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<Paper uid="P93-1028">
  <Title>A LOGICAL SEMANTICS FOR NONMONOTONIC SORTS</Title>
  <Section position="11" start_page="213" end_page="213" type="concl">
    <SectionTitle>
CONCLUSION
</SectionTitle>
    <Paragraph position="0"> This paper has shown how the method ofnonmonotonic sorts is grounded in the well-established theories of Kasper-Rounds logic and Reiter's default logic. This is, to our knowledge, the first attempt to combine Reiter's theory with feature systems.</Paragraph>
    <Paragraph position="1"> Most previous attempts to fuse defaults with feature structures have relied on procedural code-a state of affairs that is highly inconsistent with the declarative nature of feature systems. Methods that do not rely on procedures still suffer from the necessity to specify what order information is received in.</Paragraph>
    <Paragraph position="2"> It seems to us that the major problem that has plagued attempts to add defaults to feature systems is the failure to recognize the difference in kind between strict and default information. The statement that the present participle suffix for English is '+ing' is a very different sort of statement than that the past participle suffix is '+ed' by default.</Paragraph>
    <Paragraph position="3"> The former is unassailable information. The latter merely describes a convention--that you should use '+ed' unless you're told otherwise. The method of nonmonotonic sorts makes this important distinction between strict and default information. The price of this method is in the need to find solutions to NSFSs. But much of the cost of finding solutions is dissipated through the unification process (through the elimination of inconsistent and redundant defaults). In a properly designed lexicon there will be only one solution, and that can be found simply by unifying all the defaults present (getting a unification failure here means that there is more than one solution--a situation that should indicates an error).</Paragraph>
    <Paragraph position="4"> The semantics given for NSs can be extended in a number of ways. In particular, it suggests a semantics for one kind of default unification. It is possible to say that two values are by default equal by giving the formula Dp -p2. This would be useful in our German verbs example to specify that the past tense root is by default equal to the present tense root. This would fill in roots for spiel and mahl without confounding zwing. Another extension is to use a prioritized default logic to allow for resolution of conflicts between defaults. The natural prioritization would be parallel to the lexicon structure, but others could be imposed if they made more sense in the context.</Paragraph>
  </Section>
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