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<Paper uid="T78-1031">
  <Title>PATH-BASED AND NODE-BASED INFERENCE IN SEMANTIC NETWORKS</Title>
  <Section position="8" start_page="223" end_page="224" type="concl">
    <SectionTitle>
9. Summary
</SectionTitle>
    <Paragraph position="0"> We have presented and compared two styles of inference in semantic networks, path-based inference and node-based inference. The former is more efficient, while the latter is more general. We showed the equivalence of an arc-relation to a two case case frame, and described how path-based inference could be incorporated into the match routine of a node-based inference mechanism, thereby combining the strengths of the two inference styles. We discussed the use of equivalence paths to represent the extensional equivalence of intensional concepts. Finally, we urged authors of inheritance hierarchies to explicate their hierarchies by displaying the path-based inference rules that govern inheritance in them.</Paragraph>
    <Paragraph position="1"> We also presented a syntax for path-based inference rules which can be summarized as follows: I. A a~ is either an arc-relation or a path as described in part 2 enclosed in parentheses. Parentheses may be omitted whenever an ambiguity does not result.</Paragraph>
    <Paragraph position="2">  2. If P and Q are paths and z, ~, and z are nodes, paths may be formed as follows: a. Converse: if P is a path from x to y, ~ is a path from y to z.</Paragraph>
    <Paragraph position="3"> b. Composition: if P is a path from z to z and Q is a path from z to ~, P/Q is a path from z to y.</Paragraph>
    <Paragraph position="4"> c. qomposition .zero or more times: IX P composed with itself zeroor  more times describes a path from z to y, P* is a path from z to y.</Paragraph>
    <Paragraph position="5"> d. Composition one or more times: If P composed with itself one or more times is a path from z to y, P+ is a path from z to y.</Paragraph>
    <Paragraph position="6"> e. Union: If P is a path from z to y or Q is a path from z to ~, pvQ is a path from z to y.</Paragraph>
    <Paragraph position="7"> f. Intersection: If P is a path from z to ~ and ~ is a path from x to y, P&amp;Q is a path from x to y.</Paragraph>
    <Paragraph position="8"> g. Cgmplement: If there is no path P from z to ~, ~ is a path from x to Y.</Paragraph>
    <Paragraph position="9"> h. Irreflexive restriction: If P is a path from z to y and z#y, pR is a path from z to y.</Paragraph>
    <Paragraph position="10"> i. Exception: If P is a path from z to ~ and there is no path Q of length equal to or less than the length of P, P\Q is a path from z tO y.</Paragraph>
    <Paragraph position="11"> j. Domain restriction: If P is a  path from z to y and Q is a path from z to z, (Q z)P is a path from xtoy.</Paragraph>
    <Paragraph position="12"> k. Range restriction: If P is a path from z to y and Q is a path from y to z* P(Q z) is a path from x to y.</Paragraph>
    <Paragraph position="13"> 3. A path-based inference rule is of the form &lt;defined path&gt; / &lt;defining path&gt; where &lt;defining path&gt; is any path described by parts I or 2 above* and &lt;defined path&gt; is either a) a single arc-relation, or b) a composition of n arc relations for some fixed n, i.e. using only &amp;quot;/&amp;quot;, not &amp;quot;$&amp;quot; or &amp;quot;+&amp;quot;. The rule is interpreted to mean that if the &lt;defining path&gt; goes from some node x to some node y then: a) the arc that is the &lt;defined path&gt; is inferred to exist from z to y; b) the n arcs that are the &lt;defined path&gt; and n-1 new intermediate nodes are inferred to exist from z to y.</Paragraph>
  </Section>
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