OT 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.
The main idea of OT is that the observed forms of language arise from the interaction between conflicting constraints. There are three basic components of the theory. GEN generates the list of possible outputs, or candidates, CON provides the criteria, violable constraints, used to decide between candidates, and EVAL chooses the optimal candidate. OT assumes that these components are universal. Differences in grammars reflect different rankings of the universal constraint set, CON. Language acquisition can be described as the process of adjusting the ranking of these constraints.
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. OT 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 very lowly-ranked constraints.
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 witness roots like
taynan (faithfulness to the input prevents deletion of the final /n/). But, in the reduplicated 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.
|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.
/cat + z/ → [cats] (also smirks, hits, crepes)
/dog + z/ → [dogz] (also wugs, clubs, moms)
/fish + z/ → [fishiz] (also classes, glasses, bushes)
Also consider the following constraint set:
M: Agree(Voi) - one violation for every pair of adjacent obstruents in the output which disagree in voicing
M: *SS - one violation for every pair of adjacent sibilants in the output
F: Ident(Voi) - one violation for each segment that differs in voicing between the input and output
F: Max - one violation for each segment in the input that doesn't appear in the output (deletion)
F: Dep - one violation for each segment in the output that doesn't appear in the input (insertion)
(M: markedness, F: faithfulness)
|fish + z||*SS||Agree||Max||Dep||Ident|
|dog + z||*SS||Agree||Max||Dep||Ident|
|cat + z||*SS||Agree||Max||Dep||Ident|
No matter how the constraints are re-ordered, the 'is' allomorph will always lose to 'iz.' For example, there is no way to rerank the constraints such that 'dogis' will win. This is called harmonic bounding. The violations incured by the candidate 'dogiz' are a subset of the violations incured 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
|fish + z||*SS||Agree||Max||Dep||Ident|
|fishiz ~ fishis||e||e||e||e||W|
|fishiz ~ fishz||W||W||e||L||e|
|fishiz ~ fish||e||e||W||L||e|
|fishiz ~ fishs||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 fishiz and fishz. 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
*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 often casually referred to as a Hasse diagram.
Another objection to OT 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 OT 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, OT as a framework is best described as a scientific paradigm.
A more serious objection to OT 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 OT, 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/ -> [tspIk]) 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 occuring 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 OT, 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 OT's basic architecture, and therefore tend to be highly controversial. Frequently, such alterations add new types of constraints (which aren't Universal Faithfulness or Markedness constraints), or change the properties of GEN 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 shifts, i.e. cases where input /X/ maps to output [Y], but input /Y/ maps to output [X]. Many versions of OT predict this to be impossible (see Moreton 2004, Prince 2007). It is not certain whether patterns of this sort occur in natural languages.
OT 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. The most common rebuttal to this argument is that OT is purely representational. In this view, OT is taken to be a model of Linguistic competence, and is not intended to explain the specifics of Linguistic performance. Further, work by Heinz, Kobele, and Riggle (forthcoming) shows that in fact, OT is computationally tractable, under certain reasonable assumptions.