Lexically conditioned variation in Harmonic Grammar

OCP-5, Toulouse-Le Mirail, 01-26-08
Lexically conditioned variation in
Harmonic Grammar
Joe Pater, University of Massachusetts, Amherst
with the collaboration of
Paul Boersma, University of Amsterdam
Andries Coetzee, University of Michigan
Isabelle Racine, Université de Genève

Lexically conditioned variation:
(1) A variable process whose probability of application is
conditioned by the lexicon
Three extremely well-studied variable phonological
processes that display lexical conditioning:
(2) English vowel reduction (Fidelholtz 1975 et seq.)
embrace > emporium
English t/d-deletion (Labov et al. 1968 et seq.)
jus(t) > bus(t)
French ‘schwa’ deletion (Dell 1973 et seq.)
s(e)maine > s(e)mestre

Lexically conditioned variation is a particular focus of usagebased
and exemplar-based approaches to phonology:
(3) English:
Bybee (2001), Pierrehumbert (2001), Phillips (2006)
French:
Sobbotta (2006), Eychenne and Pustka (2007)
Key observation (Dell 1973, Fidelholtz 1975)
(4) Word frequency correlates positively with frequency of
application of these variable processes

Argument for usage-based phonology:
(5) Frequency of use ~ frequency of application
correlation not captured by other models of phonology
A definition of the domain of phonological theory:
(6) Native speaker knowledge of the sound patterns of
language
(7) The acquisition of that knowledge
It remains unclear whether the correlation in (5) is in (6), and
therefore whether phonology should account for it (that is,
the correlation could well be a product of use, as per Bybee)

However, since speakers do at least know that words differ
in their probability of application of variable processes, and
since they learn this probability, an adequate theory of
phonology must provide a way of representing lexically
conditioned variation, and its associated learning theory
should provide an account of its acquisition.
Current phonological theory provides the needed ingredients
(HG = Harmonic Grammar, Smolensky and Legendre 2006)
(8) Theory of variation (Boersma 1997 et seq.)
Stochastic OT/Noisy HG
Theory of lexical conditioning (Pater 2000 et seq.)
Lexically indexed constraints
Theory of learning (Boersma 1997, Boersma and Pater 2008)
Gradual learning algorithm for OT/HG

Coetzee and Pater (2008) illustrate this approach to lexically
conditioned variation with English t/d-deletion
Today:
§1. Introduction to the theories of grammar (HG), variation
(noisy HG) and learning (HG-GLA) I’ll be assuming, with
French e-deletion as the illustrative example
§2. Presentation of data on lexical conditioning of French edeletion,
especially from Racine’s (2007) study of native
speaker judgments
§3. Further analysis and learning simulations
§4. Other HG approaches to lexical conditioning of edeletion
§5. Broader implications

1. HG, variation, exceptionality, and learning
In HG (Legendre, Miyata and Smolensky 1990, Smolensky
and Legendre 2006) well-formedness, or Harmony (H) of
representation (R), is the sum of its weighted constraint
violations/scores (constraint score vector C and weights W)
(9) H(R) = 〈C, W〉
Prince and Smolensky (1993/2004:236) note that HG Harmony
can be used to choose the optimum in a candidate set:
(10)
CON-1 CON-2
Input-1
2 1
Output-11 -1 -2
Output-12 -1 -1

Applied to e-deletion (where [ә] is the vowel represented by orthographic
e, which varies from dialect to dialect)
(11)
*[ә] MAX
sәmɛn 2 1
sәmɛn -1 -2
smɛn -1 -1
Constraint definitions:
(12) *[ә]
Assign a score of -1 for each vowel [ә]
MAX
Assign a score of -1 for each vowel in the input that
lacks an output correspondent

Boersma’s (1997 et seq.) theory of variation:
(13) Noisy evaluation
Each time the grammar is used to evaluate a
candidate set, add a Gaussian random variable Nk to
each constraint weight wk
Applied to e-deletion (post-noise values in parentheses)
(14)
sәmɛn
*[ә]
1
(1.1)
MAX
1
(0.9)
sәmɛn
*[ә]
1
(0.9)
MAX
1
(1.1)
sәmɛn –1 –1.1 sәmɛn –1 –0.9
smɛn –1 –0.9 smɛn –1 –1.1
(see Andreassen’s 2004 similar ‘floating constraint’ analysis of French schwa)

The distribution of [ә] is subject to categorical restrictions
(Martinet 1969, Dell 1973; cf. Walker 1993):
(15) a. Word-initial deletion never occurs after a
tautomorphemic cluster (*gr(e)nouille, *Br(e)ton)
b. [ә] occurs only after consonants, and is
productively deleted after vowels (vous joueriez vs.
vous parleriez from jouer and parler)
A constraint satisfied by the presence of [ә] (assuming e-deletion
results in an empty-headed syllable, as in Rialland 1986, though cf. Steriade
2000 – the constraint may be better defined in articulatory or perceptual terms):
(16) LICENSE-C
Assign a violation mark to a consonant in syllable
without a vocalic nucleus

In HG, the difference between the C_ and CC_
environments can be analyzed as the difference between
one or two violations of LICENSE-C
(See Pater, Bhatt and Potts 2007 for critical assessment of extant arguments for
strict domination, and discussion of outstanding issues)
(17)
sәmɛn
*[ә]
1.5
LIC-C
1
brәtɔ̃
*[ә]
1.5
LIC-C
1
sәmɛn –1 –1.5 brәtɔ̃ –1 –1.5
smɛn –1 –1 brtɔ̃ –2 –2
And the restriction of [ә] to post-consonantal position can be
understood as a ‘gang effect’ between LICENSE-C and MAX,
as in the following Richness of the Base tableau
(see Dell 1973 for a rule-based analysis of post-V deletion, including a Richness
of the Base approach to that phonotactic gap, and an MSC against initial [ә])

(18)
(19)
*[ә] LIC-C MAX
CәCVC 1.5 1 1
CәCVC –1 –1.5
CCVC –1 –1 –2
*[ә] LIC-C MAX
CVәCVC 1.5 1 1
CVәCVC –1 –1.5
CVCVC –1 –1
This analysis is intermediate between the analyses of
‘schwa’ as epenthetic (Martinet 1969, Côté 2006) and underlying:
(20) Underlying ‘schwa’ can surface only when it serves to
satisfy a markedness pressure (e.g. LICENSE-C)

To account for exceptions to e-deletion, I use a lexically
specific version of MAX
(lexically specific faithfulness introduced to OT in Pater 2000 to account for
lexical conditioning of English vowel reduction; see also esp. Ito and Mester 1995
et seq. for applications to lexical conditioning in Japanese)
(21) MAX-L
Assign a violation mark for every input segment that
belongs to lexical item L and that lacks an output
correspondent
A word like belon (a type of oyster), whose first vowel
apparently never undergoes deletion (Angoujard 2006, Eychenne
2007), is distinguished from semaine in terms of the relative
ranking of the MAX-L constraint indexed to each of them.

How does an analyst find a weighting for the constraints that
generates the patterns in a given language? How does a
learner find such a weighting?
For analysis of categorical patterns in HG, and comparison
of typology in HG and standard OT:
(22) HaLP (Potts, Becker, Bhatt, Pater 2007)
OT-Help (Becker, Pater, Potts 2007)
For patterns of variation, and simulation of human learning:
(see Jäger to appear for an earlier similar proposal)
(23) HG-GLA in Praat (Boersma and Weenink 2007)

The HG-GLA is a very simple learning algorithm, which
adapts a machine learning procedure (perceptron, stochastic
gradient ascent) to the learning of HG grammars, and
closely resembles Boersma’s (1997 et seq.) OT-GLA
Unlike the OT-GLA for stochastic OT, it is guaranteed to
converge on correct weightings for categorical data:
(24) HG-GLA convergence
Fischer 2005, Boersma and Pater 2008
OT-GLA/stochastic OT non-convergence
Pater 2008

I provided the HG-GLA with the following distribution of data:
(25) semaineL1 50% deletion
belonL2 0% deletion
bretonL3 0% deletion
Initial constraint weights:
(see Jesney and Tessier 2007 on high Mark and low Faith in HG learning)
(26) LICENSE-C, *[ә] 50
MAX, MAX-L1, MAX-L2, MAX-L3 0
Settings were Praat’s defaults for these parameters:
(27) Noise SD = 2.0
Plasticity = 1.0 (decreased by a factor of 0.1 after
each of 4 sets of 100,000 learning data)

The grammar model was run in Linear OT mode (Keller 2006),
under which it interprets all sub-zero weights as zero
(28) LICENSE-C 50.3
*[ә] 49.7
MAX-belon 17.0
MAX-breton 0.0
MAX –0.3
MAX-semaine –17.3
Probability of e-deletion with grammar in (28), noise 2.0
(29) a. semaine 50% belon 0% breton 0%
b. әCVC 100% CVәCVC 100%

3. Lexically conditioned e-deletion: data
The simplified data in the previous section could be handled
by any standard theory of generative phonology (e.g. Dell 1973)
(30) semaine subject to an optional rule of e-deletion
belon marked as an exception to the rule
breton does not meet conditions of the rule
joueriez subject to obligatory post-V e-deletion
*әCVC due to a Morpheme Structure Constraint
Dell (1973) provides an example of the type of lexical
conditioning that cannot easily be handled by the theory he
was working with, but which falls out from the one in §2.

In general, schwa deletion is blocked by a preceding
consonant (judgments from a native speaker in Nantes):
(31) la s’maine ✓ une s’maine ??
Dell writes his rule “VCE1” to apply only after vowels.
However, he notes that (p. 207 in 1980 English translation):
(32) Contrary to what we said above, in very rapid speech
the schwa of a small number of words beginning with
#C __ can be dropped even if the preceding word
ends in a consonant: quelle semaine is sometimes
pronounced [kɛlsmɛn]...The other words that have
this property in our speech are je, semelle, cerise,
chemise, fenêtre and petit...there are other words
which always behave according to VCE1: semestre,
seringue, chenille (glosses and transcriptions omitted)

The generalization:
(33) The probability of schwa deletion is greater for words
like semaine than for words like semestre
Further evidence of finer distinctions than optional
application vs. non-application:
(34) a. Dictionaries find the two-way categorization
inadequate (Walker 1996)
b. Corpus-based studies note that some words show
greater frequency of deletion than others (e.g. Hansen
1994, Eychenne 2007, Eychenne and Pustka 2007)
c. Racine and Grosjean (2002) provide data from a
production study showing a wide range of deletion
frequencies across words

Dell (1973) notes that exceptions to schwa deletion tend to
be rarely used or literary words (as well as proper names)
He also claims to have systematically looked for
phonological generalizations, and came up empty-handed
(see also Walker 1996)
Is it “just” usage frequency that determines deletability of
schwa?

No.
(35) Racine and Grosjean (2002) find a correlation
between deletion and frequency ratings, but note that
the correlation is not perfect.
According to Fougeron, Goldman and Frauenfelder (2003):
(36) Overall the results do not support our hypothesis:
lexical frequency and competition do not appear to
influence strongly whether liaison and elision are
realised or not.
(they also cite Adda-Decker et al. 1999 as having reached the same conclusion)
Therefore, not only do speakers need to learn whether a
word has a “stable” or “unstable” e, but they need to learn its
degree of stability, or profil de maintien (Walter 1977)

Racine’s (2007, in prep.) judgment study provides
particularly convincing evidence of speakers’ knowledge of
individual words’ profil de maintien
Method:
12 native-speakers from Nantes, France (and 12 from Neuchâtel,
Switzerland)
All 2189 nouns containing schwa in BRULEX database (10
eliminated from analysis for being judged as [œ]/[ø])
Presented orthographically with preceding la/le
The list was presented twice, with an interval of several
days; once all words were rated with e present, and once
judged with it absent
Rated on a scale of 1 (infrequent) to 7 (very frequent); data
here are the means over the 12 subjects for each word

n=30 n=338

elon –5.4 semestre –4.6 semaine 0.0

4. Analysis of probabilistic lexical conditioning
Constraint for e-deletion with preceding consonant-final
word:
(35) *C.C.
An unlicensed consonant must be preceded by a
vowel
Probability of deletion in learning data:
(36) la semaineL1 50% quelle semaineL1 10%
le semestreL2 10% quel semestreL2 0%
le bretonL3 0% quel bretonL3 0%
la belonL4 0% quelle belonL4 0%
The markedness constraints again started out at 50, and the
five faithfulness constraints (MAX, MAXL1...4) at zero

The constraint weights found by the learner:
(37) *[ә] 50.3
LICENSE-C 49.7
MAX-belon 15.0
*C.C. 4.9
MAX-semestre 4.8
MAX-breton 0.0
MAX –0.3
MAX-semaine –20.1
Deletion rates:
(38) la semaine 52% quelle semaine 10%
le semestre 11% quel semestre 1%
le breton 0% quel breton 0%
la belon 0% quelle belon 0%
әCVC 100% CVәCVC 100%

4. Alternative accounts in HG
4.1 Lexically scaled weights (≈ connectionist lexicon)
The numerically valued constraints of HG allow for views of
lexical representation that diverge much further from
“standard” generative phonology than lexically specific
constraints
Coetzee and Pater (2008) sketch one such alternative: that
individual lexical items (or segments) bear numerical indices
that rescale the basic weight of faithfulness constraints (see
also Goldrick 2008)
For the word semaine, the value of the faithfulness constant
would be relatively low, thus leading to variable deletion

(39)
*[ә] LIC-C MAX
/sәmɛn/ 1 2.0 1.0 1*1=1
[sәmɛn] –1 –2
[smɛn] –1 –1 –2
And for belon, the value of the faithfulness constant would
be relatively high, thus leading to consistent retention
(40)
/bәlɔ̃/2
*[ә]
2.0
LIC-C
1.0
MAX
1*2=2
[bәlɔ̃] –1 –2
[blɔ̃] –1 –1 –3
Lexical constants are more restrictive than lexically specific
constraints, and faithfulness constraint scaling can be
extended to register/style differences (Coetzee and Pater 2008; see
van Oostendorp 1998 on register-based reranking of faithfulness)

4.2 Probabilistic allomophy (≈ exemplarist lexicon)
In OT, “allomorphy” is used to describe a case when the
phonology chooses between two lexically supplied forms of
a morpheme (e.g. Kager, Mascaró, Tranel).
If the lexicon provides in addition a default probability
distribution over the allomorphs, then this could interact with
the contextual probabilities provided by the grammar to yield
the observed conditioning by lexicon and context
One way of formalizing this, similar in spirit to lexically
specific constraints, is with a set of “Use-/X/” constraints
(Kager 1996, Boersma 1999, Apoussidou 2006)

5. Broader consequences of lexically conditioned
variation
Lexically specific constraints, and the related approaches in
HG discussed in §4, are highly interactive theories of the
lexicon-grammar relationship
This high degree of interaction seems to be required to
account for the fine-grained consequences of the lexicon on
probability of e-deletion
Coetzee and Pater (2008) point out that lexically conditioned
variation is problematic for some widespread assumptions
about the relationship between the lexicon and the
phonological grammar

The hard question: what type of process is e-deletion?
(41) Lexicon → Early Phonology → Late Phonology
→ Phonetic Implementation
As Walker (1996) points out, e-deletion has contradictory
properties under the view that processes at each of these
levels have a set of fixed characteristics (a view most closely
associated with classical Lexical Phonology; e.g. Kiparsky 1985)
(42) i. Has exceptions (Lex/EP)
ii. Sensitive to morphology (Lex/EP) (Dell 1973)
iii. Variable (LP/PI)
iv. Non-structure preserving, and may even lead to
between category outcomes (LP/PI) (Fougeron and
Steriade 1997, Barnes and Kavitskaya 2003; cf. Côté and Morrison
2007)

The fine-grained lexical conditioning of rate of variation in edeletion
(and the English processes mentioned in 2) seems
to put the final nail in the coffin of the idea that processes at
each of the levels in (41) have non-overlapping
characteristics (see already Kiparsky 1993 on variation in OT)
The fact that this variable process is sensitive to morphology
and the lexicon places it firmly within the domain of
phonology, and makes it hard to imagine how one could
maintain a “categorical vs. probabilistic” distinction for
distinguishing phonology from phonetics

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