When to posit new constraints

When is it necessary to posit a new constraint?
In what sense are ranking paradoxes symmetrical?
- Consider the following two ERCS:
  - <L, W, L> and <e, L, W>
  - What are ways a new constraint could resolve this paradox?

L	W	L
e	L	W

Justifying constraints

There are three ways to justify a constraint:
- Formal: resembles other constraints in CON.
- Functional: reflects articulation, perception, or memory.
  - Examples: Agree, Ident-Onset[Voice]
  - Potentially includes audience design
- Typological: its cross-linguistic typological predictions are borne out.
No matter how a constraint is justified, its addition to the constraint set makes predictions with respect to factorial typology that must be addressed.

Phonological operations in different languages seem to be aiming for the same surface pattern (target), and achieving it in different ways (process).
- McCarthy (2003) calls this Homogeneity of Target, Heterogeneity of Process
- This is similar to – but distinct from – within-language conspiricies.
Example: consider the typological predictions of the following constraint *V[–voice]V along with the many faithfulness constraints we’ve discussed (Max, Dep, Ident[voice], Linearity).
- What rankings determine whether the marked structure should be avoided?
- What rankings determine how the marked structure should be avoided?
- How does OT capture homogeneity of target?
- How does OT capture heterogeneity of process?

Example: cognate infixes in some Western Austronesian languages, from proto *um or *m (Zuraw & Lu 2009).
What constraint could be responsible?
What faithfulness constraints are violated in each case?

	Tagalog (Philippines)	Timugon Murut (Indon.)	Sarangani Blaan (Phil.)	Palauan (Palau)	Limos Kalinga (Philippines)
p/f	pili, pumili	patoj, matoj	fati, mati	–	pija, kumija
t	takbo, tumakbo	tuun, tumuun	tiis, tmiis	toŋakl, tmoŋakl
s	sulat, sumulat		saloʔ, smaloʔ	sisijʔ, smisijʔ
k/q	kuha, kumuha		kaan, kmaan	kiwt, kmiwt	kan, kuman
b/v/β	bili, bumili	bigod, migod	bunal, munal	basəʔ, masəʔ	bali, ɡumali
d/ð	datiŋ, dumatiŋ		dado, dmado	ðakl, ðmakl	dakol, dumakol
ɡ	ɡawa, ɡumawa	ɡajo, ɡumajo
labial later				ðobəʔ, ðwobəʔ

	Acehnese (Indonesia)	Tjuabar Paiwan (Taiwan)	Toba Batak (Indonesia)	Kavalan (Taiwan)
p/f	paɟoh, sɯmaɟoh	pajsu, pənajsu	paddita, uppadita	paʁit, pmaʁit
t	tulak, tɯmulak	təkəɭ, təm(ə)kəɭ	tibbo, tumibbo	tajta, tmajta
s	saluɛn, sɯmaluɛn	supu, səmupu		sum, smum
k/q	kalɤn, kɯmalɤn	kan, kəman	–	kiɾim, kmiɾim
b/v/β	–	vəli, vənəli	balga, ubbalga	βuɾa, uβuɾa
d	dɯŋɤ, dɯmɯŋɤ	dapəs, dəmapəs	deŋɡan, dumeŋɡan	–
ɡ	ɡantoŋ, ɡɯmantoŋ		ɡabe, ɡumabe	–
labial later		təvəɭa, tənvəɭa

What’s the constraint used in Pater (2009)?
Let’s come up with rankings for the cases below:
These rules are attested in a variety of languages:
- Post-nasal voicing NT → ND (Japanese, Puyo Pungo Quechua)
- Nasal deletion NT → T (Kelanatan Malay, Swahili)
- Denasalization NT → TT (Toba Batak, Kaingang, Mandar)
- Nasal substitution NT → N (Indonesian, Kihehe)
A number of languages have multiple processes:
- Modern Greek: NT → ND, MPS → PS
- Karpathos Greek: NT → ND, N#T → T#T
- OshiKwanyama: NT → ND, N#T → N
- Kihehe: NT → N, NS → S
My contribution: *NC̥ blocks phrase-final devoicing in Dholuo
- Dholuo: D# → T#, ND# → ND#
Some rules. Why isn’t this solution better?
- Deletion: [+nas] → Ø / __ [-voice]
- Epenthesis: Ø → V / [+nas] __ [-voice]
- Post-nasal voicing: [-son] → [+voice] / [+nas] __
- Denasalization: [+nas] → [-nas] / __ [–voice]

Ranking paradoxes require new constraints.
New constraints should be posited with care:
- Clearly defined.
- With an understanding of typological predictions.
- Functional motivation is a plus.
We’ve seen a few examples of how to motivate a constraint typologically.
- OT’s ability to model “homogeneity of target; heterogeneity of target” follows from the assumptions that…
  - CON is universal.
  - Languages differ with respect to their constraint rankings.