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<Paper uid="P91-1033">
  <Title>FEATURE LOGIC WITH WEAK SUBSUMPTION CONSTRAINTS</Title>
  <Section position="7" start_page="261" end_page="261" type="concl">
    <SectionTitle>
5 Conclusion
</SectionTitle>
    <Paragraph position="0"> We proposed an extension to the basic feature logic of variables, features, atoms, and equational constraints. This extension provides a means for one-way information passing. We have given a simple, but nevertheless completely formal semantics for the logic and have shown that the satisfiability (or unification) problem in the logic involving weak subsumption constraints is decidable in polynomial time. Furthermote, the first part of the algorithm is a surprisingly simple extension of a standard unification algorithm for feature logic. We have formulated the second part of the problem as a simple property of the regular language which the outcome of the first part defines. Hence, we could make use of standard techniques from automata theory to solve this part of the problem. The algorithm has been proved to be correct, complete, and guaranteed to terminate. There are no problems with cycles or with infinite chains of subsumption relations as generated by a constraint like z ~ zf. s The basic algorithmic requirements to solve the problem being understood, the challenge now is to find ways how solutions can be found in a more incremental way, if we already have solutions for subsets of a clause. To achieve this we plan to amalgamate more closely the two parts algorithms, for instance, through implementing the check for clash-freeness also with the help of (a new form of) constraints. It would be interesting also from a theoretical point of view to find out how much of the complexity of the second part is really necessary.</Paragraph>
  </Section>
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