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<Paper uid="P90-1022">
  <Title>EXPRESSING DISJUNCTIVE AND NEGATIVE FEATURE CONSTRAINTS WITH CLASSICAL FIRST-ORDER LOGIC.</Title>
  <Section position="6" start_page="177" end_page="177" type="concl">
    <SectionTitle>
CONCLUSION
</SectionTitle>
    <Paragraph position="0"> This paper has shown how attribute-value structures and constraints on them can be axiomatized in a decidable class of first-order logic. The primary advantage of this approach over the &amp;quot;designer logic&amp;quot; approach is that important properties of the logic of the feature constraint language, such as soundness, completeness, decidability and compactness, follow immediately, rather than proven from scratch. A secondary benefit is that the substantial body of work on satisfiability algorithms for first-order formulae (such as ATMS-based techniques that can efficiently evaluate some disjunctive constraints \[13\]) can immediately be applied to feature structure constraints.</Paragraph>
    <Paragraph position="1"> Further, first-order logic can be used to axiomatize other types of feature structures in addition to attribute-value structures (such as &amp;quot;set-valued&amp;quot; elements) and express a wider variety of constraints than equality constraints (e.g. subsumption constraints). In general these extended systems cannot be axiomatized using only quantifier-free formulae, so their decidability may not follow directly as it does here. However the decision problem for sublanguages of first-order logic has been intensively investigated \[4\], and there are decidable classes of first-order formulae \[8\] that appear to be expressive enough to axiomatize an interesting variety of feature structures (e.g.</Paragraph>
    <Paragraph position="2"> function-free universally-quantified prenex formulae can express linguistically useful constraints on &amp;quot;set-valued&amp;quot; elements). An objection that might be raised to this general approach is that classical first-order logic cannot adequately express the inherently &amp;quot;partial information&amp;quot; that feature structures represent. While the truth value of any formula with respect to a model (i.e. an interpretation and variable assignment function) is completely determined, in general there will be many models that satisfy a given formula, i.e. a formula only partially identifies a satisfying model (i.e. attribute-value structure). The claim is that this partiality suffices to describe the partiality of feature structures.</Paragraph>
  </Section>
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