Phonemes, allophones, and contrast in OT

The challenge

In rule-and-constraint based phonology, to describe a language you need:

an ordered list of rules
a list of URs (the lexicon)
a phoneme inventory (Steriade 2007 calls this an “underlying alphabet”)
maybe restrictions on combinations of segments in URs (called Morpheme Structure Constraint (MSCs))
maybe restrictions on the segments allowed in outputs or derivations
- called “Wellformedness constraints” or “Surface phonetic constraints”
- Steriade (2007) talks about this with respect to structure preservation: a structure preserving phonological process doesn’t create sounds not found in the segmental inventory of the language.

Some of the restrictions above seem redundant: the Duplication Problem.

In OT, all you have is…

a list of URs (the lexicon)
a ranked list of constraints
The lack of an underlying alphabet – or any constraints on the structure of URs – is a property called Richness of the Base.

So how can we account for which sounds do and don’t contrast, without stating the phoneme inventory?

How do we state the inventory, generally?
This seems potentially problematic given Richness of the Base…

Probably not surprising: inventories and contrast come solely from constraint ranking.

Contrast in OT comes from faithfulness constraints, which preserve contrast in a certain environment.
Markedness constraints militate against the faithful realization of inputs containing sounds illicit in a language.

Possible patterns of contrast

No contrast

How do we know it when we see it?

Full contrast

How do we know it when we see it?

Contextually limited contrast

How do we know it when we see it?
How does this relate to positional neutralization?

No contrast - free variation

How do we know it when we see it?
The version of OT we’re considering isn’t built to model it.
EVAL results in a single optimal candidate, or multiple optimal candidates if they have identical violation profiles. ¹

Complementary distribution between sounds (no contrast)

Imagine a language where [p] and [b] are in complementary distribution, and allophones of a single phoneme.

In rule terms:

/p/ → [b] / V__V no phoneme /b/
/p/ → [p] elsewhere (since there’s no rule)
Why is [b] only between vowels?
Why is [p] everywhere else?

Translate into OT using:

*V[-voice]V
*[+voice,-son]
Ident([voice])

Assume these inputs

/ap/ ‘dog’ (real word)
/ap+a/ ‘dogs’ (real word)
/ab/ ‘?’ (hypothetical input)
/ab+a/ ‘?(plural)’ (hypothetical input)

/p/ and /b/ don’t contrast, because the grammar won’t let you have a minimal pair.

What is it about the ranking that makes that so?

Full contrast between sounds

Imagine a different language, where /p/ and /b/ are separate phonemes, with no voicing alternations.

Same constraints

*V[-voice]V
*[+voice,-son]
Ident([voice])

Find the ranking for:

/ap/ ‘dog’
/ap+a/ ‘dogs’
/ab/ ‘cat’
/ab+a/ ‘cats’

/p/ and /b/ contrast fully-you can get a minimal pair in any environment.

What is it about the ranking that makes that so?

Contextually-limited contrast (positional neutralization)

Imagine language with a voicing contrast (phonemes /p/ and /b/), but also intervocalic voicing.

In rule terms:

/p/ → [b] / V__V
/p/ → [p] elsewhere
/b/ → [b] everywhere

Same constraints

*V[-voice]V
*[+voice,-son]
Ident([voice])

Find the ranking for:

/ap/ ‘dog’
/ap+a/ ‘dogs’
/ab/ ‘cat’
/ab+a/ ‘cats’

/p/ & /b/ contrast in some environments – but in other environments, you get neutralization.

What is it about the ranking that makes that so?

Have we missed any members of the factorial typology for these three constraints?

There are 3! rankings – any other patterns?

Contextually limited contrast two ways

Example: coda devoicing (German, Catalan, Russian, etc.)

In onsets, obstruents contrast in voicing.
That contrast does not occur in coda position.
Results in both positional neutralization and contextually-limited contrast.

Two approaches in OT:

Context-specific markedness constraints
- Cause neutralization in a particular environment
- Example: *Coda-voice
Contextually-limited faithfulness constraints (we’ll revisit this later)
- Preserve contrast in a particular environment
- Example: Ident-onset([voice])

Lexicon optimization

Does Richness of the Base mean anything can be in underlying representations?

In theory, yes – there are no hard limits on URs.

Does Richness of the Base mean underlying representations in a language include everything?

For an actual language, no – learners won’t posit “weird” or “crazy” URs without evidence.

Prince & Smolensky (1993/2004) suggest a learning procedure called Lexicon Optimization.

For a given phonetic form, the chosen UR will be the one that maps onto the SR with the fewest violation of highest-ranked constraints.
In the absence of aleternations, learners will pick a UR that gives a mapping minimizing the violation of faithfulness constraints: the UR matches the SR.
This runs contrary to the idea that we should minimize the number of underlying sounds in a language, and it especially runs contrary to the usage of abstract phonemes to minimize the number of underlying sounds.

An example: imagine a non-alternating phonological property – like the aspiration of initial [kʰ] in [kʰæt] in English.

The correct grammar for English will ensure the surface occurrence of [kʰ] in [kʰæt] no matter whether [kʰ] or [k] is present underlyingly.
The advantage of the mapping /kʰæt/ ➞ [kʰæt] over /kæt/ ➞ [kæt] is that the former avoids a faithfulness violation, e.g. Ident([spread glottis]).
So learners will posit the mapping /kʰæt/ ➞ [kʰæt].
Non-alternating phonological properties will always be present in URs.

Recap of important ideas

Capturing contrast in OT

Richness of the Base

Lexicon Optimization

Contextually-limited contrast as…

Contextual markedness
Positional faithfulness

Very simplified descriptions of some possibilities (feel free to ask me about any of these privately): free variation comes from ties: obvious but difficult to work out, since constructing a tie often requires ignoring some active constraints; Partially Ordered Constraints (Anttila 1997 et seq): constraints are only partially ordered, and unordered constraints are randomly reordered at evaluation; Stochastic OT (Boersma 2000): constraints are partially ordered on a numerical scale, which is used to randomly generate a ranking at evaluation; MaxEnt Harmonic Grammar (Goldwater & Johnson 2007): constraints are weighted, resulting in every candidate getting a numerical harmony score, which is converted into a probability; Noisy HG: like Stochastic OT, but with weighted constraints; Markedness suppression (Kaplan 2011): violations for designated constraints are ignored at random at evaluation. ↩