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Metathesis in English and HebrewA Computational Account of Usage-Based Phonology

Paul De PalmaGeorge LugerDepartments of Computer ScienceGonzaga UniversityUniversity of New Mexico(depalma@gonzaga.edu)

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Metathesis

Reversal of the expected linear ordering of sounds Instead of xy we find yx Examples

tl shift: borrowed noun chipotle chipolte (SAE: a spice) ts shift: binyan 5 hitsader histader (Modern Hebrew: “he

got organized” ) hr shift: dative singular tehernek dative plural terhek

(Hungarian: “load”) rh shift: Expected tiirhisaskhus actual tihriasku (Pawnee:

“he is called”) Metathesis Myth: sporadic, irregular, due to

performance errors String of sounds realized as xy in language A can be yx in

language B

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Model Levels

A usage-based phonological account (Elizabeth Hume) primarily synchronic

Can be extended to language change Utterance Selection Theory (William Croft)

Genetic Algorithm operationalizes Utterance Selection Theory

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A Usage-Based Account

Metathesis requires two conditions1. An indeterminate speech signal2. Output that conforms to existing patterns in

language Example: chipotle/chipolte

In SAE, tl (stop consonant preceding a lateral) is indeterminate

Stop consonant following the lateral is frequent in post-vocalic position (cold,sold,mold,fold,molt,bolt,jolt,colt)

SAE speakers transform tl to lt

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Utterance Selection Theory

Natural Selection requires: A population of individuals with distinct characteristics A mechanism for replicating those characteristics Interaction among individuals and the environment Selective pressure from the environment producing

differential reproduction of the individuals and characteristics Extended to language:

Language: A population of utterances (not a system of signs or a collection of words and rules that operate on them)

Normal replication: utterance conforms to the conventions of language use

Altered replication: utterance violates convention Selection: graduate establishment of a new convention

through use

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Genetic Algorithm (GA)

Operationalizes (i.e, renders computationally precise) Usage-based account of metathesis Usage-based account of language

change Based loosely on the Darwinian notion of

natural selection

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More Precisely

GA(){

Initialize(population); //build initial populationComputeCost(population); //apply cost functionSort(population); //rank populationwhile (population has not converged on a good-enough solution)

{Pair(population); //decide which members reproduceMate(population); //exchange characteristicsMutate(population); //randomly perturb genes Sort(population); //rank populationTestConvergence(population); //has a new species appeared?

}}

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Cost Function

Embodies most of the theory being modeled. For example,

1. Prevocalic stop (e.g., te) is more salient than a postvocalic stop. Give a fitness boost.

2. Penalize words with postvocalic stops (e.g., et)3. Glottals (e.g., g), liquids (e.g., l), glides (e.g., w)

bleed into adjacent sounds when followed by a stop (e.g., t). Penalize sequences like lt.

4. A stop followed by any non-stop consonant (e.g., tl) is perceptually weak. Penalize stop/non-stop consonant sequences

5. A stop followed by a strident (e.g., ts) is perceptually weak. Penalize prestrident stops.

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As A Result

Each utterance in the population is tagged with a collection of boosts and penalties

The collection makes the underlying phonological theory computationally precise

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Method

Encode the GA as a collection of objects in Java executable under Linux

Parameters Population size: 64 strings Mutation factor: .5% For each of 1, 2, 4 base strings in the population, begin at

parity then double the number of target strings three times Fill out the balance of the population with randomly

generated character sequences For each population configuration

Run GA 250 times 250 generations per run Collect results per run

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More Precisely

1. Input an initial population of the base word and the target word

2. Generate random sequences of characters that fill out the population.

3. Assign a fitness value to each of the sequences that comprise the population.

4. Sort the population by fitness value5. Collect the population into two-tuples from highest to

lowest fitness6. Exchange pieces of sounds between each pair7. Randomly shift a fixed fraction of the sounds the action

of chemical/biological/radiological mutagens on individuals.

8. Sort the population. Stop if some predetermined condition is met, else go to step 3.

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Results

chipotle/chipolteAfter 60 generations chipolte tokens are

95% of the populationchipotle disappears within 3 generations

hitsader/histader After 48 generations histader tokens are

97.3% of the populationhitsader disappears within 2 generations

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Metathesis: Conclusions

Accurate but underspecified Computational model supplies missing

precision Usage-based aspect modeled as a

frequency affect Target tokens tends stabilize more quickly at

a higher fraction as their number in the initial population increases

The larger the number of base tokens in the initial population, the better the performance

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Utterance Selection: Conclusions

Hume’s account of metathesis can be reframed as an account of (one type) of language change

Can be rendered computationally precise using the Genetic Algorithm

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Base:Target Influences Stabilization

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Data: ChipotleRatio of Base to Target

GenerationChipotle Disappeared

GenerationChipolte Stabilized

Percent of Chipolte Tokens at Stabilization

1:1 3 119 73.4

1:2 3 68 93.7

1:4 3 60 96.8

1:8 2 44 98.4

2:2 3 90 92.1

2:4 3 72 96.8

2:8 2 50 98.4

2:16 2 31 98.4

4:4 3 58 96.8

4:8 2 44 98.4

4:16 2 33 98.4

4:32 1 26 98.4

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Data: Hitsader

Ratio of Base to Target

GenerationHitsader Disappeared

GenerationHistader Stabilized

Percent of Histader Tokens at Stabilization

1:1 2 79 84.3

1:2 2 65 98.4

1:4 2 55 98.4

1:8 2 39 98.4

2:2 2 59 98.4

2:4 2 47 98.4

2:8 2 43 98.4

2:16 1 33 98.4

4:4 2 49 98.4

4:8 1 43 98.4

4:16 1 32 98.4

4:32 1 23 100

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Future Research

Use transcribed corpora to determine the frequency of both vulnerable cues and the targets of metathetic change

Use frequencies to weight penalties and rewards (adding precision to statement like, “[they] contribute to indeterminacy: /t/ with perceptually vulnerable cues and /l/ with stretched out features,” Hume, 2004, p.223)

Generate all instances of metathesis within a language

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References

Croft, W. (2000). Explaining Language Change: An Evolutionary Approach. Harlow, England: Pearson.

Hume, E. (2004). The Indeterminancy/Attestation Model of Metathesis. Language 80(2): 203-237.