Roberts/HT 2014 Week 2

Phonology

Nuts and Bolts of OT: Building foot structure.

Footing parameters vs. OT constraints

Foot structure in Metrical Phonology (Hayes 1995, Liberman and Prince 1977)

Parameters:

Typological predictions:

Two settings for each of four parameters = 2⁴ = 16 different behaviours (× all the different kinds of extrametricality!)

Foot structure in Optimality Theory (Kager 1999: 161ff.)

A constraint schema: Generalized Alignment (McCarthy and Prince 1993)

Align-[Cat₁, Edge₁, Cat₂, Edge₂]

Where Cat₁, Cat₂ ∈ {Prosodic categories} ∪ {Grammatical Categories}, Edge₁, Edge₂ ∈ {Right, Left}

For every Edge₁ of a Cat₁ that is not coincident with an Edge₂ of a Cat₂, assess a number of violations commensurate with the amount of material that intervenes.

Examples:

Factorial typology:

10 different constraints ∴ 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800 possible constraint rankings.

but, many rankings will predict equivalent grammars!

Note that McCarthy (2003) modifies the definition of Generalized Alignment he and Prince put forward in McCarthy and Prince (1993): the definition of Alignment we’re working with here is 1993-vintage, with one violation per syllable between the edges that the constraint wants to align. 2003-vintage Alignment constraints are argued to be categorical: for every pair of edges they examine, they are allowed to assess either one violation (if they are not aligned) or none at all (if they are). McCarthy’s arguments are based on the different typological predictions and computational requirements of categorical vs. gradient constraints, and I commend them to your attention.

OT footing in practice: the Latin penultima rule.

/murmuris/ FtBin NonFinality Weight-To-Stress FtType(T) Parse-σ Align-[Σ, R; ω, R] Align-[Σs, R; ω, R]
1.(ˈmur.mu)ris * * * *
2.(ˈmur)mu.ris * **! ** **
3.(mur.ˈmu)ris **! * * * *
4.(ˌmur.mu)(ˈris) *! *
5.(ˈmur.mu)(ˌris) *! * *
6.(ˌmur)mu(ˈris) *! * **
7.(ˈmur)mu(ˌris) *! * ** **
8.(ˌmur)(mu.ˈris) *! * **
9.(ˈmur)(mu.ˌris) *! * ** *
10.(ˌmur)(ˈmu.ris) *! * **
11.(ˈmur)(ˌmu.ris) *! * ** *
12.mur.mu(ˈris) *! * **
13.(mur.ˌmu)(ˈris) *! * * *
14.(mur.ˈmu)(ˌris) *! * * * *
15.mur(mu.ˈris) *! * * *
16.mur(ˈmu.ris) *! ** *
17.(ˌmur)(ˈmu)ris *! * * *** *
18.(ˈmur)(ˌmu)ris *! * * *** **
19.mur(ˈmu)ris *! ** ** * *
20.(ˌmur)(ˌmu)(ˈris) *! * ***
21.(ˈmur)(ˌmu)(ˌris) *! * *** **
22.(ˈmur.mu.ris) *! * *
23.mur(ˌmu)(ˈris) *! * * * *
24.mur(ˈmu)(ˌris) *! * * * * *
25.(mur.mu.ˈris) *! * * *

The comparative tableau (Prince 2002)

/refektus/ FtBin NonFinality Weight-To-Stress FtType(T) Parse-σ Align-[Σ, R; ω, R] Align-[Σs, R; ω, R]
re(ˈfek)tus 0 0 1 0 2 1 1
1.(re.ˈfek)tus 0 0 1 1W 1L 1 1
2.(ˈre.fek)tus 0 0 2W 0 1L 1 1
3.re(ˌfek)(ˈtus) 0 1W 0L 0 1L 1 0L
4.re(ˈfek)(ˌtus) 0 1W 0L 0 1L 1 1
5.(re.ˌfek)(ˈtus) 0 1W 0L 1W 0L 1 0L
6.(re.ˈfek)(ˌtus) 0 1W 0L 1W 0L 1 1
7.(ˌre.fek)(ˈtus) 0 1W 1 0 0L 1 0L
8.(ˈre.fek)(ˌtus) 0 1W 1 0 0L 1 1
9.re(ˈfek.tus) 0 1W 1 0 1L 0L 0L
10.re.fek(ˈtus) 0 1W 1 0 2 0L 0L
11.re(fek.ˈtus) 0 1W 1 1W 1L 0L 0L
12.(ˌre)(ˈfek)tus 1W 0 1 0 1L 3W 1
13.(ˈre)(ˌfek)tus 1W 0 1 0 1L 3W 2W
14.(ˈre)fek.tus 1W 0 2W 0 2 2W 2W
15.(ˌre)(ˌfek)(ˈtus) 1W 1W 0L 0 0L 3W 0L
16.(ˈre)(ˌfek)(ˌtus) 1W 1W 0L 0 0L 3W 2W
17.(ˌre)(ˈfek.tus) 1W 1W 1 0 0L 2W 0L
18.(ˈre)(ˌfek.tus) 1W 1W 1 0 0L 2W 1
19.(ˌre)fek(ˈtus) 1W 1W 1 0 1L 2W 0L
20.(ˈre)fek(ˌtus) 1W 1W 1 0 1L 2W 2W
21.(re.fek.ˈtus) 1W 1W 1 1W 0L 0L 0L
22.(ˌre)(fek.ˈtus) 1W 1W 1 1W 0L 2W 0L
23.(ˈre)(fek.ˌtus) 1W 1W 1 1W 0L 2W 1
24.(ˈre.fek.tus) 1W 1W 2W 0 0L 0L 0L

Further Reading

With the exception of the Kager book, all the readings suggested here are available online. Check the web-based version of this handout for links.

References

Crosswhite, Karen (2001) Vowel reduction in Optimality Theory. New York: Garland.

Hayes, Bruce (1995) Metrical stress theory: principles and case studies. University of Chicago Press.

Jacobs, Haike (2000) “The revenge of the uneven trochee: Latin main stress, metrical constituency, stress-related phenomena and OT.” in Lahiri, Aditi ed. Analogy, Levelling, Markedness Berlin: Mouton de Gruyter.

Jacobs, Haike (2004) “Rhythmic vowel deletion in OT: syncope in Latin.” Probus 16:63-89.

Kager, René (1999) Optimality Theory. Cambridge University Press.

Liberman, Mark and Alan S. Prince (1977) “On stress and linguistic rhythmLinguistic Inquiry 8:249-336.

Lombardi, Linda (1999) “Positional faithfulness and voicing assimilation in Optimality TheoryNatural Language and Linguistic Theory 17:267‒302.

McCarthy, John J. and Alan S. Prince (1993) “Generalized alignmentYearbook of Morphology 1993:79-153.

McCarthy, John J. (2007) “OT constraints are categoricalPhonology 20:75‒138.

Prince, Alan S. (2002) “Arguing Optimalityin Coetzee, Andries, Angela Carpenter and Paul de Lacy, eds. Papers in Optimality Theory II Amherst, MA: GLSA.

Sen, Ranjan (2012) “Exon’s Law and the Latin syncopes” in Probert, Philomen and Andreas Willi, eds. Laws and Rules in Indo-European Oxford University Press.