *
b. ɹəɪt *

The suffix -er is appended at the word level. We assume that the word-level co-phonology outputs [ɹəɪtɚɹ], which is taken as the input to the phrase-level co-phonology, along with any other words in the utterance.

Phrase-level constraint ranking:

Ident-V, *ˈVtVIdent-C
Input: /ðə ɹəɪtɚɹ əv bʊks/ Ident-V *ˈVtV Ident-C
a. ðə ˌɹɑɪtɚɹ əv ˈbʊks *! *
b. ðə ˌɹəɪtɚɹ əv ˈbʊks *!
c. ðə ˌɹɑɪɾɚɹ əv ˈbʊks *!
d. ðə ˌɹəɪɾɚɹ əv ˈbʊks *

Predictions of Stratal OT

Organising our model of phonology has certain empirical consequences

Opacity only possible between levels

Each level’s co-phonology is a Classic OT machine. Classic OT cannot handle opacity, therefore generalisations with the same domain cannot interact opaquely.

So far this prediction holds up: wherever we observe opacity, we find that the rule that applies first is sensitive to more kinds of boundary than the ones that apply later.

Factorial typology now factorial-cubed typology

To specify a grammar in full, you need to know three constraint rankings.

For each level (assuming they all use the same Con), there are n! possible rankings.

Rankings are formally independent of one another, so there are (n!)3 possible combinations of stem-level, word-level and phrase-level rankings.

This seems like a lot, but there are two reasons not to be worried:

  1. Depending how many new constraints it adds, a theory that tries to handle opacity in a single level may end up with more possible rankings than Stratal OT. The factorial series grows faster than the exponential series, so (3n)! is actually bigger than (n!)3 for values of n > 1

    Therefore, a method of dealing with opacity that involves multiplying |Con| by more than about 2.35 will actually predict more possible grammars than Stratal OT.

  2. In any case, although there is no formal coupling between the levels in Stratal OT, we tend to find that, diachronically, the word-level ranking arises out of previous generations’ phrase-level rankings, and the stem-level ranking out of their word-level rankings. This restricts the number of possible Stratal OT grammars we expect to find in practice even further, and is known as the life cycle of phonological generalisations.

Diachronic predictions — the life cycle

Over time, phrase-level processes tend to become word-level, and word-level processes tend to become stem-level. This observation predates the terminology I’m using, going back at least as far as Baudouin de Courtenay (1895).

An example of this in action is Latin rhotacism Roberts2012:

Phrase-level: intervocalic /s/ tends to be voiced (not directly attested in Latin, but a common precursor to rhotacism in other languages; see Catford 2001).
Word-level generalisation: /s/ surfaces as [r] between vowels. Endings containing [VsV] sequences become lexically [VrV] at this stage, e.g. -ārum, -ōrum, -ērum from earlier [aːzom] etc.
Stem-level generalisation: rhotacism becomes sensitive to morpheme boundaries, e.g. in de-sili-ō ’I jump down’, ni-sī ‘unless’. This replaces the earlier word-level generalisation (cf. Touratier 1975).
Lexical listing: finally, the domain of the generalisation becomes impossible to learn (e.g. because loanwords like basis ‘pedestal’ and cisium ‘cabriolet’ obscure its environment beyond recognition. At this point, the generalisation is lexicalised, i.e. surface [r] is taken to reflect underlying /r/ wherever it is found.


Baudouin de Courtenay, Jan N. I. (1895) Versuch einer Theorie phonetischer Alternationen: ein Kapitel aus der Psychophonetik. Strasbourg: Trübner.

Bermúdez-Otero, Ricardo (1999) Constraint interaction in language change: quantity in English and Germanic. PhD thesis, University of Manchester and Universidad de Santiago de Compostela.

Catford, J. C. (2001) “On Rs, rhotacism and paleophony“ Journal of the International Phonetic Association 31:171‒186.

Kiparsky, Paul (2000) “Opacity and Cyclicity.” The Linguistic Review 17:351‒365.

Roberts, Philip J. (2012) “Latin rhotacism: a case study in the life cycle of phonological processes.” Transactions of the Philological Society 110:80‒93.

Touratier, Christian (2006) “Rhotacisme Synchronique du latin classique et Rhotacisme diachronique.” Glotta 53:246‒281.