Day 4 Classic OT Although we’ve seen most of the ingredients of OT, there’s one more big thing you need to know to be able to read OT papers and listen.

Day 4 Classic OT Although we’ve seen most of the ingredients of OT, there’s one more big thing you need to know to be able to read OT papers and listen to OT talks Constraints interact through strict ranking instead of through weighting

Analogy: alphabetical order
Constraints HaveEarly1stLetter HaveEarly2ndLetter HaveEarly3rdLetter HaveEarly4thLetter HaveEarly5thLetter ...

Harmonic grammar Cabana wins because it does much better on less-important constraints 1st w=5 2nd w=4 3rd w=3 4th w=2 5th w=1 harm. banana -1 -13 -57 azalea -25 -11 -4 -126 azote -14 -19 -184 cabana -2 -26

Classic Optimality Theory
Strict ranking: all the candidates that aren’t the best on the top constraint are eliminated “!” means “eliminated here” Shading on rest of row indicates it doesn’t matter how well or poorly the candidate does on subsequent constraints 1st 2nd 3rd 4th 5th banana 1! 13 azalea 25 11 4 azote 14! 19 cabana 2! 1

Classic Optimality Theory
Repeat the elimination for subsequent constraints Here, the two remaining candidates tie (both are the best), so we move to the next constraint Winner(s) = the candidates that remain 1st 2nd 3rd 4th 5th banana 1! 13  azalea 25 11 4 azote 14! 19 cabana 2! 1

Example tableaux: find the winner
Constraint1 C2 C3 C4 a. * b. c.

C1 C2 C3 C4 a. ** * b. c.

C1 C2 C3 C4 a. * b. *** c.

C1 C2 C3 C4 a. ** * b. c. ***

“Harmonically bounded” candidates
A fancy term for candidates that can’t win under any ranking Simple harmonic bounding: What can’t (c) win under any ranking? C2 C3 C4 a. * b. c. **

“Harmonically bounded” candidates
Joint harmonic bounding: What can’t (c) win under any ranking? C1 C2 a. ** b. c. *

Why this matters for variation
“Multi-site” variation: more than one place in word that can vary Which candidates can win under some ranking? /akitamiso/ Max-V *i a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso] /akitamiso/ *i Max-V a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso]

Why this matters for variation
Even if the ranking is allowed to vary, candidates like (b) and (c) can never occur /akitamiso/ Max-V *i a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso] /akitamiso/ *i Max-V a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso]

How about in MaxEnt? Can (b) and (c) ever occur? /akitamiso/ *i Max-V
a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso]

How about in Noisy Harmonic Grammar?
Suppose the two constraints have the same weight /akitamiso/ *i w=1 Max-V a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso]

Special case in Noisy HG
/apataka/ *aCa w=a Ident(lo) w=b harmony wins (or ties) if a. [apataka] *** -3a a < ½ b b. [epataka] ** * -2a-b -- c. [apetaka] -a-b a < b < 2a d. [apateka] e. [apatake] f. [epateka] -2b b < a g. [epatake] -a-2b d. [apetake]

Summary for harmonic bounding
In OT, harmonically bounded candidates can never win under any ranking means that applying a change to one part of a word but not another is impossible In MaxEnt, all candidates have some probability of winning. In Noisy HG, harmonically bounded candidates can win only in special cases. See Jesney 2007 for a nice discussion of harmonic bounding in weighted models.

Is it good or bad that (b) and (c) can’t win in OT?
/akitamiso/ *i Max-V a. [akitamiso] ** b. [aktamiso] * c. [akitamso] d. [aktamso] In my opinion, probably bad, because there are several cases where candidates like (b) and (c) do win...

French optional schwa deletion
There’s a long literature on this. See Riggle & Wilson 2005, Kaplan 2011 Kimper 2011 for references. La queue de ce renard no deletion La queue d’ ce renard some deletion La queue de c’ renard some deletion La queue de ce r’nard some deletion La queue d’ ce r’nard as much deletion as possible, without violating *CCC

Pima plural marking Munro & Riggle 2004, Uto-Aztecan language of Mexico, about 650 speakers [Lewis 2009]. Infixing reduplication marks plural. In compounds, any combination of members can reduplicate, as long as at least one does: Singular: [ʔus-kàlit-váinom], lit. tree-car-knife ‘wagon-knife’ Plural options: ʔuʔus-kàklit-vápainom ‘wagon-knives’ ʔuʔus-kàklit-váinom ʔuʔus-kàlit-vápainom ʔus-kàklit-vápainom ʔuʔus-kàlit-váinom ʔus-kàklit-váinom ʔus-kàlit-vápainom

Simplest theory of variation in OT: Anttila’s partial ranking (Anttila 1997)
Some constraints’ rankings are fixed; others vary I’m using the red line here to indicate varying ranking /θɪk/ Max-C Ident(place) *θ Ident(cont) *Dental  a [θɪk] *  b [t̪ɪk] c [ɪk] *! d [sɪk]

Anttilan partial ranking
Max-C Ident(place) *θ Ident(continuant) *Dental

Linearization In order to generate a form, the constraints have to be put into a linear order Each linear order consistent with the grammar’s partial order is equally probable grammar linearization 1 (50%) lineariztn 2 (50%) Max-C Max-C Max-C Ident(place) Ident(place) Id(place) *θ Ident(cont) Ident(cont) *θ *θ Id(cont) *Dental *Dental *Dental  [t̪ɪk]  [θɪk]

Properties of this theory
No learning algorithm, unfortunately Makes strong predictions about variation numbers: If there are 2 constraints, what are the possible Anttilan grammars? What variation pattern does each one predict?

Finnish example (Anttila 1997)
The genitive suffix has two forms “strong”: -iden/-iten (with additional changes) “weak”: -(j)en (data from p. 3)

Factors affecting variation
Anttila shows that choice is governed by... avoiding sequence of heavies or lights (*HH, *LL) avoiding high vowels in heavy syllables (*H/I) or low vowels in light syllables (*L/A)

Anttila’s grammar (p. 21) (Without going through the whole analysis)

Sample of the results (p. 23)

Day 4 summary We’ve seen Classic OT, and a simple way to capture variation in that theory But there’s no learning algorithm available for this theory, so its usefulness is limited Also, predictions may be too restrictive E.g. if there are 2 constraints, the candidates must be distributed 100%-0%, 50%-50%, or 0%-100%

Next time (our final day)
A theory of variation in OT that permits finer-grained predictions, and has a learning algorithm Ways to deal with lexical variation

Day 4 references Anttila, A. (1997). Deriving variation from grammar. In F. Hinskens, R. van Hout, & W. L. Wetzels (Eds.), Variation, Change, and Phonological Theory (pp. 35–68). Amsterdam: John Benjamins. Jesney, K. (2007). The locus of variation in weighted constraint grammars. In Workshop on Variatin, Gradience and Frequency in Phonology. Presented at the Workshop on Variatin, Gradience and Frequency in Phonology, Stanford University. Kaplan, A. F. (2011). Variation Through Markedness Suppression. Phonology, 28(03), 331–370. doi: /S Kimper, W. A. (2011). Locality and globality in phonological variation. Natural Language & Linguistic Theory, 29(2), 423–465. doi: /s Lewis, M. P. (Ed.). (2009). Ethnologue: languages of the world (16th ed.). Dallas, TX: SIL International. Munro, P., & Riggle, J. (2004). Productivity and lexicalization in Pima compounds. In Proceedings of BLS. Riggle, J., & Wilson, C. (2005). Local optionality. In L. Bateman & C. Ussery (Eds.), NELS 35.

Day 5: Before we start Last time I promised to show you numbers for multi-site variation in MaxEnt If weights are equal: /akitamiso/ *i w= 1 Max-V w = 1 harmony prob. a. [akitamiso] ** e-2 0.25 b. [aktamiso] * c. [akitamso] d. [aktamso]

Day 5: Before we start As weights move apart, “compromise” candidates remain more frequent than no-deletion candidate /akitamiso/ *i w= 1 Max-V w = 2 harmony prob. a. [akitamiso] ** e-2 = 0.14 0.57 b. [aktamiso] * e-3 = 0.05 0.21 c. [akitamso] d. [aktamso] e-6 = 0.002 0.01 sum = 0.24

Stochastic OT Today we’ll see a richer model of variation in Classic (strict-ranking) OT. But first, we need to discuss the concept of a probability distribution

What is a probability distribution
It’s a function from possible outcomes (of some random variable) to probabilities. A simple example: flipping a fair coin which side lands up probabiliy heads 0.5 tails

Rolling 2 dice sum of 2 dice probability 2 (1+1) 1/36 3 (1+2, 2+1)
2/36 4 (1+3, 2+2, 3+1) 3/36 5 (1+4, 2+3, 3+2, 4+1) 4/36 6 (1+5, 2+4, 3+3, 4+2, 5+1) 5/36 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) 6/36 8 (2+6, 3+5, 4+4, 5+3, 6+2) 9 (3+6, 4+5, 5+4, 6+3) 10 (4+6, 5+5, 6+4) 11 (5+6, 6+5) 12 (6+6)

Probability distributions over grammars
One way to think about within-speaker variation is that, at each moment, the speaker has multiple grammars to choose between. This idea is often invoked in syntactic variation (e.g., Yang 2010) E.g., SVO order vs. verb-second order

Probability distributions over Classic OT grammars
We could have a theory that allows any probability distribution: Max-C >> *θ >> Ident(continuant): 0.10 (t̪ɪn) Max-C >> Ident(continuant) >> *θ: 0.50 (θɪn) *θ >> Max-C >> Ident(continuant): 0.05 (t̪ɪn) *θ >> Ident(continuant)>> Max-C: 0.20 (ɪn) Ident(continuant) >> Max-C >> *θ: 0.05(θɪn) Ident(continuant) >> *θ >> Max-C: 0 (ɪn) The child has to learn a number for each ranking (except one)

Probability distributions over Classic OT grammars
But I haven’t seen any proposal like that in phonology Instead, the probability distributions are usually constrained somehow

Anttilan partial ranking as a probability distribution over Classic OT grammars
Id(place) *θ Id(cont) means Id(place) >> *θ >> Id(cont): 50% Id(place) >> Id(cont) >> *θ: 50% *θ>> Id(place) >> Id(cont): 0% *θ>> Id(cont) >> Id(place): 0% Id(cont) >> *θ>> Id(place): 0% Id(cont) >> Id(place) >> *θ: 0%

A less-restrictive theory: Stochastic OT
Early version of the idea from Hayes & MacEachern 1998. Each constraint is associated with a range, and those ranges also have fringes (margem), indicated by “?” or “??” p. 43

Stochastic OT Each time you want to generate an output, choose one point from each constraint’s range, then use a total ranking according to those points. This approach defines (though without precise quantification) a probability distribution over constraint rankings.

Making it quantitative
Boersma 1997: the first theory to quantify ranking preference. In the grammar, each constraint has a “ranking value”: *θ 101 Ident(cont) 99 Every time a person speaks, they add a little noise to each of these numbers then rank the constraints according to the new numbers. ⇒ Go to demo [Day5_StochOT_Materials.xls] Once again, this defines a probability distribution over constraint rankings An Anttilan grammar is a special case of a Stochastic OT grammar

Boersma’s Gradual Learning Algorithm for stochastic OT
Start out with both constraints’ ranking values at 100. You hear an adult say something—suppose /θɪk/ →[θɪk] You use your current ranking values to produce an output. Suppose it’s /θɪk/ → [t̪ɪk]. Your grammar produced the wrong result! (If the result was right, repeat from Step 2) Constraints that [θɪk] violates are ranked too low; constraints that [t̪ɪk] violates are too high. So, promote and demote them, by some fixed amount (say 0.33 points) /θɪk/ *θ Ident(cont) the adult said this [θɪk] * demote to 99.67 your grammar produced this [t̪ɪk] promote to

Gradual Learning Algorithm
demo (same Excel file, different worksheet)

Problems with the GLA for stochastic OT
Unlike with MaxEnt grammars, the space is not convex: there’s no guarantee that there isn’t a better set of ranking values far away from the current ones And in any case, the GLA isn’t a “hill-climbing” algorithm. It doesn’t have a function it’s trying to optimize, but just a procedure for changing in response to data

Problems with GLA for stochastic OT
Pater 2008: constructed cases where some constraints never stop getting promoted (or demoted) This means the grammar isn’t even converging to a wrong solution—it’s not converging at all! I’ve experienced this in appyling the algorithm myself

Still, in many cases stochastic OT works well
E.g., Boersma & Hayes 2001 Variation in Ilokano reduplication and metathesis Variation in English light/dark /l/ Variation in Finnish genitives (as we saw last time)

Type variation All the theories of variation we’ve used so far predict token variation In this case, every theory wrongly predicts that both words vary /mão+s/ Ident(round) *ãos mãos * mães /pão+s/ pãos pães

Indexed constraints Pater 2009, Becker 2009
Some constraints apply only to certain words /mão+s/TypeA Ident(round)TypeA *ãos Ident(round)TypeB mãos * mães *! /pão+s/TypeB pãos pães

Indexed constraints If the grammar is itself variable, we can have some words whose behavior is variable (Huback 2011 example) /sidadão+s/TypeC Ident(round)TypeC weight: 100 *ãos weight: 98 sidadãos * sidadães

Where to go from here: R and regression
Download R Download Harald Baayen’s book Analyzing Linguistic Data: A Practical INtroduction to Statistics using R Work through the analyses in the book Baayen gives all the R commands and lets you download the data sets, so you can do the analyses in the book as you read about them

Where to go: Optimality Theory
Read John McCarthy’s book Doing Optimality Theory: Applying Theory to Data A practical guide for actually doing OT If you enjoy that, read John McCarthy’s book Optimality Theory: A Thematic Guide Goes into more theoretical depth There is a book in Portuguese, João Costa’s 2001 Gramática, conflitos e violações. Introdução à Teoria da Optimidade Download OTSoft If you give it the candidates, constraints, and violations, it will tell you the ranking

Where to go: Stochastic OT and Gradual Learning Algorithm
Read Boersma & Hayes’s 2001 article “Empirical tests of the Gradual Learning Algorithm” Download the data sets for the article and play with them in OTSoft under part 3 Try different GLA options Try learning algorithms other than GLA

Where to go: Harmonic Grammar and Noisy HG
Unfortunately, I don’t know of any friendly introductions to these Download OT-Help and try the examples people.umass.edu/othelp/ The OT-Help manual might be the easiest-to-read summary of Harmonic Grammar that exists! Try the sample files

Where to go: MaxEnt The original proposal to use MaxEnt for phonology was Goldwater & Johnson 2003, but it’s difficult to read Andy Martin’s 2007 UCLA dissertation has an easier-to-read introduction (chapter 4) You could try using OTSoft to fit a MaxEnt model to the Boersma/Hayes data

Where to go: MaxEnt’s Gaussian prior
To use the prior (bias against changing weights from default), download the MaxEnt Grammar Tool In addition to the usual OTSoft input file, you need to make a file with mu and sigma2 for each constraint (there is a sample file) Good examples to read of using the prior Chapter 4 of Andy Martin’s dissertation White & Hayes 2013 article, “Phonological naturalness and phonotactic learning” /

Where to go: lexical variation
Becker’s 2009 UMass dissertation, “Phonological Trends in the Lexicon: The Role of Constraints”, develops the lexical-indexing approach Hayes & Londe’s 2006 paper “Stochastic phonological knowledge: the case of Hungarian vowel harmony” uses another approach (Zuraw’s UseListed)

Thanks for attending! Stay in touch: kie@ucla.edu
Working on a phonology project (with or without variation)? I’d be interested to read it.

Day 5 references Becker, M. (2009). Phonological trends in the lexicon: the role of constraints (Ph.D. dissertation). University of Massachusetts Amherst. Boersma, P. (1997). How we learn variation, optionality, and probability. Proceedings of the Institute of Phonetic Sciences of the University of Amsterdam, 21, 43–58. Boersma, P., & Hayes, B. (2001). Empirical tests of the gradual learning algorithm. Linguistic Inquiry, 32, 45–86. Goldwater, S., & Johnson, M. (2003). Learning OT Constraint Rankings Using a Maximum Entropy Model. In J. Spenader, A. Eriksson, & Ö. Dahl (Eds.), Proceedings of the Stockholm Workshop on Variation within Optimality Theory (pp. 111–120). Stockholm: Stockholm University. Hayes, B., & Londe, Z. C. (2006). Stochastic Phonological Knowledge: The Case of Hungarian Vowel Harmony. Phonology, 23(01), 59–104. doi: /S

Day 5 references Hayes, B., & MacEachern, M. (1998). Quatrain form in English folk verse. Language, 64, 473–507. Hayes, B., & White, J. (2013). Phonological Naturalness and Phonotactic Learning. Linguistic Inquiry, 44(1), 45–75. doi: /LING_a_00119 Huback, A. P. (2011). Irregular plurals in Brazilian Portuguese: An exemplar model approach. Language Variation and Change, 23(02), 245–256. doi: /S Martin, A. (2007). The evolving lexicon (Ph.D. Dissertation). University of California, Los Angeles. Pater, J. (2008). Gradual Learning and Convergence. Linguistic Inquiry. Pater, J. (2009). Morpheme-specific phonology: constraint indexation and inconsistency resolution. In S. Parker (Ed.), Phonological argumentation: essays on evidence and motivation. Equinox. Yang, C. (2010). Three factors in language variation. Lingua, 120(5), 1160–1177. doi: /j.lingua

Day 4 Classic OT Although we’ve seen most of the ingredients of OT, there’s one more big thing you need to know to be able to read OT papers and listen.

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Day 4 Classic OT Although we’ve seen most of the ingredients of OT, there’s one more big thing you need to know to be able to read OT papers and listen.

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