0. Introduction

This paper addresses some very basic assumptions in standard Optimality Theory1 (OT) (Prince and Smolensky 1993, McCarthy and Prince 1995; for a detailed description of Optimality Theory, see for instance Kager 1999); namely, it discusses the consequences of the principle of the Richness of the Base (ROTB), Lexicon Optimization (LO) with respect to underlying representations (UR’s). We will try to show how the above notions lead to some most disturbing contradictions concerning UR’s.

We will start with the original claim that there are no restrictions or constraints on underlying representations in OT. As a result, any language may have any kind of segment or structure in the Lexicon, and it will be the language-particular ranking of the universal constraint set, CON, that determines the segment inventory of the particular language. However, many linguists have suggested that ROTB is just an inconvenience which may be quite irrelevant. If we want to keep to the original assumption that ROTB is a principle present in the grammar, then we should set up CON so that it produces possible output forms independent of the inputs. It does not mean, of course, that all input forms should yield existing forms but it does mean that all output forms should be well-formed.

The second problem to be addressed is that of Lexicon Optimization addressed by Beckman and Ringen (2003), Inkelas (1995), McCarthy (2003), and Szentgyörgyi (2004, to appear), among others. As the original formulation of LO only works on single forms, Inkelas (1995) suggested an alternation sensitive version (LO’), which takes into consideration all the possible contexts of a form and determines the underlying representation on the basis of the sum of violations by the output forms in all the possible environments. Inkelas claims that the application of LO’ will yield underspecified inputs whenever there is a surface alternation. However, this is only true if we assume that faithfulness constraints are not violated by the filling in of a binary feature. On the other hand, if we assume the opposite, as many do, then inputs will be fully specified but it will always be the structure occurring in the majority of the environments that will be posited as underlying. A significant consequence of this is the fact that in the case of x alternating with y, it is very much possible that both x and y will be found underlyingly as demonstrated in Siptár and Szentgyörgyi (2002) and Szentgyörgyi and Siptár (2004) for Hungarian H-type segments and in Szentgyörgyi (to appear) for RP English /l/ variants.

For instance, Hungarian [x] and [h] will both occur as underlying segments in the language as there are non-alternating forms with both of these segments. To make matters a bit more complicated, we have to note that Hungarian has two more variants of so-called H-types segments: a fronted variant of the voiceless velar fricative and a voiced variant of the glottal one. For the sake of simplicity of the argumentation and the tableaux to be presented we will only concentrate on [x] and [h] and will leave the other two versions out of the discussion. Note though that none of the arguments presented hinges upon the number and exact quality of the surface variants of the underlying H-type segment(s), i.e. the same arguments are valid for an analysis taking all four allophones into consideration. As a result of both [x] and [h] appearing underlyingly, these segments normally considered to be allophones of the same phoneme will have independent underlying status, which is clearly against the usual assumptions made by generative phonological theories. The paper attempts to show how such undesirable results may be avoided.

1. Richness of the Base: setting up the constraint system for predictable variation

The basic assumption of phonological theories concerning predictable alternating and non-alternating segments that appear in complementary distribution is that they should be represented with the same underlying segment. Then it is the responsibility of the constraint hierarchy of an OT grammar to select which of the possible surface forms will occur in a given environment.

The example that we are going to use throughout the paper is a well-known alternation of Hungarian H-type segments: that of the voiceless velar, [x], and voiceless glottal [h] variants:

(1) Alternating and non-alternating Hungarian H-type segments

The usual assumption concerning the above data is that the UR of these segments is always a glottal /h/ and in codas it surfaces as [x]. To achieve this, the following constraints are necessary:

(2) *Coda-h Glottal fricatives are prohibited in codas.
(3) ID Place Correponding segments have the same specification for Place features.
*Coda-h >> ID Place

Note that only the absolutely relevant constraints are shown throughout the paper. For the same reason, candidates involving deletion, insertion, metathesis etc. will not be indicated in tableaux as they are not relevant for the present discussion.

As can be seen in tableau (4), candidate (a) with the glottal [h] in coda position violates the higher ranked markedness constraint while candidate (b) with the velar [x] in the same position violates the lower ranked identity constraint and thus is judged to be optimal. Similarly, in tableau (5) the phonetically correct candidate containing an onset [h], (a), is selected as optimal as it does not violate either constraint, while candidate (b) does violate the identity constraint because of an underlying glottal /h/ corresponding to a surface velar [x].
Because of the Richness of the Base, however, other input forms must also be considered:

Tableau (6) demonstrates that an input with a velar /x/ in coda position will also yield the same optimal candidate as in (4) above. However, in tableau (7) it can be seen that a UR with an onset velar /x/ will result in the selection of a phonetically incorrect output form as optimal. This form, candidate (7b) does not violate either constraint as it does not contain a glottal [h] in a coda and it does not involve any change with respect to the input form. Note that it is not necessary that the same constraint hierarchy yield the same optimal output form for a different input: there is only one requirement, namely that all optimal output forms should be phonologically and phonotactically possible forms, which is clearly not the case here. Thus a new constraint must be introduced to exclude a velar fricative, [x], in onsets:

(8) *Onset-x Velar fricatives are prohibited in onsets.
*Coda-h, *Onset-x >> ID Place

The tableaux (9)-(12) demonstrate that adding the new markedness constraint to the hierarchy will always result in the attested being forms selected as optimal, a desired outcome. The same surface forms are achieved regardless of the choice of the underlying H-type segment.
Another possible solution would be to collapse the two markedness constraints:

(13) H-Place H-type segments are velar if and only if in the coda.

As is clear from tableaux (14)-(17), the new markedness constraint does the very same job just as well as the two separate constraints above. In both cases there is a (set of) constraint(s) which prohibits one surface variant in some environments and other variants in others. If there were no such constraint(s), in some environments, it would not be the actual surface form that would be selected as optimal, i.e. such a constraint (set) is necessary for the treatment of predictable variation.

2. Lexicon Optimization: selecting the underlying representation

The next question to be answered in this section is how we can treat those cases where two or more different input forms yield phonetically identical optimal outputs. Prince and Smolensky (1993) adopted the mechanism of Lexicon Optimization to deal with the problem:

Suppose that several different inputs I1, I2, ..., In when parsed by a grammar
G lead to corresponding outputs O1, O2, ..., On, all of which are realized as
the same phonetic form ? — these inputs are all phonetically equivalent with
respect to G. Now one of these outputs must be the most harmonic, by
virtue of incurring the least significant violation marks: suppose this optima
one is labelled Ok. Then the learner should choose, as the underlying
form for ?, the input Ik. (Prince and Smolensky 1993:192)

That is, we have to compare the phonetically identical optimal cases arising from different inputs and select the one with the fewest violations; it is the input form belonging to this optimal candidate that will be selected as the UR of the lexical item.

In non-alternating cases it is the input belonging to some of the surface variants that is selected in some environments and the input belonging to other surface variants that is selected in others as demonstrated by the tableaux below.



Tableaux (18)-(21) contain only the input forms and the selected optimal candidates from tableaux (14)-(17). If we compare (18) and (19), where both the input with a glottal /h/ and the other one with a clear /x/ result in the optimal output containing a surface velar [x], it is the input with the velar segment that scores the fewest violations as, besides not violating the markedness constraint, it does not violate the lower ranked faithfulness constraint either. In cases of onset /h/, it is just the opposite; therefore, the input with a glottal /h/ will be selected as the UR of the optimal output.

However, this kind of mechanism clearly leads to a contradiction: although we started out by assuming that the same UR is used for H-type segments in all cases – and that is also the assumption made by most phonological theories – we arrived at a conclusion that contradicts this. Both surface segments underlie, i.e. they contradict, the traditional notion of underlying segments/phonemes. Let us now turn to alternating cases and see how a modified version of LO can or cannot treat those.

3. Alternation-sensitive Lexicon Optimization: full specification or underspecification?

In alternating stem final cases, the surface realization of the H-type segment depends on the following segment: before vowels it can be syllabified into the onset, i.e. it will be realized as a glottal [h], while before a consonant or a pause it will be syllabified into the coda, i.e. it will surface as a velar [x].

Unfortunately, traditional LO would predict two different UR’s for the same morpheme, i.e. it would suggest a morpheme with at least two different underlying forms, a clearly unwanted result:


/1/
(To be more precise, we have to note that intervocalic and intersonorant occurrances of H-type segments are realised as a voiced [?]. However, this is one of the two surface realisations that we are not discussing here.)

For the stem doh~dohos [dox]~[do.ho?] ’musty smell’~’with a musty smell’, (23) with an underlying velar /x/ is selected by normal LO if no suffix follows (or before a consonant-initial suffix), while (24) with an underlying glottal /h/ is selected before a vowel-initial suffix, i.e. the two different underlying forms would be: /dox/~/doh/.
A possible solution may be presented by underspecification: if in both cases the input with an H-type segment underspecified for place features won, we would have one UR for lexical items involving alternations. Let us now turn to such underspecified inputs and see whether they can be selected as the UR by LO. An H-type segment underspecified for place features is indicated with a capital H in the paper.

Tableaux (26) and (27) raise a very important question in connection with underspecified inputs: does the filling in of a binary feature count as a violation of identity constraints? If it does, then (23) is preferred over (26), and (24) is preferred over (27), i.e. fully specified inputs will be preferred to underspecified ones.

However if filling in a binary feature does not count as a violation of ID constraints, then (23) and (26), and (24) and (27) are equally well-formed. But then how can they be distinguished? SPECIFY, a constraint requiring outputs fully specified for binary features, clearly does not work as it cannot refer to inputs, just like any other constraint cannot solely refer to inputs. Instead, DEP [feature] constraints will prefer fully specified inputs over underspecified ones, as they penalise those output features that do not have a correspondent in the input representation.

(28) DEP Place. Place features in the output have correspondents in the input.

This way even if the filling in of a binary feature counts as a violation of an IDENTITY [F] constraint, fully specified inputs are still preferred to underspecified ones by LO. Thus we may conclude that whether IDENTITY [F] constraints are violated by filling in a binary feature or not, underspecified input forms will be dispreferred by Lexicon Optimization.

Consequently, the forms in (23) and (24) are selected as the optimal underlying representations of the word forms in question, i.e. in all such cases we have one morpheme with two underlying forms on the one hand, and we also have two segments in complementary distribution which will both be found in underlying forms as seen earlier.

Another way of approaching this problem would be to change LO in a way to enable it to address alternations. Such a version of LO, let us call it LO’, has been suggested by Inkelas (1995):

Given a grammar G and a set S = {S1, S2, ... Si} of surface phonetic forms
for a morpheme M, suppose that there is a set of inputs I = {I1, I2, ... Ij},
each of whose members has a set of surface realizations equivalent to S.
There is some Ii ? I such that the mapping between Ii and the members of S
is the most harmonic with respect to G, i.e.it incurs the fewest marks for
the highest ranked constraints. The learner should choose Ii as the underlying
representation for M. (Inkelas 1995:7)

That is, we have to compare the phonetically identical optimal outputs corresponding to different input forms, evaluate them in all the relevant environments, and see which one fares best on the constraint hierarchy all in all. Let us take a look at such a complex evaluation for one of the above examples. Markedness constraints are not indicated in these tableaux as they are equally violated by the candidates regardless of the input specifications.

DEP Place and ID Place may be ranked whichever way; it will not influence the selection of the optimal candidates in any of the earlier tableaux. However, it does influence the choice of the winning candidate in (29). If DEP Place dominates ID Place then it is clearly candidate (b) with the underlying velar fricative that is the most optimal input form as it causes no violation of the higher ranked DEP Place, while candidates (a) and (c) do. Note that for this we assume that glottal segments do not have Place features. As a result changing an underlying velar into a surface glottal does not violate DEP Place but it does violate ID Place. However, should the ranking be the reverse, i.e. should ID Place dominate DEP Place, then the choice of the optimal input, yet again, depends on whether ID constraints are violated by the filling in of a binary feature. If they are, then candidate (b) is selected again as it causes the fewest violations of ID Place. To be more precise, it causes one violation of ID Place just like the first input candidate, but while in (b) there is no violation of the other constraint, DEP Place, there is a violation for candidate (a).On the other hand, if ID constraints are not violated by filling in binary features, candidate (c) with the underspecified input will be selected as optimal, as it causes no violation of ID Place, while the outputs of the other two input candidates do.

Whichever the case, it is still not a desired result at all. Let us remember that in some non-alternating cases – in those lexical items where the H-type segment is always in onset position – a glottal /h/ will be selected as the optimal input form, while in others – in those with the H-type segment always in the coda – an underlying velar /x/ is selected by LO. Note that Inkelas’s (1995) LO’ will not have any influence in these non-alternating cases, i.e. these segments remain stable regardless of the environment. Thus there are at least two, but possibly three, different underlying representations for surface H-type segments: two for the non-alternating cases; and, depending on the ranking of ID Place and DEP Place in (29) and depending on whether the filling in of binary features violates ID constraints, even underspecified underlying H-type segments may appear, which is the third possible input form. It seems then that regardless of how we treat filling in underspecified features and regardless of the ranking of constraints, there must be at least two different UR’s for H-type segments.

One might wonder whether changing the interpretation of the relevant environments would have any effect on the selection of the ideal input forms. In the above discussion we considered just two environment types: onset and coda positions. However, one might suggest two more subtypes of the latter that matter: before consonants and before a pause.

However, it can be seen that the very same arguments hold for the input and output forms in tableau (30) as in tableau (29). As a result, we can safely claim that whatever the relevant environment(s), the number of underlying representations suggested by LO or LO’ is at least two. That is, this way it is not possible to reduce the number of UR’s for allophonic variation. Let us now turn to the possible solutions that may be proposed to answer this challenge.

4. Possible solutions to the problems

In the above discussion we have seen that if we take the Richness of the Base seriously, and if we apply either Prince and Smolensky’s LO or Inkelas’s LO’, we get a solution which contradicts the usual assumption that alternating segments have a common underlying representation. Thus either it is the ROTB that is incorrect, or LO (or LO’), or the general claim concerning UR’s. Let us take a look at these three factors - and one more at the end – and see how they could be modified and what kind of consequences these modifications would entail.

Richness of the Base Abandoned

One possibility is to give up the idea of the Richness of the Base. However, this would lead to some undesirable problems that would challenge the very core of the theory: on the one hand giving up ROTB would mean imposing restrictions on UR’s. Since not everything is a possible UR, UR’s are limited; moreover, they have to be stipulated as there are no clearcut mechanisms to calculate them from output forms. This would lead to a grammar that is far more powerful than the current version of OT allows: it is very much possible that a grammar flawlessly works on the stipulated input forms, but fails to select grammatically possible optimal output forms in cases where a different input form occurs.

Lexicon Optimization (or LO’) Modified

Another possible amendment could be to give up or change Lexicon Optimization – or Inkelas’s alternation sensitive version. What are the necessary modifications that we have to apply to make LO work?
We have to ensure that allophonic variation results from one underlying segment – it was this assumption that our results above contradicted. That is, if two surface segments are in complementary distribution, then they have to come from the same input form, i.e. even if traditional or alternation sensitive LO suggests two (or three) different input segments, another mechanism has to undo this. For instance, we could suggest that the underlying forms in such cases will always contain the underlying segment found in alternating forms – i.e. either /dox/ or /doH/ depending on the ranking of ID Place and DEP Place in (29) and (30). The choice between these two may be governed by Grammar Optimization (GO):

The optimal grammar is the most transparent, i.e. the one in which
alternations are maximally structure-filling. In terms of Optimality Theory,
this means that PARSE [i.e. members of the MAX constraint family
in the Faithfulness version of OT] is ranked as high as possible.’ (Inkelas 1995:11)

On this basis, MAX or ID constraints must be ranked higher than DEP constraints to maximize transparency in the grammar. If this is applied to our case, then in (30) DEP Place must be ranked below ID Place. Moreover, if ID constraints are violated by feature filling, (30b) is selected as optimal while if ID is not violated by feature filling, (30c) with an underspecified input is selected to be the UR. That is if we assume that ID constraints are not violated by feature filling and we also apply Grammar Optimization, then we will get underspecified inputs in the case of alternating forms. Then we may also assume that GO goes one step further and the underlying form in alternating cases will be extended to non-alternating cases by analogy as described above. This way the system can be made to work without one principle contradicting the other.

No Underlying Representations

A third possibility is to give up the idea of underlying representations, i.e. the traditional notion of underlying segments/phonemes would not be used any more. This way we would have to claim that UR’s do not exist, and as a result, there would be no need to calculate them by applying LO. Thus Lexicon Optimization would be deemed unnecessary as well. Also, if there are no UR’s, there could be no input-output faithfulness constraints, i.e. the MAX and DEP constraint families would cease to exist. Even in the case of ID constraints, ID input-output constraints would be ruled out and only output-output correspondence would play a role in determining faithfulness. This way underlying representations would be replaced by paradigms along the lines suggested by Burzio (1998), Kenstowicz (2001), Padgett (2001) and (Rebrus and Törkenczy 2004).

Only Unary Features

As some of the problems have been caused by a question concerning violations of ID constraints by filling in binary feature specifications, one might suggest that this kind of problem could be avoided if we had only unary features. Note also that in such a case, the abovementioned modification of LO is not an option because it is based on the proposal that in cases of allophony and alternation, an underspecified input form should be preferred. As underspecification does not make sense in the case of unary features, the modification of LO would not be an option. Also note that unary features result in a much more constrained grammar along the lines of element theory proposed in Government Phonology, CV-phonology and VC-phonology.

5. Conclusion

In this paper we wanted to show how the different assumptions made by generative phonology in general and OT in particular may lead to contradiction in the treatment of very simple allophonic data, like the H-type segments in Hungarian. Also, we showed that there are three possible options for avoiding these problems: either Lexicon Optimization must be modified and complemented by Grammar Optimization, or the use of underlying representations should be given up and grammar should be based on output-output correspondence relations in paradigms, or feature representations should be more restricted, i.e. only unary features should be allowed. Of course, any combination of the above three suggestions is also a viable option.

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