OT learning 2.6. Variable output

Each time you press Command-2, which invokes the command Evaluate (noise 2.0) from the Edit menu, you will see the disharmonies changing. If the distance between the constraint rankings is 10, however, the winning candidates will very probably stay the same.

So starting from the NOCODA example, we edit the rankings of the constraints again, setting the ranking value of PARSE to 88 and that of NOCODA to 85. If we now press Command-2 repeatedly, we will get [pat] in most of the cases, but we will see the finger pointing at [pa] in 14 percent of the cases:

ranking value disharmony plasticity
PARSE 88.000 87.421 1.000
NOCODA 85.000 85.585 1.000


ranking value disharmony plasticity
NOCODA 85.000 87.128 1.000
PARSE 88.000 85.076 1.000

As a more functionally oriented example, we consider nasal place assimilation. Suppose that the underlying sequence /an+pa/ surfaces as the assimilated [ampa] in 80 percent of the cases, and as the faithful [anpa] in the remaining 20 percent, while the non-nasal stop /t/ never assimilates. This can be achieved by having the articulatory constraint *GESTURE ranked at a short distance above *REPLACE (n, m):

"OTGrammar 2"
decisionStrategy = <OptimalityTheory>
leak = 0.0
3 constraints
"*G\s{ESTURE}" 102.7 0 1
"*R\s{EPLACE} (n, m)" 100.0 0 1
"*R\s{EPLACE} (t, p)" 112.0 0 1
0 fixed rankings
2 tableaus
"an+pa" 2
    "anpa" 1 0 0
    "ampa" 0 1 0
"at+ma" 2
    "atma" 1 0 0
    "apma" 0 0 1

You can create this grammar with Create place assimilation grammar from the New menu. In the editor, it will often look like follows:

ranking value disharmony plasticity
*REPLACE (t, p) 112.000 109.806 1.000
*GESTURE 102.700 102.742 1.000
*REPLACE (n, m) 100.000 101.044 1.000

If you keep the Command-2 keys pressed, however, you will see that the tableaus change into something like the following in approximately 20 percent of the cases:

ranking value disharmony plasticity
*REPLACE (t, p) 112.000 113.395 1.000
*REPLACE (n, m) 100.000 103.324 1.000
*GESTURE 102.700 101.722 1.000

We see that /at+ma/ always surfaces at [atma], because *REPLACE (t, p) is ranked much higher than the other two, and that the output of /an+pa/ is variable because of the close rankings of *GESTURE and *REPLACE (n, m).

If you try this with a Harmonic Grammar or in Linear OT, you will see the same kind of variation. Although in HG, e.g. in Smolensky & Legendre (2006), the variation is usually obtained at the candidate level, namely by giving each candidate a probability proportional to exp(harmony/temperature), in our version of HG the variation comes about at the constraint level, namely by the noise that is temporarily added to the ranking of each constraint at evaluation time.

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© ppgb, July 25, 2007