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<Paper uid="W98-0904">
  <Title>Optimal Morphology</Title>
  <Section position="7" start_page="3" end_page="3" type="concl">
    <SectionTitle>
8 Locality and Directionality
</SectionTitle>
    <Paragraph position="0"> In Mende tone patterns marked (tonal) structure appears as far to the right as possible. Although this seems to be the unmarked case in tone languages the mirror image too seems to exist (e.g. Kannakuru, Odden, 1995:460). To describe such cases it's sufficient to use candidate automata that are interpreted from right to left.</Paragraph>
    <Paragraph position="1"> Directionality effects like the ones found in tone mapping are also typical in many other phonological domains, e.g. foot construction (Hayes, 1985; Kager, 1995), root and pattern morphology (McCarthy, 1979), and syllabification (Ito 1988). Even if a locality-based reanalysis isn't possible in all of these cases traditionally handled by derivational mapping and parsing devices, this is a promising area for further research on locality and markedness.</Paragraph>
    <Paragraph position="2">  mapping in OT isn't regular in the general case even if GEN and the constraints are implemented as finite state transducers. This result carries over immediately to OM under global constraint evaluation. However if local evaluation is used there seems to be an algorithm to construct an equivalent finite state transducer.</Paragraph>
    <Paragraph position="3"> Since the complete algorithm requires a more elaborate representation of morpheme structure 3than I can give here I illustrate only the basic idea. is Let's first consider a slightly modified version of (2') and the corresponding transduc- null (a, C, C/0), (V, C, C/0),(C, C, C/0) (A, \7, V/0), (C, V, V/0),(V, V, V/0) For convenience abstract morphemes are represented by numbers that are repeated for each segment realizing the respective morpheme.</Paragraph>
    <Paragraph position="4"> The following algorithm yields from a candidate transducer and an evaluation transducer a transducer with three tapes integrating caMP date generation and their mapping to markedness values. The first tape of this new transducer (Kx23C) corresponds to the candidate set, the second one to the morphological signatures and the third one to the evaluation under the constraint: XSproblems for the described method arise with recursivity since '33' mapped to 'aa' is ambiguous between two aomorpemes and one aa-morpheme. Further states that can be reached and left by transitions of the same morphological index would need a seperate treatment in the procedure described on p. 9.</Paragraph>
    <Paragraph position="5"> 19the regular expression for the phonological part is exactly as in (2').</Paragraph>
    <Paragraph position="7"> Again we can find the optimal output for a certain morphological input in a local way. E.g.</Paragraph>
    <Paragraph position="8"> traversing (14) and the automaton corresponding to '1+3+' (HAP+OBJ) at once we will arrive without choice at , C4 ('111'). There we choose locally to go to V6 over e30 since this is less marked than the transition over j3/1 to C5.</Paragraph>
    <Paragraph position="9"> We get 1113/hape.</Paragraph>
    <Paragraph position="10"> Alternatively we can also dispense with the evaluation tape altogether: We delete each transition from every state S if there is another transition from S with the same morphemic index and a smaller number on the third tape. For (14) this means that we remove the transition from V4 to V6 over e3/1 since there is a &amp;quot;better&amp;quot; transition namely over j3/0 to C5. Similarly the transition from C4 to Cs over j3/1 is eliminated in favour of the transition over e3/0 to V6. Since for each state and every index there remains only one transition the third tape becomes superfluous and is removed. The result is an input/output transducer mapping '1113' (i.e.</Paragraph>
    <Paragraph position="11"> HAP+OBJ) to hape and '2233' (i.e. PI+OBJ) to pije: ~degA is mnemonic for candidate, O for constraint transducer. IA, Io and FA, Fo are the initial and final states  It's quite probable that locality as developed in the preceeding three sections is too simple to account for phonological data that require evaluation of segments at a certain distance from each other. But the point was to show that locality of constraint evaluation in the introduced framework even in this form is empirically supported and preferable on theoretical grounds.</Paragraph>
    <Paragraph position="12"> A promising extension would be to evaluate locally in lnultiple phonological domains using autoseglnental representations along the lines of Eisner (1997), but the technical realization of this still has to be worked out. As the Albanian data the tonal patterns in Mende reveal the advantages of using OM's violable constraints in the context of lexicalized candidate sets. On the other hand this lexicalization allows a simple generation procedure. Parsing phonological output forms onto morphological signatures in OM is relatively straightforward while the question is not even adressed seriously in finite state formalizations of OT. (Ellison, 1994; Eisner, 1997). Both parsing and generation are even simpler if OM is interpreted as a finite state transducer under local constraint evaluation. It remains to be seen, if the specific mixture of OM borrowing from DP AND OT will give rise to further linguistically worthwhile analyses and to efficient computation of morphophonology.</Paragraph>
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