Optimal Paradigms1 John J. McCarthy University of Massachusetts, Amherst Abstract ...

70 Pages·2002·0.36 MB·English

Revised November 21, 2002.
Optimal Paradigms1
John J. McCarthy
University of Massachusetts, Amherst
Abstract
Transderivational Correspondence and Uniform Exponence are two recent theories
of surface resemblances among morphologically related words. This chapter presents
Optimal Paradigms theory (OP), which incorporates elements of both. In OP,
candidates consist of entire inflectional paradigms. Within each candidate paradigm,
there is a correspondence relation from every paradigm member to every other
paradigm member. Faithfulness constraints on this intraparadigmatic correspondence
relation resist alternation within the paradigm. This model is illustrated and
supported with a type of evidence that has not figured in previous discussions, the
templatic structure of the Classical Arabic verb. Arabic verb templates pose a
problem for Generalized Template Theory, which demands that templatic restrictions
emerge from independently motivated constraints. The OP model supplies the
necessary link between this restrictive theory of templates and the Arabic data.
1. Introduction
Traditional ideas of analogy, SPE(cid:146)s phonological cycle, and recent proposals about output-
output faithfulness all have the same goal: to account for surface resemblances among
morphologically related words. For instance, the trisyllabic participial form lightening has a syllabic
n because of its relationship to the verb lighten (cid:151) a relationship not shared with the disyllabic noun
lightning. Phenomena like this have figured prominently in discussions of analogy and its successors.
1For feedback on earlier versions of this chapter, I am grateful to the editors of this volume, to the participants in phonology
seminars at the University of Massachusetts, to an audience at the University of Tromsł (particularly Curt Rice), and to John
Alderete, Jonathan Bobaljik, Andries Coetzee, Paul de Lacy, Diamandis Gafos, Maria Gouskova, Yoonjung Kang, Maria-
Rosa Lloret, Linda Lombardi, Paula MenØndez-Benito, Joe Pater, Alan Prince, Lisa Selkirk, and Jeroen van de Weijer.
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In one thread of recent research (see §2 below), words have a surface resemblance because
of shared membership in a paradigm. A paradigm is a set of inflected forms based on a common
lexeme or stem: +lighten, lightens, lightened, lightening, is an example. The idea is that members
of a paradigm should have similar surface phonology, such as the syllabic n that appears consistently
throughout the lighten paradigm.
In this article, I will introduce a novel formalization of surface resemblance through shared
paradigm membership, couched within Optimality Theory (Prince and Smolensky 1993) and
correspondence theory (Benua 1997, McCarthy and Prince 1995, 1999). In this Optimal Paradigms
model (OP), an OT constraint hierarchy evaluates candidates consisting of entire paradigms. Within
a paradigm qua candidate, every output realization of a lexeme stands in correspondence with every
other output realization of that lexeme. Faithfulness constraints on this intraparadigmatic output-
output correspondence relation resist alternation within the paradigm. Through interaction with
markedness and other faithfulness constraints, they account for surface resemblance and failure of
resemblance among members of a paradigm.
The OP model is illustrated and supported by a type of data that has not figured in previous
discussions of the surface-resemblance problem. Certain properties of Classical Arabic root-and-
pattern morphology, I will argue, cannot be satisfactorily explained without the OP model. This
argument also shows how OP supports the minimalist goals of Generalized Template Theory (GTT),
which seeks to eliminate templates and similar stipulations from linguistic theory, replacing them
with independently motivated constraints. The analysis of Arabic templates sets in clear contrast the
differences between OP and serial-derivational models, including proposals for melding OT with
Lexical Phonology (see §4).
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2 Background to and Overview of the OP Model
This section provides an informal introduction to the Optimal Paradigms model and to the
analysis of Arabic templates. Later sections fill in the details of the theory and the analysis.
Benua(cid:146)s (1997) Transderivational Correspondence Theory (TCT) says that a morphologically
derived surface form stands in a relation of output-output (O-O) correspondence with its
morphologically simplex counterpart, called the base. For example, lightening is in O-O
correspondence with lighten. Harmonic evaluation proceeds recursively, from the base outward, by
a principle of Base Priority. The surface phonology of the base lighten is carried over, by obedience
to O-O faithfulness constraints, to the derived form lightening. Base Priority disallows influences
running in the other direction, so derived lightening can never influence the base lighten via O-O
correspondence. Because of Base Priority, TCT is inherently asymmetric: if form A influences the
phonology of a morphologically related form B, then form B can never influence the phonology of
form A.
Another approach to the surface-resemblance problem is inherently symmetric, requiring that
morphologically related words (or even individual morphemes) resemble one another without
assigning priority:
(1) a. Uniform Exponence (Kenstowicz 1996)
Minimize the differences in the realization of a lexical item (morpheme, stem, affix,
word).
b. Metrical Consistency (Burzio 1994: 228)
Every morpheme must be as metrically consistent as possible.
In later work, Burzio (1996, 1999) generalizes Metrical Consistency to a principle of Anti-
Allomorphy, which requires consistent realization of morphemes in all their phonological properties,
not just stress. With this generalization, these principles become equivalent: morphemes, stems, or
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words should not vary in their phonological realizations. Unlike TCT, this theory is inherently
symmetric: it is possible for form A to influence the phonology of form B, while at the same time
form B influences the phonology of form A.
These two theories of surface resemblance among related words are more complementary
than competing. TCT deals with the classic cases of cyclic or stratal behavior, such as English
condØnse/c(cid:242)ndŁnsÆtion (Chomsky and Halle 1968, Pater 2000): ranked faithfulness constraints on
surface forms, formalized under correspondence theory, enforce similarity, but by virtue of Base
Priority they effectively enforce it only on the derived form, not the basic form. Uniform Exponence
(UE) has been applied to paradigm-uniformity phenomena inter alia, preventing alternations among
forms that are related inflectionally, typically where no morphologically simplex base is identifiable.
TCT is not applicable to inflectional paradigms because it is an asymmetric, base-prioritizing
theory (though see Benua 1997: Chapter 6 for a different view). In TCT, the base is the first step in
the recursive evaluation. The derived form, which is the next step in the recursive evaluation, is
obtained from the base by applying a morphological operation, such as affixation. Inflectional
paradigms have no base in this sense: Latin amat (cid:145)he loves(cid:146) is not derived from amÇ (cid:145)I love(cid:146) or vice-
versa; rather, both are derived from the lexeme /am-/. This deficiency in TCT might be remedied by
invoking morphosyntactic unmarkedness, rather than morphological underivedness, as a way of
identifying the base form in an inflectional paradigm (cf. Kenstowicz 1996, Kiparsky 1998: 31-2,
Kraska-Szlenk 1995, Kurylowicz 1945-1949, Selkirk 2001). If this criterion is applied, then Latin
amat is presumably the base of the /am-/ verbal paradigm. But this method of base identification will
not work for the Arabic example discussed here (see §4.3).
Just as TCT has difficulties with inflectional morphology, so too UE runs into problems with
derivational morphology. If applied to derivation, UE overpredicts surface-resemblance effects. With
UE, it is possible for the derived form to influence the phonology of the base or for a bound
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morpheme in one word to influence the phonology of that morpheme in another word. Solid
synchronic examples of these predictions do not seem to exist.2 Furthermore, UE represents more
of an intuition than a usable phonological principle. In OT, a constraint is a function from a linguistic
expression to zero or more violation-marks. Injunctions like (cid:147)minimize the differences(cid:148) or (cid:147)be as
metrically consistent as possible(cid:148) are not well-defined constraints. Moreover, expressions like
(cid:147)minimize X(cid:148) and (cid:147)as X as possible(cid:148) incorporate into themselves part of the definition of EVAL, and
so they should not appear in constraint definitions (McCarthy 2002: 40). (See van de Weijer (1999)
for an improved formalization of UE and Buckley (1999) for related discussion.)
The Optimal Paradigms (OP) model proposed here synthesizes the best elements of TCT and
UE. From TCT it draws the idea of using correspondence theory as a foundation. Correspondence
theory supplies a range of well-defined, rankable constraints enforcing resemblance between forms.
From UE, OP incorporates the idea of evaluating surface resemblance symmetrically across
inflectionally related forms. The central premises of the OP model are therefore these:
2For example, Kenstowicz (1996) proposes that the leveling of the prefix des- as deh- in aspirating dialects of Spanish is a
consequence of UE acting on all instances of this bound morpheme. But there is no evidence that this is part of the synchronic
grammar: since deh- shows up in all contexts, there is no justification for underlying /des-/. Another example: Burzio (1994:
201) proposes that English words with the suffix -ic have penult stress to maintain uniformity with the same words ending
in -ical: e.g., acadØmical affects acadØmic (cf. Chomsky and Halle 1968: 88). One problem with this analysis is that many
words in -ic have no related form in -ical (sulfuric, Ethiopic, Olympic, Byronic) or they have a related form that is found in
dictionaries but not used (taxonomic(al), semantic(al), prosodic(al), genetic(al)). Another problem is that other suffixes, such
as -id and -ish, have the same stress behavior without a longer derivative to explain it.
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(2) OP in Outline
a. Candidates consist of entire inflectional paradigms, where an inflectional paradigm
contains all and only the words based on a single lexeme (for similar ideas, see Bonet and
Lloret 2001, Kenstowicz 1996: 385, McCarthy 1998, Raffelsiefen 1995, 1999, Tesar and
Smolensky 2000).3
b. Markedness and input-output faithfulness constraints evaluate all members of the
candidate paradigm. The violation-marks incurred by each paradigm member are added to
those incurred by all the others.4
c. The stem (output form of the shared lexeme) in each paradigm member is in a
correspondence relation U with the stem in every other paradigm member. (That is, for
OP
every candidate paradigm P there is a relation U on P(cid:215)P.) There is no distinctive base(cid:151)
OP
rather, every member of a paradigm is a base of sorts with respect to every other member.5
d. There is a set of output-output faithfulness constraints on the U correspondence relation.
OP
For example, suppose we have a language with no suffix in the singular and the suffix -i in
the plural. Suppose this language also has coronal palatalization before i. From the lexeme /mat/,
GEN will produce such candidate paradigms as +mat, mati,, +mat, ma±i,, and +ma±, ma±i,. Each
candidate paradigm brings with it a correspondence relation U that relates the stems in each
OP
3Here, I assume that paradigms are (cid:147)flat(cid:148), consisting of a list of all paradigm members. It is conceivable, however, as John
Alderete and Diamandis Gafos point out, that paradigms have internal hierarchical structure. For example, Latin noun
paradigms might decompose into separate subparadigms for singular and plural: ++pater, patris, ..., , +patre+s, patrum, ..., ,
sg. pl.
(glosses: ++father (nom.), father (gen.), ...,, +fathers (nom.), fathers (gen.), ...,,). The correspondence relations and OP
faithfulness constraints can be adapted to this proposal in various ways (cid:151) e.g., perhaps OP faith is violated once for every
(sub)paradigm that hosts an alternation, or perhaps there are distinct correspondence relations (and distinct OP faithfulness
constraints) within and between subparadigms. This possibility, though certainly intriguing, will not be pursued here because
the evidence under discussion does not require it.
4The violation profile of a form is a vector representing all of its constraint violations in rank order, such as +*, **, (cid:216), ***,
(Samek-Lodovici and Prince 1999). The violation profile of an entire paradigm is the vector sum of the violation profiles of
all members of that paradigm. E.g., +*, **, (cid:216), ***, + +(cid:216), *, **, (cid:216), = +*, ***, **, ***,.
5Limitation of the correspondence relation to the shared lexeme recalls Alderete(cid:146)s (1998) notion of stem-to-stem
correspondence, which is required in his accounts of pre-accentuation in Cupeæo and accent shift in Japanese.
Since U is a relation on P(cid:215)P, every member of a paradigm is also in correspondence with itself. This is harmless,
OP
since self-correspondence can never lead to faithfulness violations.
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paradigm member: mat U ma±i and, symmetrically, ma±i U mat. (The portions standing in OP
OP OP
correspondence are underlined.) The candidate +mat, ma±i, violates the constraint OP-IDENT(high)
(or whatever feature distinguishes t from ±).6
The OP model presupposes a distinction between inflectional morphology, which is
organized into paradigms, and derivational morphology, which is organized hierarchically by the
relation (cid:147)is derived from(cid:148). (See Spencer (1991: Chapter 6) for a review of the issues surrounding this
assumption.) Derivational morphology, I assume, is analyzed within TCT, as before. But inflectional
paradigms are different from derivational hierarchies; in paradigms, all members are co-equal in their
potential to influence the surface phonology of other members of the paradigm. This is formalized
by U correspondence, which gives every paradigm member a chance to affect any other member.
OP
Whether it does or does not depends on the ranking.7
As we will see in greater detail in §4 and §5, this model predicts certain interactional patterns
that set it apart from other approaches, particularly TCT. One pattern is overapplication-only. Given
a language with a general process of coronal palatalization, there are two ways to level alternations
within the paradigm of /mat/: +ma±, ma±i, or +mat, mati,. The first of these paradigms shows
overapplication of the palatalization process (cid:151) there is palatalization of /t/ even in the unsuffixed
form, where the conditioning i is absent. The second paradigm shows underapplication of
palatalization: the process is blocked in the suffixed form mati because there is no palatalization in
the unsuffixed form mat. OP-IDENT(high) is satisfied either way, but the paradigm with
6Technically, the paradigm +mat, ma±i, receives two marks from OP-IDENT(high), one for the mat U ma±i correspondence
OP
relation and the other for its symmetric counterpart. The paradigm +ma, ma±i, incurs one violation of OP-MAX for the ma
U ma±i relation and one violation of OP-DEP for the ma±i U ma relation.
OP OP
7Jeroen van de Weijer and the members of the Leiden Phonology Group raise an objection: the phonological effects of
derivational and inflectional morphology are sometimes the same. For example, English stress-neutral suffixes can be both
derivational (-ness) and inflectional (-ing). This is exactly as the OP model predicts: under ranking permutation, we expect
to find cases where OP faithfulness constraints, which pertain to inflection, and OO faithfulness constraints, which pertain
to derivation, are ranked similarly. The model also predicts, however, that inflection and derivation can act differently (cid:151) for
example, only derivation can show true underapplication effects, and only inflection can show phonological influences from
different paradigm members simultaneously (see §4.3).
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underapplication cannot be obtained in the OP model. (Some care is required in defining what over-
and underapplication mean in the context of a constraint-based theory like OT, so this statement
should not be applied indiscriminately. See §5.2.)
The problem with underapplication is that it competes with overapplication. Overapplication
satisfies the high-ranking markedness constraint that is responsible for the basic palatalization
process, but underapplication does not. Underapplication does better on IO faithfulness, but that is
irrelevant, because the assumed existence of the process in the language as a whole shows that IO-
IDENT(high) is ranked below the responsible markedness constraint. This means that there is only
one way for underapplication to win: some other constraint must block overapplication. For an
example of overapplication-only, see §4.1. For examples where overapplication is blocked and
underapplication happens instead, see §4.2 and §5.2. For a general evaluation of the overapplication-
only hypothesis, see §5.2. And for the reduplicative parallel, upon which this argument is based, see
McCarthy and Prince (1995, 1999).
A related prediction of OP is attraction to the unmarked. I will call a paradigm member an
attractor if other members of its paradigm are forced to resemble it by visibly active OP faithfulness
constraints. For example, in the leveled paradigm +ma±, ma±i, from /mat/, the form ma±i is the
attractor, with ma± forced to resemble it by OP-IDENT(high). Now suppose we have a situation
where there are two different ways to satisfy an OP constraint (cid:151) two different ways to level a
paradigm, depending on which member is acting as the attractor. That is, there are candidates +A1,
B1, and +A2, B2, that equally satisfy the high-ranking OP constraint, but differ in which paradigm
member is doing the attracting: in the first paradigm, A1 is the attractor, but in the second paradigm,
B2 is the attractor. Unless IO faithfulness is decisive, the winning paradigm will be determined by
markedness, according to the following logic:
(i) Identify the highest-ranking markedness constraint that favors A1 over A2. Call it
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M(A1™A2).
(ii) Identify the highest-ranking markedness constraint that favors B2 over B1. Call it
M(B2™B1).
(iii) If M(A1™A2) dominates M(B2™B1), then A1 is the superior attractor and so the
paradigm +A1, B1, wins.
(iv) But if M(B2™B1) dominates M(A1™A2), then B2 is the superior attractor and so the
paradigm +A2, B2, wins.
In other words, the markedness of the attractor is what matters.
Attraction to the unmarked follows directly from the theory: in OP, the markedness violations
of a candidate paradigm are the summed markedness violations of its individual members. The
markedness violations incurred by +A1, B1, are those incurred by A1 or B1, so if the A1-favoring
markedness constraint dominates the B2-favoring one, the paradigm that contains A1 is optimal.
Here are some hypothetical examples to illustrate this prediction; for real-life cases, see §4.2
and Raffelsiefen (1995, 1999). Overapplication vs. underapplication in +ma±, ma±i, vs. +mat, mati,
is perhaps the simplest example that can be constructed; indeed, overapplication-only is a special
case of attraction to the unmarked. In +ma±, ma±i,, the suffixed form ma±i is the attractor, while in
+mat, mati, unsuffixed mat is the attractor. Which paradigm wins depends on which markedness
constraint is higher ranked: M(ma±i™mati) or M(mat™ma±). Under the assumption that this language
has a general process of coronal palatalization, M(ma±i™mati) is top-ranked, so overapplication
wins. A more complex example can be constructed from a language with a -u suffix in the singular
and -i in the plural, with Japanese-style phonology of t before these vowels: affrication to ° before
u and palatalization to ± before i. Then there is competition between two different ways to overapply,
+ma°u, ma°i, vs. +ma±u, ma±i,. By attraction to the unmarked, the choice between them comes
down to this question: is M(ma°u™ma±u) ranked higher or lower than M(ma±i™ma°i)? The answer
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could go either way; in fact, this might be the only situation where these two constraints can be
brought into conflict.
The OP model also predicts the possibility of majority-rules effects, where the pattern that
is most common in a paradigm acts as an attractor for others. Majority-rules effects are not a routine
matter in the OP approach; the empirical circumstances and constraint rankings that will produce
them are highly specific, as we will see in §5.1. But when conditions are propitious, we expect to
see results like the following. Stems followed by a consonant-initial suffix alternate one way, in
accordance with undominated markedness constraints. Stems followed by a vowel-initial suffix
alternate another way, also in accordance with those undominated constraints. If markedness does
not decide how stems with no suffix will alternate, then they will be attracted to the pattern that is
more common in the rest of the paradigm, which of course depends on whether consonant-initial or
vowel-initial suffixes happen to be more frequent. This result follows from minimization of OP
faithfulness violations (cid:151) though some OP faithfulness violation is unavoidable because markedness
forces differences between the two suffixed conditions, fewer violations of OP faithfulness are
incurred if the unsuffixed form conforms to the more common of the two suffixed patterns.
It is important to realize that attraction to the unmarked, overapplication-only, and majority-
rules effects are not special stipulations or auxiliary principles. Rather, they are consequences of the
OP model that devolve from its basic architecture. It is also important to realize that OP, as a theory
of paradigms, only asserts these claims about inflectional morphology, not derivational. If
inflectional morphology turns out to conform to these predictions, then the OP theory receives strong
support. If the predictions turn out to be wrong, then the problem is profound and there is no easy
way to patch around it because the predictions are so deeply connected to the tenets of the theory.
Needless to say, whether they are right or wrong, our theories should always make such strong,
falsifiable claims.
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