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<Paper uid="T78-1031">
  <Title>PATH-BASED AND NODE-BASED INFERENCE IN SEMANTIC NETWORKS</Title>
  <Section position="3" start_page="0" end_page="219" type="intro">
    <SectionTitle>
2. Path-Based Inference
</SectionTitle>
    <Paragraph position="0"> Let us refer to a relation (perforce binary) that is represented by an arc in a network as an arc-relation. If R is an arc-relation, an arc la~elled R from node a to node b represents that the relationship aRb holds. It may be that this arc is not present in the network, but aRb may be inferred from other information present in the network and one or more inference rules. If the other information in the network is a specified path of arcs from a to b, we will refer to the inference as path-based. The ways in which such paths may be specified will be developed as this paper proceeds.</Paragraph>
    <Paragraph position="1"> The two clearest examples of the general use of path-based inference are in SAMENLAQ II \[18\] and Protosynthex III \[13\]. Both these systems use what might be called &amp;quot;relational&amp;quot; networks rather than =semantic = networks since arc-relations include conceptual relations as well as structural relations (see \[14\] for a discussion of the difference). For example, in Protosynthex III there is an arc labelled COMMANDED from the node representing Napoleon to the node representing the French army, and in SAMENLAQ II an arc labelled EAST.OF goes from the node for Albany to the node for Buffalo. Both systems use relational calculus expressions to form path-based inference rules. The following relational operators are employed (we here use a variant of the earlier notations): I. Relational Converse -- If R is a relation, R C is its converse.</Paragraph>
    <Paragraph position="2">  SO, ~x,~(xRC~ &lt;--&gt; ~Rz).</Paragraph>
    <Paragraph position="3"> 2. Relational Composition -- If R a--n-d~ a-~ relations; R/S is R composed with S. So, Vz,y(zR/Sy &lt;--&gt; ~n(zRn ~ ~SY=)).</Paragraph>
    <Paragraph position="4"> 3. Domain Restriction -- If R and S (S z)R is the relation R with its domain restricted to those objects that bear the relation S to 8. So, Vz,~,n(z(S z)R~ &lt;--&gt; (zSn &amp; zR~)).</Paragraph>
    <Paragraph position="5"> 4. Range Restriction -- If R and S  are relations, R(S ~) is the relation R with its range restrictto those objects that bear the  relation S to ~. So, V=,y,z(zR(S ~)y &lt;--&gt; (zRy 6 ySz)).</Paragraph>
    <Paragraph position="6"> 5. Relational Intersection -- If R and S are relations, R&amp;S is the intersection of R and S. So, %Zz,y(xR&amp;Sy &lt;--&gt; (zRy &amp; zSy)).</Paragraph>
    <Paragraph position="7"> Notice that VQ,R,S,z,y,~(zR(Q ~)/Sy &lt;--&gt; C/R/(Q z)Sy) so we can use the notation R(Q z)S unambiguously.</Paragraph>
    <Paragraph position="8">  In SAMENLAQ II, path-based inference rules are entered by using the relational operators to give alternate definitions of simple arc labels. For example (again in a variant notation):</Paragraph>
    <Paragraph position="10"> declares that a father is a male parent.</Paragraph>
    <Paragraph position="11"> SIR \[11\] is another relational network system that uses path-based inference. Although the original expressed inference rules in the form of general LISP functions, the reproduction in \[16, Chap. 7\] uses the notion of path grammars. The relation operators listed above are augmented with R*, meaning zero or more occurrences of R composed with itself, R +, meaning one or more occurrences of R composed with itself, and RvS, meaning the union of R and S. The following relations are used: z EQUIV y means x and y are the same individual  z SUBSET y means z is a subset of y = MEMBER y means z is a member of the set y POSSESS y means z owns a member of the set y POSSESS-BY-EACH y means every member  of the set z owns a member of the set ~.</Paragraph>
    <Paragraph position="12"> To determine if z POSSESS y, the network is searched using the following rule:</Paragraph>
    <Paragraph position="14"> The widest use of path-based inference is in \]SA hierarchies. Fig. I is based on probably the most famous \]SA hierarchy, that of Collins and Quillian \[2\]. The two important rules here are</Paragraph>
    <Paragraph position="16"> As McDermott \[8) points out, ISA hierarchies have been abused as well as used.</Paragraph>
    <Paragraph position="17"> In Section 8, we will propose a method authors can use to describe their hierchies precisely.</Paragraph>
  </Section>
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