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<Paper uid="C90-2018">
  <Title>Feature Logic with Disjunctive Unification</Title>
  <Section position="6" start_page="0" end_page="0" type="evalu">
    <SectionTitle>
&lt;!:.5 Maxwell and Kaplan's Approach
</SectionTitle>
    <Paragraph position="0"> An approach which ours is especially interesting to con&gt; pare with is the disjunctive constraint satisfaction procedure given in \[Maxwell/Kaplan 89\], because of the similar representations involved in the two approaches. They use also disjunction names and contexts to represent disjunctive constraints and propose ,~ general transformation procedure which turns a rewrite system for non-disjunctive constraints into one which handles disjunction of constraints with the use of corttexted constraints, having the impli.cational form (k-~ d), where C/ is some non-disjanctlw.' constraint. This is done by replacing every rewrite rule by its &amp;quot;contexted versimF', e.g., C/1 A C/2 ~ C/a is replaced by (k:t -~ (/)1) A (k2 -~ ~2) --'+ (kl A &amp;quot;~k2 ~ (/)1) A (k~ A ~k~ --, O~) A (&lt; A k~ --, 0~), where k~ and k~ are variables for context descriptions. There are two severe efficiency-critical problems if we want to use the outcome of this translation without further optimization. First, any rule of the generated form should only apply to a pair of contexted constraints whose contexts are compatible, i.e. kl A/c2 is not contradictory. But now, since context descriptions taay include conjunction and negation at any level, this test itself is an A/P-complete problem, which has to be solved before every application of a rule. The second problem concerns substitution. Consider a rule like z - yA~ ~ ~,a-.~.</Paragraph>
    <Paragraph position="1"> The translation produces a rule in which (P is rewritten to both ~ and (I)v_x , indexed with different context descriptions. Thu,~, we cannot simply perform a replacement, but instead, have to make a copy of 45 (or at least those parts of 45 containing y). Unfortunately, this prevents also the efficient union/find method to be employed for bnilding equivalence classes for variables instead of actual substitution. All of I, hese problems arc avoided if we let the context description ,:)f a contexted constraint depend implicitly on the variables in it through the introduction of context-unique variables.</Paragraph>
    <Paragraph position="2"> From this point of view, our method can be seen as an optirnized implementation of the translated rewrite system for unification in feature logic wittt sorts and negation.</Paragraph>
  </Section>
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