Learnability in Optimality Theory
Bruce Tesar
Paul Smolensky
In this article we show how Optimality Theory yields a highly general
Constraint Demotion principle for grammar learning. The resulting
learning procedure specifically exploits the grammatical structure of
Optimality Theory, independent of the content of substantive con-
straints defining any given grammatical module. We decompose the
learning problem and present formal results for a central subproblem,
deducing the constraint ranking particular to a target language, given
structural descriptions of positive examples. The structure imposed on
the space of possible grammars by Optimality Theory allows efficient
convergence to a correct grammar. We discuss implications for learn-
ing from overt data only, as well as other learning issues. We argue
that Optimality Theory promotes confluence of the demands of more
effective learnability and deeper linguistic explanation.
Keywords: Optimality Theory, learning, acquisition, computational
linguistics
How exactly does a theory of grammar bear on questions of learnability? Restrictions on what
counts as a possible human language can restrict the learner’s search space. But this is a coarse
observation: alone it says nothing about how data may be brought to bear on the problem, and
further, the number of possible languages predicted by most linguistic theories is extremely large.1
It would clearly be a desirable result if the nature of the restrictions imposed by a theory of
grammar could contribute further to language learnability.
The central claim of this article is that the character of the restrictions imposed by Optimality
Theory (Prince and Smolensky 1991, 1993) have demonstrable and significant consequences for
central questions of learnability. Optimality Theory explains linguistic phenomena through the
complex interaction of violable constraints. The main results of this article demonstrate that those
constraint interactions are nevertheless restricted in a way that permits the correct grammar to
be inferred from grammatical structural descriptions. These results are theorems, based on a formal
We are greatly indebted to Alan Prince, whose challenges, insights, and suggestions have improved nearly every
page of this article. We are also grateful for important comments and encouragement from John McCarthy, Ge´raldine
Legendre, Jane Grimshaw, Bruce Hayes, Linda Lombardi, Luigi Burzio, Clara Levelt, Vieri Samek-Lodovici, and several
anonymous LI reviewers. For helpful questions and suggestions we thank the participants and organizers of the First
Rutgers Optimality Theory Workshop (ROW-1), the Las Cruces meeting of the Association for Computational Linguistics,
the University of Maryland Learnability Workshop, the MIT Workshop on Optimality in Syntax, and the Royaumont
Workshop on Approaches to Phonology. We are grateful to the Institute of Cognitive Science at the University of Colorado
at Boulder for partial support of ROW-1, where some of this work was first presented (and reported in Tesar and Smolensky
1993; see also Tesar and Smolensky 1995). Bruce Tesar acknowledges the support of an NSF Graduate Fellowship, Paul
Smolensky the support of a Guggenheim Fellowship, and both authors the support of NSF grant IRI-9213894.
1 Even a Universal Grammar with only 20 binary parameters admits over a million grammars.
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Linguistic Inquiry, Volume 29, Number 2, Spring 1998
229–268
q 1998 by the Massachusetts Institute of Technology

230 B R U C E T E S A R A N D P A U L S M O L E N S K Y
analysis of the Optimality Theory framework; proofs of the theorems are contained in an appendix.
The results have two important properties. First, they derive from central principles of the Opti-
mality Theory framework. Second, they are nevertheless independent of the details of any substan-
tive analysis of particular phenomena. The results apply equally to phonology, syntax, and any
other domain admitting an analysis in terms of Optimality Theory. Thus, these theorems provide
a learnability measure of the restrictiveness inherent in Optimality Theory’s account of cross-
linguistic variation per se: constraint reranking.
The structure of the article is as follows. Section 1 formulates the learning problem we
investigate. Section 2 addresses this problem by developing the principle of Constraint Demotion,
which is incorporated into an error-driven learning procedure in section 3. Section 4 takes up
some issues and open questions raised by Constraint Demotion, and section 5 presents conclusions.
An appendix contains the formal definitions, theorems, and proofs.
1 Learnability and Optimality Theory
Optimality Theory (henceforth, OT) defines grammaticality by optimization over violable con-
straints. The defining reference is Prince and Smolensky 1993 (henceforth, P&S). Section 1.1
provides the necessary OT background, and section 1.2 outlines the approach to language learnabil-
ity proposed here, including a decomposition of the overall problem; the results of this article
solve the subproblem involving direct modification of the grammar.
1.1 Optimality Theory
In this section we present the basics of OT as a series of general principles, each exemplified
within the Basic CV Syllable Theory of P&S (which draws upon ideas from McCarthy 1979,
Selkirk 1981, Steriade 1982, Clements and Keyser 1983, Itoˆ 1989).
1.1.1 Constraints and Their Violation The first principle is not unique to Optimality Theory;
it is a principle of generative grammar having particular significance for the present discussion.
(1) Grammars specify functions
A grammar is a specification of a function that assigns to each input a structural descrip-
tion or output. (A grammar per se does not provide an algorithm for computing this
function, e.g., by sequential derivation.)
In Basic CV Syllable Theory (henceforth, CVT), an input is a string of Cs and Vs (e.g.,
/VCVC/). An output is a parse of the string into syllables, denoted as follows:
(2) a. .V.CVC. 4 [
s
V] [
s
CVC] onsetless open syllable ` closed syllable
b. kVl.CV.kCl 4 V [
s
CV] C single onsetted open syllable
c. kVl.CV.CM´ . 4 V [
s
CV] [
s
CM´ ] two onsetted open syllables
d. .MV.CV.kCl 4 [
s
M V] [
s
CV] C two onsetted open syllables
(These four forms will be referred to frequently in the article and will be consistently labeled
a–d.)
Output a is an onsetless open syllable followed by a closed syllable; periods denote the