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<Paper uid="W98-0904">
  <Title>Optimal Morphology</Title>
  <Section position="2" start_page="0" end_page="3" type="metho">
    <SectionTitle>
CVV CVCCV
</SectionTitle>
    <Paragraph position="0"> 'he falls' 'you opened' Since hapje is ungrammatical as V+OBJ but grammatical as V+IMF:2SG there seems no purely phonological way to predict the observed contrasts.By lexicalizing the alternations though, say by stating that OBJ is -je after vowels and -e after consonants we lose the insight that the process is motivated by the perfectly natural and crosslinguistically observable avoidance of of CC and VV (cf. Prince &amp; Smolensky, 199:3). The solution I propose to this dilemma is the following:  (4) a. Replace the CV-constraint by a soft constraint marking CC and VV as constraint violations.</Paragraph>
    <Paragraph position="1"> b. Annotate the candidate set with independently needed morphosemantic interpretation and choose as the correct form for certain morphological features (e.g.PI+OBJ) the phonologically optimal form annotated with it.  More concretely (2) is replaced by (2'):  The phonological constraint following Ellison (1994) has the form of a regular relation mapping phonological strings into sequences of constraint violation marks ('1') and 'O's which stand for no violation. The effect of the constraint can best be seen in tableau form familiar  Differently from OT optimal forms are not computed with respect to an underlying phonological form, but directly referring to a morphological characterization of the generated word form.</Paragraph>
  </Section>
  <Section position="3" start_page="3" end_page="3" type="metho">
    <SectionTitle>
2 Formalism
</SectionTitle>
    <Paragraph position="0"> An OM grammar is a quintuple {MA, PA,M,P,(0,1}} where MA and PA are sets of symbols, the morphological and the phonological alphabets. M is a finite set of regular relations, each mapping MA into PA, while P is a finite sequence of regular relations mapping MP into {0, 1}. 27</Paragraph>
  </Section>
  <Section position="4" start_page="3" end_page="3" type="metho">
    <SectionTitle>
3 Generation Morphology
</SectionTitle>
    <Paragraph position="0"> Specific word forms are characterized as strings of abstract morphems, e.g. PI+OBJ 4. Specific candidate sets are obtained by the crossover product of word forms 5 with the candidate relation. For ease of exposition I give the algorithm for finite state automata and transducers which are formally equivalent to regular expressions and binary regular relations respectively. For a transducer T and an automaton A the crossover product AxT is generated in the following way.</Paragraph>
    <Paragraph position="1"> IT and Ih are the initial, FT and FA the final states:</Paragraph>
    <Paragraph position="3"> 6 then add to AxT an arc 7 from (x,z) to (y,t) labeled P. Obviously, the resulting automaton contains all and only the phonological output candidates for the given morphological input. (7) shows the application of the algorithm to PI+OBJ and the candidate set from (2'):</Paragraph>
    <Paragraph position="5"/>
  </Section>
  <Section position="5" start_page="3" end_page="3" type="metho">
    <SectionTitle>
4 For sake of readability concatenation of morpholog-
</SectionTitle>
    <Paragraph position="0"> ical symbols is represented by '+'.</Paragraph>
    <Paragraph position="1"> 5Strings are a trivial case of regular expressions. GCrossover product(A, T) is equivalent to the image of A under T (Kaplan &amp; Kay, 1994:340-42), defined as the range of the composition Id(A) o R, where Id(A) is the identity relation that carries every member of A into itself. See Frank &amp; Satta (1998:5-6) for the same concepts under different terminology.</Paragraph>
    <Paragraph position="2">  (i, B, PI/pi), (i, B, HAP/hap), (B, C, OBJ/je),(S, C, OBJ/e), (B, C, IMF/je) Resulting Candidates Initial State: (0, A) Final State: (2, C) Transitions: ((0, A), (1, B) pi), ((1, B), (2, C), e) ((1, B), (2, C), je)  Since the candidate set and the constraint in (2') are regular Ellisons (1994) algorithms for getting an automaton containing only optimal candidates, as long as candidate set and evaluation transducer are regular, can be used. For details I refer the interested reader to Ellisons paper.</Paragraph>
  </Section>
  <Section position="6" start_page="3" end_page="3" type="metho">
    <SectionTitle>
4 Parsing
</SectionTitle>
    <Paragraph position="0"> The candidate transducer constitutes a kind of backbone for parsing phonological strings into strings of abstract morphemes. For example the candidate transducer in (2') will allow correct parsing of hape into HAP+OBJ. A complication arises when the transducer maps phonological forms to more than one morphological form, possibly including incorrect ones. E.g. the example transducer will map hapje onto (correct) HAP+IMF and (incorrect) HAP+OBJ. Then given the generation procedure above for every obtained morphological string it can be checked if it generates the input phonological form. A special case of this are not existing word forms.</Paragraph>
    <Paragraph position="1"> For example we will get PI+OBJ as the only possible parse for pie. But since the optimal output for PI+OBJ isn't pie but pije there is no actual parse. 28  Optimal Morphology clearly is a hybrid. Candidate sets are given by lexicalized monotonic constraints as in DP. Phonological constraints on the other side are violable and ranked as in OT z.</Paragraph>
    <Paragraph position="2"> Looking at constraint based formalisms as tentatives to restrict the rather rich theoretical inventory of generative SPE theory (Chomsky &amp; Halle, 1968) it becomes obvious that OM indeed fills a conceptual gap:</Paragraph>
    <Paragraph position="4"> arbitrary rule/ yes yes no yes constraint order language specific yes no yes yes rules/constraints underlying yes yes no no representations Neglecting here the difference between rules and constraints, OT has chosen to eliminate language specific constraints s while maintaining underlying representations. It is not a priori clear that this is favorable to eliminating arbitrary rule (constraint) ordering or underlying representations, and indeed this last choice is what happens in OM, while DP has eliminated two of SPEs theoretical instruments. In this respect it is the most restrictive framework, but we have seen empirical and conceptual problems with its assumptions in the preceeding section. Consider the following: Lexicalized candidate sets in both DP and OM are given by language-specific constraints, thus this point makes no difference. Now, when the toy example above proves to be representative, OM (like OT) allows to maintain universal constraints where DP cannot.</Paragraph>
    <Paragraph position="5"> 7See section 6 for an example of ranking.</Paragraph>
    <Paragraph position="6"> SNote that the OT-claim to use only language-specific constraints is crucially weakened by the family of alignment-constraints that can be instantiated in a language-specific way.</Paragraph>
    <Paragraph position="7"> It might seem that OM can handle regular phonological processes only by stipulation of allomorphs with a high degree of redundancy.</Paragraph>
    <Paragraph position="8"> Thus for the case of German final devoicing we would have to assume two allomorphs for each morpheme showing the alternation, e.g.</Paragraph>
    <Paragraph position="9"> {Tod, Tot} 9 as in Tot, 'death(sig)' and Tode,'death-plu'. The choice between these allomorphs could be accomplished by the two constraints !DEVOICE that marks voiced obstruents in coda position and !VOICE that marks unvoiced obstruents generally. The ranking 1deg !DEVOICE ~&gt; !VOICE will make 'Tot'- the optimal candidate in Tot and 'Tod-' in Tode. Tot, 'dead' with an &amp;quot;underlying&amp;quot; t will remain the same in every context, assuming that this is the only allomorph. Though this works technically it seems highly undesirable to have two allomorphs for Tod one of which can be predicted.But the regular expression (Tod \[ Tot) can equally well be written as To(d\[t) or even as To\[-continuant -sonorant +coronal\] since regular languages can be enriched straightforwardly by bundles of finite-valued features (Kaplan Kayi 1994:349-351). Thus allomorphy in this and comparable cases reduces to underspecifi- null cation. 11 7 Locality of Constraint Evaluation null Ellisons (1994) algorithms offer a way of globally finding optimal candidates out of regular candidate sets. This however is not the 9 German orthography is used except for the phonemic writing of voiceless 't')  son (1994).</Paragraph>
    <Paragraph position="10"> nlt might be argued that this move doesn't explain the nonexistence of voiced Coda-obstruents in German, since nonaiternating voiced obstruents could be accomplished by fully specifying them as voiced in morphology. But there are languages like Turkish (Inkelas:1994:3), where certain morphemes resist otherwise regular final devoicing and this descriptive possibility thus seems to 29be well motivated.</Paragraph>
    <Paragraph position="11"> only possible method to generate word forms given a particular OM-grammar. In the example above the optimal word form can also be found in a much more local way: by traversing at once the candidate automaton and the evaluation transducer and choosing at each state the '0'-transition, when possible. The reader can check this by constructing finite state automata out of the regular relations in (2').</Paragraph>
    <Paragraph position="12"> Though this is a case of extreme locality, probably not representative for phonological phenomena in general, it seems promising to study, how far constraint evaluation can work locally. An argument that constraint evaluation not only can but SHOULD happen locally can be constructed out of the following well known data</Paragraph>
    <Paragraph position="14"> H: k5 'war' pdld 'house' L: @d, 'debt' b~l~ 'trousers HL: mb~ 'owl' ngihl 'dog' LH: mbd 'rice' fhndd 'cotton' LHL: rob5 'companion' nyhhti woman' are the following logical possibilities of tonal realization: null (lO) 14 mbu: mbfi felama: f~ldrnh, fdldrnf, fdlhmtl, fdhlmh, fdldmd nyaha: nydhtl, nyhh5, nydh5 The problem of selecting out of these the correct for is solved by Goldsmith (1976) through the following mapping procedure:  a. Associate the first tone with the first syllable, the second tone with the second syllable and so on.</Paragraph>
    <Paragraph position="15"> b. Tones or syllables, not associated as a result of (a) are subject to the wellformedness condition.</Paragraph>
    <Section position="1" start_page="3" end_page="3" type="sub_section">
      <SectionTitle>
Well-Formedness Condition
</SectionTitle>
      <Paragraph position="0"> H: hdwdmd 'waistline' L: kphkSl~ 'tripod chair' HL: fdldmh 'junction' LH: ndhvSld 'sling' LHL: n~ki'l~ 'groundnut' Ill Mende nouns have one of five specific tone patterns (indicated in the left column). Note that atoms of tone patterns like L in HL can be realized as sequences of high tone syllables as in fe:lhmtl or as part of contour tones 13 as in mbPS Hence for tabu, nyaha and felama, there 12The ideas presented here owe much to the concept of incremental optimization developed in Walther (1997). Locality in Constraint evaluation is also invoked in Tesar (1995}, but there it isn't conceived as empirically different from global evaluation. For an interesting hybrid of directional rule application/constraint evaluation see Kager (1993) 13Contour tones are the falling tone (mbfi) the rising tone(tubal) and the falling rising tone (mbd). Acute stands for H, grave for L tone. As Leben, I analyze contours as sequences of Hs and Ls.</Paragraph>
      <Paragraph position="1"> a. Every tone is associated with some syllable.</Paragraph>
      <Paragraph position="2"> b. Every syllable is associated with some tone.</Paragraph>
      <Paragraph position="3"> c. Association lines may not cross.</Paragraph>
      <Paragraph position="4"> This mapping procedure is (apart from its use in a wealth of other phenomena) stipulation. I will sketch how the same effects can be derived from plausible constraints on phonological wellformedness and locality of constraint evaluation. null Let's suppose that the candidate sets in (10) are given by lexical constraints realized as transducers 1S. It's natural to assume that contour tones are a marked case in human language, violating the constraint *Contour and that there's a ban on adjacent syllables with the same tone, 14In Goldsmiths system these possibilities would correspond to the possible noncrossing exhaustive associations of the stems with their respective tone pattern. For details see Trommer (1998).</Paragraph>
      <Paragraph position="5"> lSFor an implementation see Wrommer (1998). 3O an instance of the Obligatory Contour Principle</Paragraph>
      <Paragraph position="7"> ,where C stands for contour tones and S for simple tones.</Paragraph>
      <Paragraph position="9"> mbfi violates *Contour, but being the only candidate for tabu its optimal. For felama filSmh and fdldmd will be excluded since they violate both constraints and the other candidates only one. But 1~ fdldmh, fdl~rnfi and fdh~mh for that reason are all on a par. Nydhd is out because it violates two times *Contour, but there's no way to decide between nydhh and nyfh5 that violate it only once.</Paragraph>
      <Paragraph position="10"> However once locality of constraint evaluation is taken seriously only the correct candidates remain: Suppose we are following the candidate automaton for felama, for 'e' 'e&amp;quot; will be chosen since the word has to start with H and a contour tone would violate *Contour. Next, 'h' will be selected since 'd' violates !OCP(Tone) and 'd' again *Contour. For the same reason 'd' would be best for the next 'a'. But now according to the unviolable lexical constraint that requires the tone pattern for this noun, only 'd' is possible, even if it violates !OCP(Tone).</Paragraph>
      <Paragraph position="11"> a~Obviously H and L in (12) have to be spelled out segmentally, i.a. in their shape as contour tones. In Trommer (1998) I present a procedure to convert constraints on tones in constraints on corresponding segments. A more autosegmental treatment following the lines of Eisner (1997) is also considered there and shown to be compatible with the results presented here. Consonants are ommitted for ease of exposition.</Paragraph>
      <Paragraph position="12"> 17For simplicity I ignore possible results out of ranking the constraints and treat them like one complex constraint null More or less the same story can be told about nyaha. Hence the left to right-assymmetry in the mapping convention emerges out of locality or, put in a more placative way, the tendency to choose marked options as late as possible. Note that the use of violable constraints is necessary in this account to get contour tones and tone plateaus at all, but only when necessary.For example an unviolable constraint prohibiting contours would exclude correct forms as rnb~i and nyhhd.</Paragraph>
    </Section>
  </Section>
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