Correspondence theory

Our current way of doing things isn’t precise enough for handling feature changes.
- Does /tui/ → [ty] delete the /i/ or the /u/?
- Does /tui/ → [ty] violate Ident(round) or Ident(back)?
In the OT manuscript (Prince & Smolensky 1993/2004), an output candidate contains the input form – you can see what’s been inserted or deleted.
- /tui/ → [ty<i>] or /tui/ → [t<u>y]
- This is known as the containment approach (since the output contains the input).
- Changing features gets tricky, and metathesis is very hard.
- Constraints against deletion and epenthesis were called Parse and Fill, respectively.
Correspondence (McCarthy & Prince 1995) = Part-numbering
- Every segment in the input bears a unique index (and perhaps every unit of structure, including features, moras, syllables…), written as a subscript number.
The relation of correspondence between input and output segments is encoded by identical indices.

Candidates			Ident(round)	Ident(back)
/t₁ u₂ i₃/	a.	[t₁ y₂]		✳︎
	b.	[t₁ y₃]	✳︎

/p₁ a₂ t₃ o₄ k₅/ → [p₁ a₂ t₃ o₄ k₅] means that Corr(/p₁/, [p₁]), Corr(/a₂/, [a₂]), etc. where Corr(x, y) means “x corresponds to y”.
When x and y correspond, they are correspondents of one another.
These are also candidates: [p₅ a₁ t₄ o₂ k₃], [p₁ a₁ t₁ o₁ k₁], [p₆ a₇ t₈ o₉ k₁₀], but they’re so outrageously bad that we don’t usually bother including them in a tableau.
Tips for usage:
- When you see a candidate in a tableau without indices, you can assume that the correspondence relation is the obvious one (/p₁ a₂ t₃ o₄ k₅/ → [p₁ a₂ t₃ o₄ k₅]).
- Sometimes it’s not clear what the obvious correspondence relation is; in that case, you should spell it out (as in the tableau above).

Good and bad correspondence relations

Correspondence is mapping between segments in the input and segments in the ouput.
Faithfulness constraints care about various aspects of this mapping (McCarthy & Prince 1995: 79–80)
- Contiguity of mapping
- Linearity of mapping
- Anchoring of edges
- Featural identity

The set of faithfulness constraints

Here are the faithfulness constraints proposed by McCarthy & Prince. We add “IO” to specify that we’re talking about input-output correspondence
Ident(F)-IO	If an input segment and an output segment correspond, they must bear identical values for feature [F].
Max-C-IO	Every consonant in input must have a correspondent in output.
Max-V-IO	Every vowel in input must have a correspondent in output.
Dep-C-IO	Every consonant in output must have a correspondent in input.
Dep-V-IO	Every vowel in output must have a correspondent in input.
Uniformity-IO (don’t coalesce)	Nothing in the output can have more >1 correspondent in input.
Integrity-IO (don’t split)	Nothing in the input can have >1 correspondent in the output.
Linearity-IO (don’t metathesize)	If A precedes B in input, and A and B both have correspondents in the output, then A’s output correspondent must precede (but not necessarily immediately precede) B’s output correspondent.
O-Contiguity-IO (don’t intrude)	If A immediately precedes B in input, and A and B both have correspondents in the output, then A’s output correspondent must immediately precede B’s output correspondent.
I-Contiguity-IO (don’t skip)	If A immediately precedes B in the output, and A and B both have correspondents in the input, then A’s input correspondent must immediately precede B’s input correspondent.
Left-Anchor(X)-IO	If there is an input segment A at the left edge of X (X = word, stem, phrase, whatever) in the input, and an output segment B is at the left edge of X in the output, A must correspond to B.
Right-Anchor(X)-IO	If there is an input segment A at the right edge of X (X = word, stem, phrase, whatever) in the input, and an output segment B at the right edge of X in the output, A must correspond to B.

We can (and should) write these constraints in “Assign one violation” format, as is done in Doing OT.
Given the input /p₁ a₂ t₃ o₄ k₅/, devise, for each of the correspondence constraints above, an output candidate that violates it.
- Ident(F)-IO
- Max-IO
- Dep-IO
- Uniformity-IO
- Integrity-IO
- Linearity-IO
- O-Contiguity-IO
- I-Contiguity-IO
- Left-Anchor(X)-IO
- Right-Anchor(X)-IO
A master of faithfulness can provide…
- a candidate that violates Dep but not O-Contiguity
- a candidate that violates Max but not I-Contiguity
- a candidate that violates Dep and L-Anchor(Word) in the same place
- a candidate that violates Max and R-Anchor(word) in the same place
Enforcing featural faithfulness is done by Ident constraints, but could also be done by Dep and Max.
- How do Ident(F) and Max(F)/Dep(F) differ in what they presuppose about features?

Positional faithfulness constraints

Beckman (1995) accounts for contextually limited contrast using positional faithfulness constraints, now standard in OT analyses.
- Contrast is preserved in a context X because a faithfulness constraint targets segments in that context.
- Common contexts where contrast is preserved: stressed syllables, initial syllables, onsets: all contexts that are perceptually salient.
- There are many languages that support positional Ident and Max for these salient contexts.
As done in the Lombardi (1999) reading, preservation of voicing in onsets can be captured by the constraint below:
- Ident-onset-([voice])
  Let Y be an output segment in the onset, and X the corresponding input segment. Assign one violation if Y is [αvoice] and X is not [αvoice].
Could we use positional faithfulness for neutralization in intervocalic voicing?
- Recall the hypothetical [pa], [ba], [aba], [aba] example.
- Let’s sketch an analysis.

Correspondence that isn’t IO

Agreement by correspondence (Rose & Walker 2000)
- Segments in the output are in correspondence with each other
- Correspondence relationships are evaluated by violable CORR constraints
- Used to model vowel and consonant harmony
Transderivational output-output faithfulness (Benua 1997)
- Different outputs are in correspondence with each other (usually the outputs are in the same paradigm)
- Used to model some opaque phonology processes and truncation
- An asymmetrical correspondence relationship, usually between the base (e.g. cycle) and the derived form (e.g. cyclic, cyclical)
Base-reduplicant faithfulness (McCarthy & Prince 1995)
- The base and reduplicant portions of the output are in correspondence with each other
- Used to model reduplication

Recap of important ideas

Correspondence theory: why do we need? How does it work?
The commonly assumed set of universal faithfulness constraints
Positional faithfulness