Morpheme-specific Phonology:
Constraint Indexation and
Inconsistency Resolution
Joe Pater, 2008; in Steve Parker (ed.)
Phonological Argumentation: Essays
on Evidence and Motivation
Organisation of the Paper
• Exceptional triggering
and blocking of
syncope in Yine –
illustrating
markedness and
faithfulness indexing.
• The Locality question:
morpheme-specific
indexing versus other
approaches
• Indexing and learning
viz., indexing as a tool
of inconsistency
resolution.
• Conclusions
Introduction
• The different tacks to handle
morpheme-specific phonology
(MSI hereafter) in OT:
– A theory in which individual
morphemes select separate
rankings viz., the
“cophonology” approach
(Anttila 2002)
– Faithfulness-only indexing
(Fuzakawa 1999 and Ito and
Mester 1999 & 2001)
– Indexing of faithfulness AND
markedness constraints (the
present approach)
• As will be observed, the present
approach is better than the other
two for the following reasons:
– Its ease in incorporating
locality considerations which
play a definitive role in MSP’s.
– Its ability to distinguish
exceptional triggering (through
markedness-indexing) and
blocking (through faithfulnessindexing).
– Its separation of exceptionality
and variation which Anttila’s
(2002) approach wrongly
conflates.
Predecessors of Indexing in OT
• Alignment (McCarthy and Prince 1993) and
Edgemost (Prince and Smolensky 1993/2004)
represent indexation in that edges of
morphological categories/specific morphemes are
identified as being governed by specific alignment
considerations .
• Fuzukawa (1999), Ito and Mester (1999, 2001),
Kraska-Szelenk (1997, 1999) and Pater (2000)
extend morphological indexation from Alignment
to other constraints as well.
Morpheme-specific Indexing (MSI):
the Basics
• Every constraint has a general instantiation
• Some constraints may have a specific
instantiation which will be indexed to (or
“co-indexed” with) the morphemes
responsible for exceptional behaviour.
• Crux: The indexed and unindexed variants
of a constraint are essentially different
constraints in the overall hierarchy.
Hypothetical Case 1:
• NoCoda >> Max: Coda consonants always
deleted.
• Max >> NoCoda: Coda consonants always
retained.
• MaxL >> NoCoda >> Max: Indexed morphemes
(e.g., [tak]L  /tak/) will retain their coda
consonant (MaxL >> NoCoda) but unindexed ones
(e.g., [pak]  /pak/) will not (NoCoda >> Max).
Hypothetical Case 1 contd…
• Assume the language bans
complex onsets completely:
*Complex >> MaxL >> NoCoda
>> Max.
– (i) When there is external
evidence for exceptionality
(coda retention) the indexing
approach captures it with the
ranking MaxL >> NoCoda.
– (ii) When there is no such
evidence (consonant clusters)
for exceptionality, the indexing
approach disallows it:
*Complex >> MaxL
• Cophonology: In this approach,
which has only one instantiation
of a constraint, exceptional and
impossible patterns cannot be
teased apart.
– (i) Exceptional coda retention:
reversing the general ranking
NoCoda >> Max (viz., Max >>
NoCoda).
– (ii) Clusters cannot be banned
because the system allows just
about any sort of re-ranking:
there is nothing “inherent” in
the system to prevent
*Complex >> Max  Max >>
*Complex.
The Subregularity Convention
• Because the cophonology approach cannot readily
prevent rankings yielding impossible patterns,
Anttila (2002) invokes this convention.
• As per this, only (pairs of) constraints which are
unranked w. r. t one another (i.e. those in charge of
the variation) can be re-ranked whereas the rest of
the ranking remains inalterable:
– In the hypothetical example therefore, *Complex >>
Max would be fixed whereas Max, NoCoda can choose
different rankings for different morphemes.
Differences between MSI and
Cophonology
• MSI
(i) Filters out a rich base based on
positive evidence.
(ii) Separates variation from
exceptionality without
stipulation.
(iii) Distinguishes exceptional
triggering from blocking
(iv) Addresses locality effects
• Cophonology
(i) Requires a stipulation (like
SBC) to rule out spurious
rankings.
(ii) Conflates exceptionality and
variation in that pairs of
constraints which are unranked
underlie both variation and
exceptional patterns .
(iii) Cannot distinguish exceptional
triggering from blocking.
(iv) Cannot deal with locality
A Demonstration of MSI: Syncope
in Yine
Kisseberth (1970) (c.f Matteson (1965)
reviews suffix-based syncope in Yine
(formerly Piro) for its implications for a
theory of exceptions in rule-based Phonology.
Classes of Suffixes Involved:
(a) Those which trigger syncope on the preceding
morpheme (details of suffix class omitted): [-lu],
[-nu] and [-ya].
(b) Those which fail to trigger syncope: [-ta],
(another) [-nu] and [-wa] but themselves undergo
it before class (a) suffixes.
(c) Exceptional [-wa] which neither conditions nor
undergoes syncope; a homophonous [-wa],
however, undergoes syncope when placed before
class (a) suffixes.
The MSI Analysis:
• Constraint conditioning
syncope: Align-Suf-C (Align
Suffix, L, Consonant, R)
• Align-Suf-C >> Max: syncope
• To distinguish the syncopetriggering suffixes from nontriggers, Align-Suf-C (L1) (the
indexed version) is created and
the triggering suffixes share the
index (L1).
• Align-Suf-C (L1) >> Max >>
Align-Suf-C: Indexed
morphemes trigger syncope
(Align-Suf-C (L1) >> Max) and
unindexed ones do not (Max >>
Align-Suf-C).
• To distinguish suffixes which
undergo syncope from those
that do not Max (L2) is created.
• Max (L2) >> Align-Suf-C (L1)
>> Max >> Align-Suf-C:
Morphemes indexed with L2 do
not undergo syncope when they
follow L1 suffixes but
otherwise do.
Tableau 1
Align-Suf-C (L1) >> Max >> Align-Suf-C
Input
Output
Align-Suf(L1)C
a.
heta+ya(L1)
hetaya
*!
☞hetya
b. heta+wa
MAX
*
*
☞hetawa
hetwa
Align-Suf-C
*
*!
Tableau 2
MAX-L2 >> ALIGN-SUF(L1)-C >> MAX >> ALIGN-SUF-C
Input
Output
a.
heta+nu+lu(L1)
☞hetanru
b.
heta+wa(L2)+lu(
L1)
MAX(L2)
Align-Suf(L1)-C
*
hetanulu
*!
☞hetawalu
*
hetawlu
MAX
*!
*
Yine Syncope (contd…)
• Syncope is also avoided just in case it
would create a tri-consonant cluster
(*CCC).
• The overall constraint hierarchy (under the
MSI approach) for Yine syncope is: *CCC,
Max (L2) >> Align-Suf(L1)-C >> Max >>
Align-Suf-C
Yine Syncope under the
Cophonology Approach: Drawbacks
• This approach can handle syncope triggering (Align-Suf-C >> Max for
triggering morphemes) and blocking (Max >> Align-Suf-C for syncope
blocking).
• But forms like /hetanru/ (from /heta+nu+lu/) will demand Max>>
Align Suf-C for heta+nu  /hetan…/ but will demand the opposite for
nu+lu  /nru/. There is no way to get blocking and triggering within
different morphemes of the same word under this approach.
• Cophonology cannot also tackle the two instances of homophonous [wa], one which undergoes syncope and the other which does not. In
MSI, the [-wa] indexed to Max will not undergo syncope and the
unindexed one will. Under the re-ranking approach, either both [-wa]’s
will be predicted to undergo syncope or neither will.
Finnish [a+i] allomorphy (Anttila
2002)
• In Finnish, a stem-final /a/ preceding an [-i] in the plural/past suffix:
deletes: [jumala+i+ssa]  /jumalissa/;
or mutates to /o/: [tavara+i+ssa]  /tavaroissa/;
or displays free variation: [itara+i+ssa]  /itaroissa/ ~ /itarissa/.
• [a+i] configurations are allowed morpheme-internally so
deletion/mutation is a DE effect.
• Anttila’s (2002) analysis focuses on the interplay between
morphological and phonological factors conditioning the allomorphy.
• This paper, however, directly appeals to the (tentative, markedness)
constraint driving the alternation: *[ai].
MSI Analysis and Locality:
•
•
•
•
•
•
*[ai] is indexed to the [-i] in the relevant suffixes.
*[ai](L) – indexed – outranks both Max and Ident inducing repair (violating
faithfulness).
Locality convention *[X]L: “Assign a violation mark to any instance of X that
contains a phonological exponent of a morpheme specified as L.” (p. 10)
Indexed constraints apply if and only if the locus of violation contains the
indexed morpheme (or parts of it or conjunctions thereof): the locality
convention therefore gives MSI an edge over alternative theories in that it is
able to pick out sub-parts of morphemes which are active in
triggering/blocking.
*[ai](L) >> Max, Ident >> *[ai] will ensure that stem-final /a/ preceding [-i]
undergoes mutation or gets deleted.
If the stem is indexed for Max, mutation will take place: [tavara+i+ssa] 
/tavaroissa/. If it is indexed for Ident deletion would be the result:
[jumala+i+ssa]  /jumalissa/. Unindexed stems such as /itara--/ will display
free variation (tableaux later).
Assamese ATR Harmony (Mahanta
2009) and MSI:
(1) In Assamese, the front and back mid vowels surface as [e] and [o] (viz.,
[+ATR]) when followed by high + ATR vowels /u/ or /i/. Elsewhere, the
vowels come out as [-ATR] [ɛ] and [ɔ].
(2) The low vowel /a/ is generally opaque to ATR harmony except before the
suffixes [-iya] and [-uwa]:
 While /a/ normally becomes /o/ before these suffixes (e.g., /sal/ ~ /sol-iya/;
/dal/ ~ /dol-iya/), it becomes /e/ when preceded by another /e/ (e.g., /dhemeliya/).
(3) Mahanta makes use of the markedness constraint*[-ATR][+ATR] to account
for general ATR harmony and *[-ATR][+ATR] (L) to account for the
exceptional harmonising of /a/ before [-iya] and [-uwa].
(4) Ident (Low) >> *[-ATR][+ATR]: /a/ does not “generally” undergo harmony.
(5) *[-ATR][+ATR](L) >> Ident (Low) >> [-ATR][+ATR]: before [-iya] and [uwa] which are indexed for *[-ATR][+ATR](L), even /a/ undergoes harmony.
Tableau 3
Input
Output
*[-ATR][+ATR](L)
/alaxuwa/
alax-uwa
*!
IdentLow
*[-ATR][+ATR]
*
☞ alox-uwa
*
olox-uwa
**!
*
Local exceptional triggering: MSI
and other approaches – a comparison
•
•
If [a+i] sequences in Finnish occur only at morpheme junctures, Cophonology,
MSI and faithfulness-only indexing can all account for it.
But when such strings occur tautomorphemically and heteromorphemically
(e.g., /taitta-i/) only MSI with its locality convention gets the right output:
/taittoi/ or /taitti/; never */titti/ or *taittai/.
– Cophonology will demand the ranking FAITH >> *[ai] for the stem-internal [ai]
and the opposite for the one at the stem+suffix juncture. There is no way to
reconcile the rankings in such a way that the stem-internal [ai] is retained and the
morpheme-junctural one is repaired.
– In the faithfulness-only indexing approach, if the stem is indexed for FAITH (and
FAITH (L) >> *[ai] >> FAITH), then the stem-final /a/ that precedes suffixal [-i]
will never be repaired; if not, then both [ai] sequences will be repaired, contrary to
expectation.
•
Faithfulness-only indexing and Cophonology can get /taittoi/ or /taitti/ only by
resorting to a sub-theory of Derived Environment, a result obtained without
additional machinery in MSI.
The problem:
• What MSI has and the other approaches do not is the
facility to pick out parts of morphemes within a larger
string through indexed constraints, making the constraints
in turn apply to sub-word components and successfully.
• In other words, MSI’s locality convention *[X]L enables it
to deal with cases like Finnish allomorphy, Assamese
vowel harmony etc all of which are triggered locally.
• Faithfulness-indexing and Cophonology on the other hand,
because their constraints are defined over entire morphophonological strings cannot handle inter-morphemic
patterns of exceptional triggering and blocking which are
in some sense local in nature.
Finnish [a+i] Allomorphy again:
•
(i)
Recall:
*[a+i] is the marked configuration and is repaired in
Finnish when the /i/ is part of the plural or past suffix.
(ii) The repair choice varies: when the stem is indexed for
Max, the /a/ preceding the suffix undergoes mutation;
when it is indexed for Ident, it is deleted; when
unindexed, either option may be chosen.
(iii) This is the general picture and holds of tri-syllabic stems
(more generally those with odd parity of syllables).
Note: Double lines in the tableaux below indicate that the
constraints separated by them are not ranked w. r. t each
other.
Tableau 4
Input
Output
*[ai]
(L1)
/itarai(L1)ssa/
itaraissa
*!
MAX
(L2)
IDENT
(L3)
MAX
☞itaroissa
*
☞itarissa
/tavara
(L2)i(L1)ssa/
tavaraissa
/jumala
(L3)i(L1)ssa/
jumalaissa
*
*!
☞tavaroissa
*
tavarissa
jumaloissa
☞jumalissa
IDENT
*!
*
*!
*!
*
*
Finnish [a+i]: stems with an even
number of syllables (Cophonology
and
MSI
treatments
)
1) For disyllabic stems, Anttila (2002) attributes the obligatory deletion of
(mutation does not occur in this context) stem-final /a/, when there is
an /o/ preceding it, to a ban on the co-occurrence of foot-internal round
vowels (constraint: OCP/V[rd]φ (OCP for short)).
2) Anttila (2002) – OCP >> Max (his *Del): mutation is not a possibility
in this context.
3) MSI - Ident (L3), OCP >> Max (L2) >> Max, Ident: Even if a
disyllabic stem is indexed for Max (L2), the stem-final /a/ will undergo
deletion (and not mutate to /o/) if there is a preceding /o/ due to the
ranking of the constraints in boldface.
4) Tableau below shows that a final /a/ in a disyllabic stem is bound by
OCP and is therefore deleted; however, the final vowel in a tri-syllabic
stem does not have a foot-internal /o/ preceding it whence it mutates to
/o/.
5) Double lines indicate mutual lack of ranking.
Tableau 5
Input
Output
/tota
(L2)i(L1)/
☞ (toti)
(totoi)
/itota
(L2)i(L1)/
(ito)ti
☞ (ito)(toi)
IDENT
(L3)
OCP/V
[rd]φ
MAX
(L2)
MAX
*
*
*!
IDENT
*
*!
*
*
Finnish [a+i]: stems with an even
number of syllables (contd)
6) When the foot-internal vowel preceding /a/ is not /o/, mutation (based on the trisyllabic case in tableau 5) is expected to be the norm because OCP is irrelevant
. However, there is actually free variation in this case: /taita+i/  /taiti/ ~
/taitoi/.
7) To derive default mutation in even-numbered stems (the contra case of OCPdriven deletion), one needs a constraint that applies only to even numbered
stems: Pater adopts the constraint OO-Maxφ.
8) OCP/V[rd]φ >> OO-Maxφ, Ident (L3) >> Max (L2) >> Ident, Max:
(a) without pressure from OCP, unindexed (even-numbered) stems will choose
mutation (since Ident (L3) is irrelavant) which is the ‘default’ repair in this
context;
(b) stems indexed to Ident (L3) will involve free variation (never categorical
deletion because of lack of ranking between OO-Maxφ, Ident (L3));
(c) as for tri-syllabic stems, they will choose mutation if they are indexed for
Max (L2), deletion if they are indexed for Ident (L3) and free variation when
they are unindexed.
Note: 8 (a) and (b) are illustrated in tableau 6 below; 8 (c) in tableau 5 above.
Tableau 6
Input
Output
OO-MAX
φ
/taita(L3)i(L1)/
☞taiti
*
☞taitoi
/palai(L1)/
pali
IDENT
(L3)
MAX
(L2)
MAX
*
*
*
*!
☞paloi
/jumala
(L3)i(L1)-ssa/
*
☞jumalissa
jumaloissa
IDENT
*
*!
*
A comparison of approaches
• Anttila (2002) does not handle even-numbered cases
without foot-internal round vowels viz., cases like /pala+i/
 /paloi/ which involve mutation.
• The overall analysis cannot anyway be translated into his
morpheme-specific re-ranking approach:
– For instance, free variation for /taita-i/ requires Ident and Max to
be unranked (as per the Subregularity Convention whose outcome
is the conflation of exceptionality and variation as noted earlier).
– But this would mean that stems are (also) free to pick the ranking
Max >> Ident leading to consistent mutation in this environment
which runs contrary to the empirical fact.
Constraint-indexing as Inconsistency
Resolution:
• Exceptions to phonological patterns result in inconsistent data sets
(Tesar, Alderete, Horwood, Merchant, Nishitani and Prince (2003))
with which the prevalent constraint rankings are incompatible: that is,
some parts of the data may demand one ranking and others a different
one.
• Tesar and Smolensky’s (1998) Constraint Demotion Algorithm is a tool
devised to deduce this type of inconsistency.
• In a hypothetical language, for instance, which has /pa/~/pak/, /lo/ ~
lok/ and /tak/ ~ /ta/ as the winner loser-pairs, NoCoda >> Max will
pick the winner in the first two instances but the loser in the third. The
CDA “will fail to rank these constraints” and “declare the data
inconsistent.” (Prince 2002) as discussed in Pater (2008: p. 19).
• The Recursive Constraint Demotion Algorithm (RCD) (Tesar and
Smolensky 1998) is useful in picking out the locus of inconsistency:
Operation of the Recursive
Constraint Demotion Algorithm
Constraints preferring only winners installed in a stratum
|
Winner ~ loser data pairs covered by installed constraints removed
|
Constraints preferring only winners in the remaining data installed in the
next stratum
|
Process repeated until all data are covered; or there are no more
constraints preferring only winners in the residue.
|
Residue the locus of inconsistency.
RCD and Indexing
• In the case of lexical stress, location of inconsistency is ensued by
alteration to the underlying representation (Tesar et al 2003) called
“lexical surgery”.
• However, the search space of possible lexical changes is huge for other
morpheme-specific phonological patterns and “surgery” therefore
seems unlikely in these cases.
• In this context, indexing can be brought in (only) where “consistency”
ends:
(a) once the RCD deduces inconsistency, a constraint selecting winners
for all instances of some morpheme is indexed with all such
morphemes and is installed in a stratum;
(b) the RCD now iterates again, indexing other constraints if required
with morphemes for which they choose only winners, until the entire
dataset is accounted for.
Indexing as inconsistency resolution:
a re-look at syncope in Yine
• Max and Align-Suf-C, the crucial
constraints, both pick winners and losers as
seen below:
Input
W~L
Max
Align-Suf-C
heta+lu
hetlu~hetalu
L (heta)
W (lu)
heta+nu
hetanu~hetnu
W (heta)
L (nu)
heta+wa+lu
hetawalu~hetawlu
W (wa)
L (lu)
heta+nu+lu
hetanru~hetanulu
L (nu)
W (lu)
Indexing and RCD:
• At first blush, Max can be indexed only for [-wa]
because it prefers Ws and Ls for /heta/ as does
Align-Suf-C for [-lu] and [-nu].
• Once the data pairs where Max (L1) chooses only
winners are removed, Align-Suf-C chooses only
winners for [-lu] with which it can be indexed.
• The next slide shows the installation of constraints
in stratified fashion:
Stratified installation of indexed
constraints:
Max (L1) >>
Input
Max (L1) >> Align-Suf-C (L2)
W~
L
Max
heta+lu
hetlu ~
hetalu
L
(heta)
W
(lu)
heta+nu
hetanu ~
hetnu
W
(heta)
L
(nu)
hetanlu ~
hetanulu
L
(nu)
W
(lu)
heta+nu
+lu
AlignSuf-C
Input
W~L
Max
AlignSuf-C
heta+ nu
hetanu ~
hetnu
W (heta)
L (nu)
Overall ranking and implications:
• *CCC >>> Max (L1) >> Align-Suf-C (L2) >> Max >> Align-Suf-C
• *CCC is ranked on top because syncope never creates tri-consonant
clusters and its inviolability is definitive even before indexing begins
(viz., inconsistency is deduced).
• Viewed as an algorithm for inconsistency resolution, indexing as a
“meta-construct” will always be subordinated to the general constraint
ranking which will always hold primacy in generating the nonexceptional phonological patterns:
– E.g., /terka+lu/  /terkalu/ (*terklu) is decided even before inconsistency
is located because of high-ranking *CCC; so there is no way that the
learner will delay learning this phonological pattern till inconsistency is
detected by indexing /terka--/ with Max.
Representational Alternatives
•
Matteson (1965): non-triggering morphemes in Yine accounted for by
postulation of an empty V-slot before the suffix-initial consonant
(e.g., Vta) (see Wolf 2006 for an OT derivation of the account).
•
Morphemes which do not undergo syncope (exceptionally) may be
subject to faithfulness to some aspect of syllable structure (e.g., Maxmora) which blocks syncope.
•
The problem is threefold:
(i) How does the learner choose the correct representation?
(ii) And how does one know that this representation is indeed (in some
cases) a mora when the entire vowel alternates (viz., vowel quality is
not predictable)?
(iii) Even if it is plausible for the learner to restructure the input such that
a faithfulness constraint is allowed to then choose the correct output,
no currently extant learnability proposal accommodates such a
provision.
Representational versus Diacritic
Theories
•
•
•
•
See Inkelas (1994) for a version of Lexicon Optimisation resulting in
underspecified representations;
See Tesar et al (2003) for comments on the grammar-blind nature of lexical
“surgery” (Tesar and Smolensky 1998) and Tesar (2006) for contrast analysis.
Ultimately, the criterion to assess the merit of diacritic theories and
representational ones should be related to learnability and not some
abstract/aesthetic principle (p.23).
Although “diacritics” seem the way to go for the cases discussed, not all cases
of exceptionality can or should be handled by indexing (see Ito and Mester
2001, Albright 2002 and Becker 2004 for more arguments favouring diacritic
theories) :
– Mutation processes whose markedness motivation has disappeared are
more amenable to representational analyses;
– However, even proponents of representational tacks in OT also see a place
for some variant of morpheme-specific indexing (Inkelas 1999).
Among diacritic approaches
•
•
•
Though faithfulness-only indexing seems prima facie too restrictive a model to
handle all co-occurring patterns of lexically idiosyncratic phonological
patterns (Inkelas and Zoll 2003), it is difficult to find examples that cannot be
handled by faithfulness-only indexing given the M&F interactions in OT.
As for markedness-indexing (Pater 2000, 2006, Ota 2004, and Flack to appear;
see also Gelbart 2005) proposed here, it could run into one problem:
relativised to a category like Affix, markedness-indexing can subvert the metaranking Root-Faith >>Affix-Faith (McCarthy and Prince 1995) by allowing
contrasts in affixes and neutralising them in roots.
Cophonology (Anttila 2002) can account for virtually all types of
exceptionality that a theory accommodating M&F indexing (the one proposed
here) handles. It cannot, however, translate a grammar like the following
where the indexed constraint is more than one stratum away from its
unindexed counterpart:
– Con1-L >> Con2 >> Con3 >> Con1
Alternatives and intermediate
positions
• A marriage of approaches or intermediate
positions between strictly representational and
diacritic standpoints is possible: e.g., indexing of
only certain markedness constraints or “structural
hypotheses limited to surface observable forms”.
• Alternative accounts of morphology-based
phonological exceptionality include Alderete’s
(2001) antifaithfulness theory, Kurisu’s (2001)
Realize Morpheme theory and Zuraw’s (2000)
extension of Boersma and Hayes’ (1998)
Stochastic OT.