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<Paper uid="P88-1035">
  <Title>Unification of Disjunctive Feature Descriptions</Title>
  <Section position="3" start_page="286" end_page="286" type="intro">
    <SectionTitle>
2 Disjunctive Feature De-
scriptions
</SectionTitle>
    <Paragraph position="0"> We use a slightly modified version of the formula language FRL of Kasper and Rounds \[86\] to describe our feature structures. Fig. 2 gives the syntax of FRL', where A is the set of atoms and L the set of labels.</Paragraph>
    <Paragraph position="1">  In contrast to Kasper and Rounds \[86\] we do not use the syntactic construct of path equivalence classes. Instead, path equivalences are expressed using non-local path expressions (called pointers in the sequel). This choice is motivated by the fact that we use these pointers for an efficient representation below, and we want to keep FIK.' as simple as possible.</Paragraph>
    <Paragraph position="2"> The intuitive semantics of FIK/is as follows (see \[Kasper/Rounds 86\] for formal definitions):  1. NIL is satisfied by any feature structure. 2. TOP is never satisfied.</Paragraph>
    <Paragraph position="3"> 3. a is satisfied by the feature structure consisting only of a single node labelled a.</Paragraph>
    <Paragraph position="4"> 4. I : ~ requires a (sub-)structure under arc I to satisfy @.</Paragraph>
    <Paragraph position="5"> 5. @ A * is satisfied by a feature structure that satisfies ~ and satisfies ~.</Paragraph>
    <Paragraph position="6"> 6. * V * is satisfied by a feature structure that satisfies @ or satisfies 9.</Paragraph>
    <Paragraph position="7"> 7. (p) requires a path equivalence (two paths lead null ing to the same node) between the path (p) and the actual path relative to the top-level structure.2 The denotation of a formula @ is usually defined as the set of minimal elements of SAT(~) with respect to subsumption 3, where SAT(@) is the set 2 This construct is context-sensitive in the sense that the denotation of (p) may only be computed with respect to the whole structure that the formula describes.</Paragraph>
    <Paragraph position="8"> 3The subsumptlon relation _E is a partial ordering on feature structures inducing a semi-lattice. It may be defined as: FS1 C FS2 iff the set of formula~ satisfied by FS2 includes the set of formulae satisfied by FS1. of feature structures which satisfy &amp;.</Paragraph>
    <Paragraph position="9"> Example: The formula ~=subj:agr:(agr) A C/ase:(nom V ace) denotes the two graphs subj agr case subj agr case nora acc</Paragraph>
  </Section>
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