conflicting constraints an introduction to optimality theory*

ELSEVIER Lingua 104 (1998) I-12

Conflicting constraints :

An introduction to Optimality Theory*

Dicky Gilbers”,‘, Helen de Hoopb

“ Department of Linguistics, BCN, University of Groningen, Oude Kijk in ‘t Jatstraat 26, NL-9712 EK Groningen, The Netherlands

h UiL OTS, Utrecht University, Tram 10, NL-3512 JK Utrecht, The Netherlands

Abstract

In this introductory article we sketch out some of the general principles and merits of Optimality Theory, and provide a background to the articles contained in this special Lingua issue that centers around the concept and consequences of conflicting constraints within this framework.

1. Introduction

Optimality Theory (henceforth, OT) is a theory of language and grammar that has become quite a popular trend in linguistics after its introduction in 1993 by the pho- nologist Alan Prince and the cognitive scientist Paul Smolensky (Prince and Smolen- sky, 1993). In OT a grammar consists of a set of well-formedness constraints. These constraints apply simultaneously to representations of structures and they are soft, which means violable. Furthermore, the constraints are potentially conflicting and at least an important subset of these constraints is shared by all languages, forming part of Universal Grammar. Individual languages rank these universal constraints differ- ently in their language-specific hierarchies in such a way that higher ranked constraints have total dominance over lower ranked constraints. Possible output candidates for each underlying form are evaluated by means of these constraint rankings. The output that best satisfies the constraints is the optimal candidate and will be the

* We would like to thank all participants of the BCN Workshop on Conflicting Constraints, Gronin- gen, July 5, 1996, at which the papers contained in this special issue were presented. As guest editors of this special issue we wish to thank the reviewers of the submissions. Their careful comments

resulted in numerous improvements of the individual papers and they contributed considerably to the final product. The latter author furthermore gratefully acknowledges the Foundation for Language, Speech, and Logic, which is funded by the Netherlands Organization for Scientific Research, NW0 (grant 300-75-020).

0378-2166/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SOO24-3841(97)00021-1

2 D. Gilbers, H. de Hoop I Lingua 104 (1998) 1-12

realized form. By analyzing the results arising from ranking the universal constraints in all possible dominance hierarchies, one can predict and explain which surface patterns are possible in natural languages.

Of course, the concept of constraints has been proposed in other frameworks as well. The most revolutionary innovation in OT, however, is the fact that the constraints are soft which means that an output can still be grammatical if constraints are violated. The violations have to be minimal, however, such that a constraint may be violated, but only in order to satisfy a higher ranked constraint.

In this introductory article, we will discuss the basic principles and merits of OT and briefly introduce the contributions to OT that are made by the various authors of the present issue.

2. Harmony maximization

OT has its source in connectionism, or parallel distributed processing, a view on cognition that emerged in the 1980s as an alternative to what is nowadays known as the classical view. In the latter, cognition is conceived of as symbol manipulation, involving complex objects or representations that have both a syntax and a semantics. Connectionist models were developed in an attempt to construct a model that more closely resembles the structure of the human brain. A connectionist model consists of a neural network of elementary units, each of which can be activated to a certain degree. The units are connected to each other and the connections have a certain weight, so that, given the degree of activation of a unit and the weight of its connections, it will either excite or inhibit other units. Crucially, in distributed networks, the individual units are not interpreted themselves. Instead, the activation degrees of all units together constitute an activation pattern that can be interpreted. The behaviour of the system as a whole is determined by the initial degree of activation of the units plus the strengths of the weights connecting them. The emergence of connectionist models of cognition has created a great deal of controversy among those involved in the study of human cognition (see a.o., Macdonald and Macdonald, 1995).

Smolensky (1993, however, emphasizes that classical, symbolic theories and connectionist theories should be considered approaches to one and the same cognitive system, yet at different levels of abstraction. In accordance with this view, Smolensky (1995) presents a new cognitive architecture that integrates symbolic and connectionist principles. His architecture has certain basic principles, one of them being that not all important higher cognitive processes are described by symbolic algorithms, another one being that not all crucial structure in connectionist networks arises from empiricist learning. The first principle is central in Smolensky’s new architecture, and it manifests itself in OT by the fact that the well-formedness constraints are conflicting, a direct consequence of principles of connectionist computa- tion. The second principle rejects the strongly held assumption of empiricist learning in connectionism. Instead, the principle states that some structure is innate, and thus allows for the existence of Universal Grammar in OT, a set of universal well- formedness constraints that is innate and does not have to be learned. The only thing that has to be learned is the ranking of these constraints.

D. Gilbers, H. de Hoop I Lingua 104 (1998) I-I? 3

In OT as well as in its predecessor Harmonic Grammar (Smolensky, 1986, 1995) the grammatical notion of well-formedness and a connectionist notion of relative well-formedness or Harmony are brought together in an interesting way. In a connection& network, the Harmony of an activation pattern is a number that measures the degree to which the pattern is well-formed according to the connections in the network. Let us illustrate this by a simple example (see Fig. 1).

Fig. 1.

Suppose that in the above network the weight value of the connection from unit u to unit p is negative, e.g., wPa=-6. Such a connection can be interpreted as a constraint: if c1 is active, p should not be active. Similarly, the connection from y to /3 can be interpreted as a positive constraint if, e.g., wpy=+3. Suppose furthermore that cx and y are both active at a certain time, then p is subject to two conflicting constraints. If c1 and y are equally active, then the strongest constraint (in this example the negative one) will win, which means that the network will create an activation pattern that violates the positive constraint in order to satisfy the negative constraint. Such an activation pattern has maximal Harmony with respect to the pair of connections considered here. In general, this process of Harmony maximization or parallel soft constraint satisfaction applies to the complete set of connections in a network. Harmony maximization is an essential theorem in Smolensky’s theory, which states that the net effect of processing in a network is to complete the input pattern into a total activation pattern with maximal Harmony. This can be considered the optimal parse according to the grammar encoded in the network’s connections. A symbolic version of the theorem (Smolensky, 1995: 256):

(1) Given an input symbolic structure i, the Harmonic Grammar assigns to i the output symbolic structure (‘parse’) s with maximal Harmony, among those which are completions of i. The higher the value of Harmony of this parse structure s, the more well-formed the grammar judges the input.

It will be clear that this latter principle (the higher the Harmony value, the more well-formed the input) explains the possibility of gradual grammaticality judgements (suppose for instance that Harmony value 0 (zero) leads to a grammaticality judge- ment ‘?’ for the input). Given the strengths (or in OT the ranking) of the constraints, not only the optimal grammatical output but also the nearly optimal alternatives can be predicted. In a case study of French unaccusatives, Legendre et al. (1990a,b)

4 D. Gilbers, H. de Hoop ! Lingua 104 (1998) l-12

account for relative well-formedness as well as gradual unaccusativity (the fact that some verbs appear to be more unaccusative than others when subjected to syntactic and semantic tests that should properly distinguish between unergative and unaccusative verbs, cf. Legendre, 1989; Hoekstra and Mulder, 1990; Zaenen, 1993). Instead of using hard conditions and a strict distinction between unaccusative and unergative intransitives, the connectionist approach of Legendre et al. offers the possibility of formalizing both syntactic and semantic tendencies or preferences as soft conditions. More generally, tendencies or preferences in natural language are explained in OT in terms of markedness. Harmonic Grammar and OT indeed are formal theories of markedness (cf. Smolensky, 1995).

In the remainder of this article, we will show how OT contributes to linguistic theory using the central concept from connectionist processing that was the topic of this section: parallel soft-constraint satisfaction.

3. Candidate output structures

In the previous section, we learned that the Harmony function of a system cap- tures the knowledge of that system in a set of conflicting, soft conditions of various strength. The fact that the conditions are soft has far-reaching consequences: if all possible output structures violate a certain constraint, then this constraint is not relevant at all to the determination of the optimal output structure. That is, an output structure cannot be rejected because the constraints it violates are too numerous or too strong. An output structure will be rejected for one reason only: there is a better alternative in the set of possible output structures.

Prince and Smolensky (1993) claim that phonological regularities arc fundamentally representational and parallel in character, rather than derivational and serial. In rule- based approaches, linguists try to find out which rules describe the empirical data in the most generalized way. But, as Prince and Smolensky put it polemically: if you don’t want phonology to be just a technique for data-compression, you have to seek the locus of explanatory action elsewhere. Let us illustrate this with an example of alternations in Turkish, which is adapted from Clements and Keyser (1983) (cf. Burzio, 1995).

(2) Alternations in Turkish

Accusative

Degemination: ‘feeling’ hiss+i ‘right’ hakk+i

Epenthesis : ‘transfer’ devr+i ‘abdomen’ kam+i

Vowel shortening : ‘time’ zama: n+i ‘proof’ isapa: t+i

Nominative

his hak

devir karin

ZLWMll

ispat

Ablative

his+ten hak+tan

devir+den ka.rin+dan

zaman+dan ispat+tan

D. Gilbers, H. de Hoop ! Lingua 104 (1998) l-12 5

Clements and Keyser claim that these alternations can be most simply explained if we assume that the underlying form of the stems is identical to the surface accusative stem. The processes in (2) may then be described as follows. The underlying geminate consonant in the first two examples is degeminated in the nominative and the ablative, that is word-finally or before a consonant-initial suffix. In the same environment, an epenthetic vowel is inserted in the third and fourth example. As is shown in the last two examples, a long vowel is shortened before a word- final consonant or if this consonant precedes a consonant-initial suffix. In a rule- based approach, the description of these alternations involves three unrelated rules. This approach does not enable us to explain that Turkish syllables, obviously, cannot exceed the structure CVX. This well-formedness constraint on Turkish syllables triggers the above mentioned alternations. In OT, the explanation of all phonological phenomena is to be found in characteristics of output structures. The goal of OT is to develop and explore a theory of the way that representational well- formedness determines the assignment of grammatical structure (Prince and Smolensky, 1993: 1).

OT grammar has two main components: GEN (‘generator’) and H-EVAL (‘Har- mony Evaluator’). The latter OT-component, H-EVAL, determines the relative Har- mony of the possible output structures and evaluates which is the optimal output: the candidate that best satisfies the language-specific constraint ranking. GEN generates all possible structures for an underlying form, the so-called candidate ser. For example, if we want to assign main stress to an imaginary word such as papapa, the candidates are the set {pbpapa; pap&pa; papapd).

McCarthy and Prince (1993a: 20-21) claim that three principles underlie the theory of GEN. In the first place, the generator function GEN of OT does not limit the amount of structure that can be built (freedom of analysis) (McCarthy and Prince, 1993a: 20-21). All possible kinds of structure can be added to a given input form. For example, GEN can build both an output [kas] and an output [kars] (or even [skasi]) for the input /kas/ (Dutch kaas ‘cheese’). Without ‘freedom of analysis’, OT would not enable us to account for epenthetic segments in optimal outputs.

According to the principle of containment, no underlying element may be literally removed in an output candidate, in other words, all elements of the input are at least contained in all output candidates. Under this assumption phonologically deleted segments are present in the output, but unparsed syllabically. For example, [kas] and [skas] are possible outputs of Dutch kaas /kas/ ‘cheese’, but [ka] is not. Deletion is regarded as underparsing of an underlying element in the output structure. So, the hypothetical surface form [ka] for /kas/ is actually represented as [ka<s>]; in which the angled brackets indicate that the segment/s/ is present in the output, but not pho- netically realized.

The third principle holds that underlying specifications of a morpheme cannot be changed by GEN (consistency ofexponence). This means that epenthetic segments in the output, as, for example, [r] in the realisation [kars] of /kas/, is not a part of the morpheme kaas.

It is important to realize that OT is a new, developing framework, in which new insights still rapidly follow upon one another. McCarthy and Prince (1995: 268-272).

6 D. Gilbers, H. de Hoop I Lingua 104 (1998) l-12

for instance, reject the principle of containment, introduced in McCarthy and Prince (1993a), in correspondence theory. Containment is necessary if we want to evaluate candidates with unparsed segments. Only if we know that an output indeed contains an unrealized underlying segment, such as [s] in [ka<s>], can we evaluate this candidate for certain constraints, such as the faithfulness constraint Parse (all underlying segments are parsed in the output structure) and the markedness/syllabification constraint *Coda (the syllable in the output has no coda). Faithfulness constraints in standard OT, such as Parse, relate deletion to syllabification in standard OT. In correspondence theory, containment is superfluous, since underlying forms are directly compared with realized forms in this OT variant. Note, however, that containment is still crucial in Smolensky’s recent analysis of first language acquisition data (Smolensky, 1996).

H-EVAL evaluates the candidates. At this point one should realize that a network does not have to evaluate all possible output structures for a certain input structure one by one. The candidate set can in principle be infinite, but the parallel processing of the input with respect to the stored weight values of the connections, results in an increase in the Harmony of the activation pattern until the maximum has been reached (= the theorem of Harmony maximization). Of course, researchers can evaluate and analyze the possible output structures, for example because they are inter- ested in what is the exact connection pattern of the network that yields a certain output, given a certain input.

4. Conflict resolution and constraint families

Prince and Smolensky (1993) discovered that in phonology, the numerical strengths of the connections are often not important, because they are so arranged that each constraint can never be over-ruled by weaker constraints, no matter how many. This led to the proposal of OT as the non-numerical successor to Harmonic Grammar. In OT, the weight values of the connections are replaced by strict dominance hierarchies among the constraints, thus accounting for the fact that each constraint appears to be stronger than all the lower-ranked constraints combined.

In Table 1 we show an abstract example of an OT-analysis. In the table, the input is put in the highest leftmost cell. The relevant constraints are exposed hori- zontally in their strict dominance order. Thus, constraint 1 (Cl) takes priority over constraint 2 (C2), indicated as ‘Cl >> C2’. The possible output candidates are exposed vertically.

In the table, output candidate 1 violates the most important constraint Cl. This violation is fatal (indicated by ‘ ! ‘), since output candidates 2 and 3 satisfy this constraint Cl. A blank cell indicates that the constraint is satisfied. Whether or not output 1 satisfies the other constraints C2-4 is irrelevant. This is represented by means of shading the cells. The remaining competitors, outputs 2 and 3, both satisfy constraint C 1 and violate constraint C2. So, the decision is made in the evaluation of the outputs for constraint C3: output 2 satisfies C2, whereas output 3 fatally violates C3. Output 2 is the optimal candidate and will represent the realized form (indicated by ‘e’). C4 plays no role in the comparison at all.

D. Gibers, H. de Hoop I Lingua 104 (1998) 1-12 7

Tableau 1

constraints b Input candidates v

= output 2

output 3

Conflict resolution can be demonstrated on the basis of the exemplary constraints in (3). These two potentially conflicting constraints are unordered in the set of UG- constraints.

(3) Two potentially conflicting constraints UG-constraint i: stress never falls on the last syllable (Nonfinality) UG-constraint j : stress falls on the heaviest syllable (Peak Prominence)

Now, suppose that in a certain language the structure of a word is CVCVVC (papaap), in which CVVC is heavier than CV. The output, then, will be pbpaup according to constraint i, but it will be pupciap according to constraint j. The conflict has to be solved by ranking the constraints hierarchically in the language grammar.

In OT, different families of constraints are distinguished. Most phonological processes are accounted for as conflicts between members of these families. For example, so-called markedness constraints prefer unmarked structures: tu is a better syllable than scratch. However, representational optimization is not the sole component of the system, as Burzio (1995: 3) points out: “(...) There must be some other component as well, to ensure diversity”. This is taken care of by so-called COTW- spondence constraints, which relate elements of different strings, for example the input and the output string of segments (McCarthy and Prince, 1995). These constraints ensure that not too many lexical distinctions are wiped out by the markedness constraints.

Examples of markedness constraints in phonology are syllabification constraints like Ons: every syllable has an onset; and *Coda: no syllable has a coda (cf. Jakob- son, 1968 [ 19411). Ons reflects that every language allows consonant-initial syllables and that some languages allow no others. Therefore, Ons is defined as a positive constraint, while e.g. *Coda is defined in a negative way: syllables must not have a coda, since every language permits open syllables and some only those. Note that OT is not a theory of representations, in other words, the content of the constraints depends on the representations that are assumed.

An example of a correspondence constraint is Max-IO (maximal input-output correspondence), which demands that every segment of the input has a correspondent in

8 D. Gilbers, H. de Hoop / Lingua IO4 (1998) l-12

the output. This prohibits deletion; every input segment is represented in the output. Dep-IO likewise demands that every segment of the output has a correspondent in the input, which prohibits epenthesis. Ident(F)-IO is satisfied if correspondent segments are identical with respect to a feature F, which prohibits alternation. Further- more, McCarthy and Prince (1995) propose constraints such as Contiguity and Lin- earity. Contiguity demands that the correspondent elements form contiguous strings. It avoids skipping or intrusion of segments: [malk] is a better candidate output for input /melk/ (Dutch melk ‘milk’) than the candidates [m&k] or [m&k]. Linearity avoids metathesis; it demands that the order of segments in corresponding strings is the same. This means that Linearity is satisfied in the realization [wasp] for /wasp/ (wasp), but violated in the case of an output [waps]. Note that this latter output does satisfy Max-IO, because all four input segments are realized in this output candidate. As mentioned above, correspondence constraints substitute the so- called faithfulness constraints of standard OT. Max-IO (maximal input-output correspondence), for example, substitutes Parse (all underlying material is part of the output).

There are also correspondence constraints that indicate the mutual relation between output forms (output-output correspondence). These constraints reflect ‘cyclic’ effects, as exhibited in the unreduced vowel in the second syllable of condensation, if we compare this vowel with the reduced one in the second syllable of compensation, which has a quite similar rhythmic surface structure (cf. Kiparsky, 1979, 1982; Hayes, 1981). This difference in reduction possibilities has been brought forward in papers on Lexical Phonology as an argument for level ordering and/or cyclic applications of phonological rules. The reluctance of vowel reduction is explained by assuming that condensation is derived from condense, which has a stressed second syllable, whereas compensation is derived from compensate, which has an unstressed second syllable. This cyclic effect caused problems for standard OT analyses, since standard OT only allowed for one derived level, namely the output. One could opt for a revised OT version in which different levels each have their own constraint ranking or one could extend the family of correspondence constraints with output-output correspondence constraints (McCarthy and Prince, 1995). O-O-correspondence constraints forbid reduction in condensation, because they require that the structure of the ‘derived’ word is identical to the structure of its base: condense. Furthermore, McCarthy and Prince (1995) propose correspondence constraints such as uniformity and integrity to avoid coalescence and breaking.

McCarthy and Prince (1993b) propose a family of well-formedness constraints, called Generalized Alignment. They claim that the diverse ways in which constituent edges figure in morphological and phonological processes can be accounted for by means of alignment constraints. These constraints all have in common that they refer to constituent edges. All alignment constraints have the following shape:

(4) Alignment constraints Align (Cat 1 ,Edge 1 ,Cat2,Edge2) = V Cat1 3 Cat2 where Edge1 of Cat1 and Edge2 of Cat2 coincide

D. Gilbers, H. de Hoop I Lingua 104 (1998) l-12 9

The requirement in (4) demands that a designated edge 1 of all existing examples of a category 1 coincides with a designated edge 2 of a category 2, in which these cat- egories represent prosodic or morphological constituents.

5. Merits of parallel soft-constraint satisfaction

One advantage of assuming that universal constraints are soft, hence potentially violable, is that the constraints can be formulated very generally. It might be empir- ically problematic to assume that a constraint either holds absolutely or not at all in a certain language. Therefore, in derivational frameworks hard constraints often need to be restricted to certain domains of application or levels of representation in order to account for apparent violations. For instance, there are languages in which the EPP (a syntactic condition that requires the presence of a structural subject) is violated in passives of intransitives, while it must be satisfied in passives of transitives. Ackema and Neeleman (this issue) show that a typology of passive formation can be derived from the conflict between three very general constraints, namely EPP, Stay (a condition that prohibits movement) and Parse. Ackema and Neeleman furthermore argue that one does not have to worry about overgeneration in OT, firstly because different rankings may select the same output as optimal, and secondly because an output without any structure, the so-called null parse, may be more suc- cessful than other candidates.

One of the obvious merits of OT can be found in the conspiracy of constraints of different families. Since evaluation proceeds in parallel, constraints of different families interact. The surplus value of OT has to be found exactly in the possible inter- actions of constraints. Prince and Smolensky (1993: 28-32) show that, for example. in Tongan, syllabification - which is the basis of stress assignment - is itself partly dependent on the position of stress. In OT, the simultaneous working of syllabification constraints and stress position constraints enables us to account for this mutual dependency, which would not be possible in a derivational framework.

An example of a conspiracy between markedness and correspondence constraints can be found in the analysis of r-deletion/r-insertion in English proposed by Anttila and Yu Cho (this issue). Three invariant synchronic systems (no deletion, no insertion; deletion, but no insertion; deletion and insertion) are shown to follow from different rankings of three well-known constraints, the markedness constraints *Coda and Ons, and a faithfulness constraint, stating ‘don’t delete: don’t insert’. Under the assumption that constraints are partially ordered instead 01 totally ordered in natural languages, Anttila and Yu Cho account for synchronic variation as well as diachronic change in one and the same model. They derive the correct statistical predictions and generalizations with respect to both grammaticality judgments and preferences. Their model furthermore excludes the possible existence of certain dialects, such as e.g., dialects with r-insertion, but no r-deletion. Thus, OT appears to be particularly fit for modelling a theory which has to formally connect invariant and variable phenomena, synchrony and diachrony, variation and change.


As we already pointed out in Section 3, the ranking of the constraints not only predicts the optimal grammatical output, but also the nearly optimal alternatives. After demotion or promotion of a certain constraint, a nearly optimal output might become the optimal one. In this way, the OT framework enables us to account for typological variation in adjacent dialects. Baerman (this issue) examines the range of stress systems found in Macedonian dialects. He proposes a model in which the reranking of prosodic constraints describes the evolution of the Macedonian dialects. The variably-ranked correspondence constraint Head-Max, which forces faithfulness to lexically specified stress, intervenes in the fixed ranking of alignment constraints on position and foot form constraints in different places, thus leading to different optimal outputs in the different dialects.

Burzio (this issue) shows that morphologically complex words can have multiple bases, and presents a straightforward analysis in terms of correspondence constraints in OT. Since there is no limit to the number of constraints that can simultaneously apply, multiple bases simply yield multiple sets of output-output faithfulness constraints (Burzio’s notion of multiple correspondence). In Italian, in three out of four verbal conjugations, there is a widespread pattern of conflicting metrical and seg- mental faithfulness, yielding violations of either one. When a primary form of faithfulness is violated, a secondary one takes over, both for stems and affixal material. The notion of multiple correspondence finds no direct expression in a derivational framework, in so far as derivations do not contemplate multiple inputs.

Another possible surplus value of OT over derivational or parametrical theories may be found in the effect of what McCarthy and Prince (1994) call the ‘emergence of the unmarked’. To give an example: one could suggest that there is no difference between the ranking of constraints such as the above-mentioned Ons and *Coda in OT and a parameter setting of onset and coda in other frameworks. For instance, if languages such as Dutch and English allow onsetless syllables, we could say that the parameter Ons is turned off in these languages, which could have the same effect as when in OT the constraint Ons is ranked very low in the hierarchy. However, if both onsets and codas are optional, in a parametric framework we cannot decide between the syllabification of pupa as pa.pa or pupa (the dot indicates a syllable boundary). In OT, however, the working of very low-ranked constraints becomes evident if two candidates tie for all higher ranked constraints. In that case satisfaction of Ons and *Coda makes clear that paga is the optimal output: ‘the emergence of the unmarked’.

Another example of emergence of the unmarked can be found in the paper of Samek-Lodovici (this issue). Constraints in OT can not only be potentially conflicting, they can even be exact opposites, hence necessarily conflicting. Samek- Lodovici argues that the coexistence of two opposite constraints in grammar allows for mixed syntactic patterns, such that structures satisfying one of the constraints and structures satisfying the other will be in complementary distribution within one language. The language Kanakuru illustrates his point with respect to focus-alignment. Samek-Lodovici shows that the focus pattern in Kanakuru is indeed best accounted for in terms of conflicting constraints, with rightward focus emerging whenever left- ward focus is violated in order to satisfy case-adjacency. Clearly, a parameter analy-

D. Gilbers, H. de Hoop I Lingua 104 (1998) l-12 II

sis based on uniform focus positions (e.g., to the right of the VP in Italian, to the left in Podoko) would not be able to explain this focus-alignment shift in Kanakuru.

Tesar (this issue) addresses the problem of the indirect relationship between the overt forms of language available to the language learner and the space of possible grammars provided by UG, in particular the fact that there may be different structural descriptions consistent with one overt form. Tesar hypothesizes that a leamei uses the optimizing structure of OT to estimate the hidden structure associated with an overt form. This structure is then used to modify the learner’s constraint ranking, resulting in an iterative procedure. Thus, a learner can go back and forth between estimating the hidden structure and estimating the grammar, eventually converging on the correct grammar, which is supported by the results of some simulations reported on in Tesar’s paper. This work shows that the formal structure of OT can make a significant contribution to language acquisition as well.

6. Concluding remarks

In this article we briefly reviewed the basic principles of OT and recent develop- ments therein. We hope this to be sufficient to serve as a general background to the various papers in this collection which each have their own topics and aims, yet share the insight that OT provides a fruitful and interesting new view on language and grammar.

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