Optimality theory
Encyclopedia
Optimality theory is a linguistic
model proposing that the observed forms of language
arise from the interaction between conflicting constraints. OT models grammars as systems that provide mappings from inputs to outputs; typically, the inputs are conceived of as underlying representations
, and the outputs as their surface realizations. There are three basic components of the theory:
Optimality theory assumes that these components are universal. Differences in grammars reflect different rankings of the universal constraint set, CON. Part of language acquisition
can then be described as the process of adjusting the ranking of these constraints.
Optimality theory was originally proposed by the linguists Alan Prince
and Paul Smolensky
in 1993, and later expanded by Prince and John J. McCarthy
. Although much of the interest in optimality theory has been associated with its use in phonology
, the area to which optimality theory was first applied, the theory is also applicable to other subfields of linguistics
(e.g. syntax
and semantics
).
Optimality theory is usually considered a development of generative grammar
, which shares its focus on the investigation of universal principles
, linguistic typology
and language acquisition
.
Optimality theory is often called a connectionist theory of language, because it has its roots in neural network
research, though the relationship is now largely of historical interest. It arose in part as a successor to the theory of Harmonic Grammar
, developed in 1990 by Géraldine Legendre, Yoshiro Miyata and Paul Smolensky
.
must be able to deal with an input such as /flask/. Languages without complex clusters differ on how they will resolve this problem; some will epenthesize
(e.g. [falasak], or [falasaka] if all codas are banned) and some will delete (e.g. [fas], [fak], [las], [lak]). Given any input, GEN generates an infinite number of candidates, or possible realizations of that input. A language's grammar (its ranking of constraints) determines which of the infinite candidates will be assessed as optimal by EVAL.
The universal nature of CON makes some immediate predictions about language typology. If grammars differ only by having different rankings of CON, then the set of possible human languages is determined by the constraints that exist. Optimality theory predicts that there cannot be more grammars than there are permutations of the ranking of CON. The number of possible rankings is equal to the factorial
of the total number of constraints, thus giving rise to the term Factorial Typology. However, it may not be possible to distinguish all of these potential grammars, since not every constraint is guaranteed to have an observable effect in every language. Two languages could generate the same range of input-output mappings, but differ in the relative ranking of two constraints which do not conflict with each other.
For example, given constraints C1, C2, and C3, where C1 dominates C2, which dominates C3 (C1 >> C2 >> C3), A is optimal if it does better than B on the highest ranking constraint which assigns them a different number of violations. If A and B tie on C1, but A does better than B on C2, A is optimal, even if A has 100 more violations of C3 than B. This comparison is often illustrated with a tableau. The pointing finger
marks the optimal candidate, and each cell displays an asterisk for each violation for a given candidate and constraint. Once a candidate does worse than another candidate on the highest ranking constraint distinguishing them, it incurs a crucial violation (marked in the tableau by an exclamation mark). Once a candidate incurs a crucial violation, there is no way for it to be optimal, even if it outperforms the other candidates on the rest of CON.
Constraints are ranked in a hierarchy of strict domination. The strictness of strict domination means that a candidate who violates only a high-ranked constraint does worse on the hierarchy than one that doesn't, even if the second candidate fared worse on every other lower-ranked constraint. This also means that constraints are violable; the winning candidate need not satisfy all constraints. Within a language, a constraint may be ranked high enough that it is always obeyed; it may be ranked low enough that it has no observable effects; or, it may have some intermediate ranking. The term the emergence of the unmarked describes situations in which a markedness constraint has an intermediate ranking, so that it is violated in some forms, but nonetheless has observable effects when higher-ranked constraints are irrelevant.
An early example proposed by McCarthy & Prince (1994) is the constraint NoCoda, which prohibits syllables from ending in consonants. In Balangao
, NoCoda is not ranked high enough to be always obeyed, as witnessed in roots like
form
Some optimality theorists prefer the use of comparative tableaux, as described in Prince (2002). Comparative tableaux display the same information as the classic or "flyspeck" tableaux, but the information is presented in such a way that it highlights the most crucial information. For instance, the tableau above would be rendered in the following way.
Each row in a comparative tableau represents a winner-loser pair, rather than an individual candidate. In the cells where the constraints assess the winner-loser pairs, there is a W if the constraint in that column prefers the winner, an L if the constraint prefers the loser, and an e if the constraint does not differentiate between the pair. Presenting the data in this way makes it easier to make generalizations. For instance, in order to have a consistent ranking some W must dominate all L's. Brasoveanu and Prince (2005) describe a process known as fusion and the various ways of presenting data in a comparative tableau in order to achieve the necessary and sufficient conditions for a given argument.
/ˈkæt/ + /z/ → [ˈkæts] (cats)(also smirks, hits, crepes)
/ˈdɒɡ/ + /z/ → [ˈdɒɡz] (dogs)(also wug
s, clubs, moms)
/ˈdɪʃ/ + /z/ → [ˈdɪʃɨz] (dishes)(also classes, glasses, bushes)
Also consider the following constraint set, in descending order of domination (M: markedness, F: faithfulness):
M: *SS - Sibilant-Sibilant clusters are ungrammatical: one violation for every pair of adjacent sibilants in the output.
M: Agree(Voi) - Agree in specification of [voi]: one violation for every pair of adjacent obstruents
in the output which disagree in voicing.
F: Max - Maximize all input segments in the output: one violation for each segment in the input that doesn't appear in the output (This constraint prevents deletion).
F: Dep - Output segments are dependent on having an input correspondent: one violation for each segment in the output that doesn't appear in the input (This constraint prevents insertion).
F: Ident(Voi) - Maintain the identity of the [voi] specification: one violation for each segment that differs in voicing between the input and output.
No matter how the constraints are re-ordered, the 'is' allomorph will always lose to 'iz'. This is called harmonic bounding. The violations incurred by the candidate 'dogiz' are a subset of the violations incurred by 'dogis'; specifically, if you epenthesize a vowel, changing the voicing of the morpheme is gratuitous violation of constraints. In the 'dog + z' tableau, there is a candidate 'dogz' which incurs no violations whatsoever. Within the constraint set of the problem, 'dogz' harmonically bounds all other possible candidates. This shows that a candidate does not need to be a winner in order to harmonically bound another candidate.
The tableaux from above are repeated below using the comparative tableaux format.
From the above tableau for dog + z, it can be observed that any ranking of these constraints will produce the observed output dogz. Because there are no loser-preferring comparisons, dogz wins under any ranking of these constraints; this means that no ranking can be established on the basis of this input.
The tableau for cat + z contains rows with a single W and a single L. This shows that Agree, Max, and Dep must all dominate Ident; however, no ranking can be established between those constraints on the basis of this input. Based on this tableau, the following ranking has been established:
Agree, Max, Dep >> Ident
This tableau shows that several more rankings are necessary in order to predict the desired outcome. The first row says nothing; there is no loser-preferring comparison in the first row. The second row reveals that either *SS or Agree must dominate Dep, based on the comparison between dishiz and dishz. The third row shows that Max must dominate Dep. The final row shows that either *SS or Ident must dominate Dep. From the cat + z tableau, it was established that Dep dominates Ident; this means that *SS must dominate Dep.
So far, the following rankings have been shown to be necessary:
*SS, Max >> Dep >> Ident
While it is possible that Agree can dominate Dep, it is not necessary; the ranking given above is sufficient for the observed for fishiz to emerge.
When the rankings from the tableaux are combined, the following ranking summary can be given:
*SS, Max >> Agree, Dep >> Ident
or
*SS, Max, Agree >> Dep >> Ident
There are two possible places to put Agree when writing out rankings linearly; neither is truly accurate. The first implies that *SS and Max must dominate Agree, and the second implies that Agree must dominate Dep. Neither of these are truthful, which is a failing of writing out rankings in a linear fashion like this. These sorts of problems are the reason why most linguists utilize a lattice graph
to represent necessary and sufficient rankings, as shown below.
A diagram that represents necessary rankings of constraints in this style is a Hasse diagram
.
Many criticisms of optimality theory are, according to its proponents, based on fundamental misunderstanding of how it works. A well-known example of this is Noam Chomsky's
widely-repeated assertion that optimality theory would predict every lexical input to be reduced to a single optimal syllable (e.g. every word is realized as [ba]). In fact, under the premises of Optimality Theory universal neutralization of this type would only be predicted if there were no faithfulness constraints (see McCarthy 1997). In a sense, the diametrically opposite kind of criticism comes from Morris Halle: "... the existence of phonology in every language shows that Faithfulness is at best an ineffective principle that might well be done without." By "phonology," Halle clearly means disparity between inputs and outputs of a phonological system. Optimality theory would fail to predict such deviations from an underlying form only if there were no markedness constraints. In OT, input-output disparity is normally understood as the result of markedness constraints being ranked over faithfulness constraints (M >> F).
Another objection to optimality theory is the claim that it is not technically a theory, in that it does not make falsifiable predictions. The source of this issue is terminology: the term "theory" is used differently here than in physics, chemistry, and other sciences. Specific instantiations of optimality theory may make falsifiable predictions, in the same way that specific proposals within other linguistic frameworks can. What predictions are made, and whether they are testable, depends on the specifics of individual proposals (most commonly, this is a matter of the definitions of the constraints used in an analysis). Thus, optimality theory as a framework is best described as a scientific paradigm.
Yet another objection to optimality theory is the claim that it cannot account for phonological opacity
(see Idsardi 2000, e.g.). In derivational phonology effects may be seen that are inexplicable at the surface level but which are explainable through "opaque" rule ordering; but in optimality theory, which has no intermediate levels for rules to operate on, these effects are difficult to explain.
For example, in Québécois French high front vowels triggered affrication of /t/, (e.g. /tipik/ → [tˢpɪk]) but the loss of high vowels (visible at the surface level) leaves the affrication with no apparent source. Derivational phonology can explain this by saying that vowel syncope (the loss of the vowel) "counterbled" affrication - that is, instead of vowel syncope occurring and "bleeding
" (i.e. preventing) affrication, we say that affrication applies before vowel syncope, so that the high vowel is removed and the environment destroyed which had triggered affrication. Such counterbleeding rule orderings are therefore termed opaque (instead of transparent), because their effects are not visible at the surface level.
The opacity of such phenomena finds no straightforward explanation in optimality theory, since intermediate forms are not accessible (constraints refer only to the surface form and/or the underlying form). There have however been a number of proposals designed to account for it; but most of these proposals significantly alter optimality theory's basic architecture, and therefore tend to be highly controversial. Frequently, such alterations add new types of constraints (which are not universal faithfulness or markedness constraints), or change the properties of GEN (such as allowing for serial derivations) or EVAL. Some well-known examples of these include John J. McCarthy's sympathy theory and candidate chains theory, and there are many others.
A relevant issue is the existence of circular chain shift
s, i.e. cases where input /X/ maps to output [Y], but input /Y/ maps to output [X]. Many versions of optimality theory predict this to be impossible (see Moreton 2004, Prince 2007). It is not certain whether patterns of this sort occur in natural languages.
Optimality theory is also criticized as being an impossible model of speech production/perception: computing and comparing an infinite number of possible candidates would take an infinitely long time to process. Idsardi (2006) argues this position, though other linguists dispute this claim on the grounds that Idsardi makes unreasonable assumptions about the constraint set and candidates, and that more moderate instantiations of optimality theory do not present such big computational problem
s (see Kornai (2006) and Heinz, Kobele, and Riggle (2009)). Another common rebuttal to this criticism of optimality theory is that the framework is purely representational. In this view, optimality theory is taken to be a model of linguistic competence
and is therefore not intended to explain the specifics of linguistic performance
.
theory, Moraic theory, or Feature Geometry. Completely distinct from these, there are sub-theories which have been proposed entirely within optimality theory, such as positional faithfulness theory, correspondence theory (McCarthy & Prince 1995), sympathy theory, and a number of theories of learnability, most notably by Bruce Tesar.
There are also a range of theories specifically about optimality theory. These are concerned with issues like the possible formulations of constraints, and constraint interactions other than strict domination.
, but has also been applied to other areas of linguistics. Jane Grimshaw, Geraldine Legendre and Joan Bresnan
are well known for developing instantiations of OT within syntax
. Optimality theoretic approaches are also relatively prominent in morphology (and the morphology-phonology interface in particular).
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
model proposing that the observed forms of language
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
arise from the interaction between conflicting constraints. OT models grammars as systems that provide mappings from inputs to outputs; typically, the inputs are conceived of as underlying representations
Underlying representation
In some models of phonology as well as morphophonology, the underlying representation or underlying form of a word or morpheme is the abstract form the word or morpheme is postulated to have before any phonological rules have applied to it. If more rules apply to the same form, they can apply...
, and the outputs as their surface realizations. There are three basic components of the theory:
- GEN takes an input, and generates the list of possible outputs, or candidates,
- CON provides the criteria, in the form of strictly orderedOrder (mathematics)Order in mathematics may refer to:-In algebra:*Order , the cardinality of a group or period of an element*Order, or degree of a polynomial*Order, or dimension of a matrix*Order , an algebraic structure*Ordered group...
violable constraints, used to decide between candidates, and - EVAL chooses the optimal candidate based on the constraints, and this candidate is the output.
Optimality theory assumes that these components are universal. Differences in grammars reflect different rankings of the universal constraint set, CON. Part of language acquisition
Language acquisition
Language acquisition is the process by which humans acquire the capacity to perceive, produce and use words to understand and communicate. This capacity involves the picking up of diverse capacities including syntax, phonetics, and an extensive vocabulary. This language might be vocal as with...
can then be described as the process of adjusting the ranking of these constraints.
Optimality theory was originally proposed by the linguists Alan Prince
Alan Prince
Alan Sanford Prince is a professor of linguistics at Rutgers University. Prince, along with Paul Smolensky, developed Optimality Theory, which was originally applied to phonology, but has been extended to other areas of linguistics such as syntax and semantics...
and Paul Smolensky
Paul Smolensky
Paul Smolensky is a professor of Cognitive Science at the Johns Hopkins University.Along with Alan Prince he developed Optimality Theory, a representational model of linguistics...
in 1993, and later expanded by Prince and John J. McCarthy
John McCarthy (linguist)
John McCarthy is a linguist and professor in the Department of Linguistics at the University of Massachusetts Amherst with a speciality in phonology and morphology...
. Although much of the interest in optimality theory has been associated with its use in phonology
Phonology
Phonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
, the area to which optimality theory was first applied, the theory is also applicable to other subfields of linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
(e.g. syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
and semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
).
Optimality theory is usually considered a development of generative grammar
Generative grammar
In theoretical linguistics, generative grammar refers to a particular approach to the study of syntax. A generative grammar of a language attempts to give a set of rules that will correctly predict which combinations of words will form grammatical sentences...
, which shares its focus on the investigation of universal principles
Linguistic universal
A linguistic universal is a pattern that occurs systematically across natural languages, potentially true for all of them. For example, All languages have nouns and verbs, or If a language is spoken, it has consonants and vowels. Research in this area of linguistics is closely tied to the study of...
, linguistic typology
Linguistic typology
Linguistic typology is a subfield of linguistics that studies and classifies languages according to their structural features. Its aim is to describe and explain the common properties and the structural diversity of the world's languages...
and language acquisition
Language acquisition
Language acquisition is the process by which humans acquire the capacity to perceive, produce and use words to understand and communicate. This capacity involves the picking up of diverse capacities including syntax, phonetics, and an extensive vocabulary. This language might be vocal as with...
.
Optimality theory is often called a connectionist theory of language, because it has its roots in neural network
Neural network
The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...
research, though the relationship is now largely of historical interest. It arose in part as a successor to the theory of Harmonic Grammar
Harmonic Grammar
Harmonic Grammar is a linguistic model proposed by Geraldine Legendre, Yoshiro Miyata, and Paul Smolensky in 1990. It is a connectionist approach to modeling linguistic well-formedness.-Bibliography:...
, developed in 1990 by Géraldine Legendre, Yoshiro Miyata and Paul Smolensky
Paul Smolensky
Paul Smolensky is a professor of Cognitive Science at the Johns Hopkins University.Along with Alan Prince he developed Optimality Theory, a representational model of linguistics...
.
Input and GEN: the candidate set
Optimality theory supposes that there are no language-specific restrictions on the input. This is called richness of the base. Every grammar can handle every possible input. For example, a language without complex clustersConsonant cluster
In linguistics, a consonant cluster is a group of consonants which have no intervening vowel. In English, for example, the groups and are consonant clusters in the word splits....
must be able to deal with an input such as /flask/. Languages without complex clusters differ on how they will resolve this problem; some will epenthesize
Epenthesis
In phonology, epenthesis is the addition of one or more sounds to a word, especially to the interior of a word. Epenthesis may be divided into two types: excrescence, for the addition of a consonant, and anaptyxis for the addition of a vowel....
(e.g. [falasak], or [falasaka] if all codas are banned) and some will delete (e.g. [fas], [fak], [las], [lak]). Given any input, GEN generates an infinite number of candidates, or possible realizations of that input. A language's grammar (its ranking of constraints) determines which of the infinite candidates will be assessed as optimal by EVAL.
CON: the constraint set
In optimality theory, every constraint is universal. CON is the same in every language. There are two basic types of constraints. Faithfulness constraints require that the observed surface form (the output) match the underlying or lexical form (the input) in some particular way; that is, these constraints require identity between input and output forms. Markedness constraints impose requirements on the structural well-formedness of the output. Each plays a crucial role in the theory. Faithfulness constraints prevent every input from being realized as some unmarked form, and markedness constraints motivate changes from the underlying form.The universal nature of CON makes some immediate predictions about language typology. If grammars differ only by having different rankings of CON, then the set of possible human languages is determined by the constraints that exist. Optimality theory predicts that there cannot be more grammars than there are permutations of the ranking of CON. The number of possible rankings is equal to the factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
of the total number of constraints, thus giving rise to the term Factorial Typology. However, it may not be possible to distinguish all of these potential grammars, since not every constraint is guaranteed to have an observable effect in every language. Two languages could generate the same range of input-output mappings, but differ in the relative ranking of two constraints which do not conflict with each other.
EVAL: definition of optimality
Given two candidates, A and B, A is better than B on a constraint if A incurs fewer violations than B. Candidate A is better than B on an entire constraint hierarchy if A incurs fewer violations of the highest-ranked constraint distinguishing A and B. A is optimal in its candidate set if it is better on the constraint hierarchy than all other candidates.For example, given constraints C1, C2, and C3, where C1 dominates C2, which dominates C3 (C1 >> C2 >> C3), A is optimal if it does better than B on the highest ranking constraint which assigns them a different number of violations. If A and B tie on C1, but A does better than B on C2, A is optimal, even if A has 100 more violations of C3 than B. This comparison is often illustrated with a tableau. The pointing finger
Index (typography)
The symbol is a punctuation mark, called an index, manicule or fist. Though rare today, this symbol was in common use between the 12th and 18th centuries in the margins of books, and was formerly included in lists of standard punctuation marks...
marks the optimal candidate, and each cell displays an asterisk for each violation for a given candidate and constraint. Once a candidate does worse than another candidate on the highest ranking constraint distinguishing them, it incurs a crucial violation (marked in the tableau by an exclamation mark). Once a candidate incurs a crucial violation, there is no way for it to be optimal, even if it outperforms the other candidates on the rest of CON.
| C1 | C2 | C3 | |
|---|---|---|---|
| ☞A | * | * | *** |
| B | * | **! | |
Constraints are ranked in a hierarchy of strict domination. The strictness of strict domination means that a candidate who violates only a high-ranked constraint does worse on the hierarchy than one that doesn't, even if the second candidate fared worse on every other lower-ranked constraint. This also means that constraints are violable; the winning candidate need not satisfy all constraints. Within a language, a constraint may be ranked high enough that it is always obeyed; it may be ranked low enough that it has no observable effects; or, it may have some intermediate ranking. The term the emergence of the unmarked describes situations in which a markedness constraint has an intermediate ranking, so that it is violated in some forms, but nonetheless has observable effects when higher-ranked constraints are irrelevant.
An early example proposed by McCarthy & Prince (1994) is the constraint NoCoda, which prohibits syllables from ending in consonants. In Balangao
Balangao
Balangao is a term that refers to both the barangay in the Natonin, Mountain Province, Philippines as well as the tribe that inhabits it.-Balangao tribe:...
, NoCoda is not ranked high enough to be always obeyed, as witnessed in roots like
taynan (faithfulness to the input prevents deletion of the final /n/). But, in the reduplicatedReduplication
Reduplication in linguistics is a morphological process in which the root or stem of a word is repeated exactly or with a slight change....
form
ma-tayna-taynan 'repeatedly be left behind', the final /n/ is not copied. Under McCarthy & Prince's analysis, this is because faithfulness to the input does not apply to reduplicated material, and NoCoda is thus free to prefer ma-tayna-taynan over hypothetical ma-taynan-taynan (which has an additional violation of NoCoda). Constraints are also violable; the winning candidate need not satisfy all constraints, as long as for any rival candidate that does better than the winner on some constraint, there is a higher ranked constraint on which the winner does better than that rival.Some optimality theorists prefer the use of comparative tableaux, as described in Prince (2002). Comparative tableaux display the same information as the classic or "flyspeck" tableaux, but the information is presented in such a way that it highlights the most crucial information. For instance, the tableau above would be rendered in the following way.
| C1 | C2 | C3 | |
|---|---|---|---|
| A ~ B | e | W | L |
Each row in a comparative tableau represents a winner-loser pair, rather than an individual candidate. In the cells where the constraints assess the winner-loser pairs, there is a W if the constraint in that column prefers the winner, an L if the constraint prefers the loser, and an e if the constraint does not differentiate between the pair. Presenting the data in this way makes it easier to make generalizations. For instance, in order to have a consistent ranking some W must dominate all L's. Brasoveanu and Prince (2005) describe a process known as fusion and the various ways of presenting data in a comparative tableau in order to achieve the necessary and sufficient conditions for a given argument.
Example
As a simplified example, consider the manifestation of the English plural:/ˈkæt/ + /z/ → [ˈkæts] (cats)(also smirks, hits, crepes)
/ˈdɒɡ/ + /z/ → [ˈdɒɡz] (dogs)(also wug
Wug test
The wug test is an experiment in linguistics, created by Jean Berko Gleason in 1958. It was designed as a way to investigate the acquisition of the plural and other inflectional morphemes in English-speaking children....
s, clubs, moms)
/ˈdɪʃ/ + /z/ → [ˈdɪʃɨz] (dishes)(also classes, glasses, bushes)
Also consider the following constraint set, in descending order of domination (M: markedness, F: faithfulness):
M: *SS - Sibilant-Sibilant clusters are ungrammatical: one violation for every pair of adjacent sibilants in the output.
M: Agree(Voi) - Agree in specification of [voi]: one violation for every pair of adjacent obstruents
Obstruent
An obstruent is a consonant sound formed by obstructing airflow, causing increased air pressure in the vocal tract, such as [k], [d͡ʒ] and [f]. In phonetics, articulation may be divided into two large classes: obstruents and sonorants....
in the output which disagree in voicing.
F: Max - Maximize all input segments in the output: one violation for each segment in the input that doesn't appear in the output (This constraint prevents deletion).
F: Dep - Output segments are dependent on having an input correspondent: one violation for each segment in the output that doesn't appear in the input (This constraint prevents insertion).
F: Ident(Voi) - Maintain the identity of the [voi] specification: one violation for each segment that differs in voicing between the input and output.
| dish + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| ☞ dishiz | * | ||||
| dishis | * | *! | |||
| dishz | *! | * | |||
| dish | *! | ||||
| dishs | *! | * | |||
| dog + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| dogiz | *! | ||||
| dogis | *! | * | |||
| ☞ dogz | |||||
| dog | *! | ||||
| dogs | *! | * | |||
| cat + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| catiz | *! | ||||
| catis | *! | * | |||
| catz | *! | ||||
| cat | *! | ||||
| ☞ cats | * | ||||
No matter how the constraints are re-ordered, the 'is' allomorph will always lose to 'iz'. This is called harmonic bounding. The violations incurred by the candidate 'dogiz' are a subset of the violations incurred by 'dogis'; specifically, if you epenthesize a vowel, changing the voicing of the morpheme is gratuitous violation of constraints. In the 'dog + z' tableau, there is a candidate 'dogz' which incurs no violations whatsoever. Within the constraint set of the problem, 'dogz' harmonically bounds all other possible candidates. This shows that a candidate does not need to be a winner in order to harmonically bound another candidate.
The tableaux from above are repeated below using the comparative tableaux format.
| dog + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| dogz ~ dogiz | e | e | e | W | e |
| dogz ~ dogis | e | e | e | W | W |
| dogz ~ dog | e | e | W | e | e |
| dogz ~ dogs | e | W | e | e | W |
From the above tableau for dog + z, it can be observed that any ranking of these constraints will produce the observed output dogz. Because there are no loser-preferring comparisons, dogz wins under any ranking of these constraints; this means that no ranking can be established on the basis of this input.
| cat + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| cats ~ catiz | e | e | e | W | L |
| cats ~ catis | e | e | e | W | e |
| cats ~ catz | e | W | e | e | L |
| cats ~ cat | e | e | W | e | L |
The tableau for cat + z contains rows with a single W and a single L. This shows that Agree, Max, and Dep must all dominate Ident; however, no ranking can be established between those constraints on the basis of this input. Based on this tableau, the following ranking has been established:
Agree, Max, Dep >> Ident
| dish + z | *SS | Agree | Max | Dep | Ident |
|---|---|---|---|---|---|
| dishiz ~ dishis | e | e | e | e | W |
| dishiz ~ dishz | W | W | e | L | e |
| dishiz ~ dish | e | e | W | L | e |
| dishiz ~ dishs | W | e | e | L | W |
This tableau shows that several more rankings are necessary in order to predict the desired outcome. The first row says nothing; there is no loser-preferring comparison in the first row. The second row reveals that either *SS or Agree must dominate Dep, based on the comparison between dishiz and dishz. The third row shows that Max must dominate Dep. The final row shows that either *SS or Ident must dominate Dep. From the cat + z tableau, it was established that Dep dominates Ident; this means that *SS must dominate Dep.
So far, the following rankings have been shown to be necessary:
*SS, Max >> Dep >> Ident
While it is possible that Agree can dominate Dep, it is not necessary; the ranking given above is sufficient for the observed for fishiz to emerge.
When the rankings from the tableaux are combined, the following ranking summary can be given:
*SS, Max >> Agree, Dep >> Ident
or
*SS, Max, Agree >> Dep >> Ident
There are two possible places to put Agree when writing out rankings linearly; neither is truly accurate. The first implies that *SS and Max must dominate Agree, and the second implies that Agree must dominate Dep. Neither of these are truthful, which is a failing of writing out rankings in a linear fashion like this. These sorts of problems are the reason why most linguists utilize a lattice graph
Lattice (order)
In mathematics, a lattice is a partially ordered set in which any two elements have a unique supremum and an infimum . Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities...
to represent necessary and sufficient rankings, as shown below.
A diagram that represents necessary rankings of constraints in this style is a Hasse diagram
Hasse diagram
In order theory, a branch of mathematics, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction...
.
Criticism
Optimality theory has attracted substantial amounts of criticism, most of which is directed at its application to phonology (rather than syntax or other fields).Many criticisms of optimality theory are, according to its proponents, based on fundamental misunderstanding of how it works. A well-known example of this is Noam Chomsky's
Noam Chomsky
Avram Noam Chomsky is an American linguist, philosopher, cognitive scientist, and activist. He is an Institute Professor and Professor in the Department of Linguistics & Philosophy at MIT, where he has worked for over 50 years. Chomsky has been described as the "father of modern linguistics" and...
widely-repeated assertion that optimality theory would predict every lexical input to be reduced to a single optimal syllable (e.g. every word is realized as [ba]). In fact, under the premises of Optimality Theory universal neutralization of this type would only be predicted if there were no faithfulness constraints (see McCarthy 1997). In a sense, the diametrically opposite kind of criticism comes from Morris Halle: "... the existence of phonology in every language shows that Faithfulness is at best an ineffective principle that might well be done without." By "phonology," Halle clearly means disparity between inputs and outputs of a phonological system. Optimality theory would fail to predict such deviations from an underlying form only if there were no markedness constraints. In OT, input-output disparity is normally understood as the result of markedness constraints being ranked over faithfulness constraints (M >> F).
Another objection to optimality theory is the claim that it is not technically a theory, in that it does not make falsifiable predictions. The source of this issue is terminology: the term "theory" is used differently here than in physics, chemistry, and other sciences. Specific instantiations of optimality theory may make falsifiable predictions, in the same way that specific proposals within other linguistic frameworks can. What predictions are made, and whether they are testable, depends on the specifics of individual proposals (most commonly, this is a matter of the definitions of the constraints used in an analysis). Thus, optimality theory as a framework is best described as a scientific paradigm.
Yet another objection to optimality theory is the claim that it cannot account for phonological opacity
Phonological opacity
Phonological opacity was first defined by Kiparsky as a measure of how far the context or the consequences of a phonological process may be determined only by examining the surface structure...
(see Idsardi 2000, e.g.). In derivational phonology effects may be seen that are inexplicable at the surface level but which are explainable through "opaque" rule ordering; but in optimality theory, which has no intermediate levels for rules to operate on, these effects are difficult to explain.
For example, in Québécois French high front vowels triggered affrication of /t/, (e.g. /tipik/ → [tˢpɪk]) but the loss of high vowels (visible at the surface level) leaves the affrication with no apparent source. Derivational phonology can explain this by saying that vowel syncope (the loss of the vowel) "counterbled" affrication - that is, instead of vowel syncope occurring and "bleeding
Bleeding order
Bleeding order is a term used in phonology to describe specific interactions of phonological rules. The term was introduced in 1968 by Paul Kiparsky....
" (i.e. preventing) affrication, we say that affrication applies before vowel syncope, so that the high vowel is removed and the environment destroyed which had triggered affrication. Such counterbleeding rule orderings are therefore termed opaque (instead of transparent), because their effects are not visible at the surface level.
The opacity of such phenomena finds no straightforward explanation in optimality theory, since intermediate forms are not accessible (constraints refer only to the surface form and/or the underlying form). There have however been a number of proposals designed to account for it; but most of these proposals significantly alter optimality theory's basic architecture, and therefore tend to be highly controversial. Frequently, such alterations add new types of constraints (which are not universal faithfulness or markedness constraints), or change the properties of GEN (such as allowing for serial derivations) or EVAL. Some well-known examples of these include John J. McCarthy's sympathy theory and candidate chains theory, and there are many others.
A relevant issue is the existence of circular chain shift
Chain shift
In phonology, a chain shift is a phenomenon in which several sounds move stepwise along a phonetic scale. The sounds involved in a chain shift can be ordered into a "chain" in such a way that, after the change is complete, each phoneme ends up sounding like what the phoneme before it in the chain...
s, i.e. cases where input /X/ maps to output [Y], but input /Y/ maps to output [X]. Many versions of optimality theory predict this to be impossible (see Moreton 2004, Prince 2007). It is not certain whether patterns of this sort occur in natural languages.
Optimality theory is also criticized as being an impossible model of speech production/perception: computing and comparing an infinite number of possible candidates would take an infinitely long time to process. Idsardi (2006) argues this position, though other linguists dispute this claim on the grounds that Idsardi makes unreasonable assumptions about the constraint set and candidates, and that more moderate instantiations of optimality theory do not present such big computational problem
Computational problem
In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might want to solve. For example, the problem of factoring...
s (see Kornai (2006) and Heinz, Kobele, and Riggle (2009)). Another common rebuttal to this criticism of optimality theory is that the framework is purely representational. In this view, optimality theory is taken to be a model of linguistic competence
Linguistic competence
Linguistic competence is the system of linguistic knowledge possessed by native speakers of a language, it is in contrast to the concept of Linguistic performance, the way the language system is used in communication...
and is therefore not intended to explain the specifics of linguistic performance
Linguistic performance
In linguistics, performance has two senses:It is also one of the two elements in Chomsky's performance-competence distinction, which relates to Language production , with an emphasis upon how this is different from Competence, or the mental knowledge of language itself...
.
Theories within optimality theory
In practice, implementations of optimality theory often assume other related theories, such as SyllableSyllable
A syllable is a unit of organization for a sequence of speech sounds. For example, the word water is composed of two syllables: wa and ter. A syllable is typically made up of a syllable nucleus with optional initial and final margins .Syllables are often considered the phonological "building...
theory, Moraic theory, or Feature Geometry. Completely distinct from these, there are sub-theories which have been proposed entirely within optimality theory, such as positional faithfulness theory, correspondence theory (McCarthy & Prince 1995), sympathy theory, and a number of theories of learnability, most notably by Bruce Tesar.
There are also a range of theories specifically about optimality theory. These are concerned with issues like the possible formulations of constraints, and constraint interactions other than strict domination.
Use outside of phonology
Optimality Theory is most commonly associated with the field of PhonologyPhonology
Phonology is, broadly speaking, the subdiscipline of linguistics concerned with the sounds of language. That is, it is the systematic use of sound to encode meaning in any spoken human language, or the field of linguistics studying this use...
, but has also been applied to other areas of linguistics. Jane Grimshaw, Geraldine Legendre and Joan Bresnan
Joan Bresnan
Joan Wanda Bresnan is Professor of Linguistics at Stanford University. She is best known as one of the architects of the theoretical framework of Lexical-Functional Grammar....
are well known for developing instantiations of OT within syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
. Optimality theoretic approaches are also relatively prominent in morphology (and the morphology-phonology interface in particular).