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<Paper uid="E93-1033">
  <Title>Abductive Explanation of Dialogue Misunderstandings</Title>
  <Section position="3" start_page="277" end_page="277" type="intro">
    <SectionTitle>
2 The abductive framework
</SectionTitle>
    <Paragraph position="0"> We have chosen to develop the proposed account of dialogue using the Prioritized Theorist framework \[Poole el ai., 1987; Brewka, 1989; van Arragon, 1990\]. Theorist typifies what is known as a &amp;quot;proof-based approach&amp;quot; to abduction because it relies on a theorem prover to collect the assumptions that would be needed to prove a given set of observations and to verify their consistency. This framework was selected because of its first-order syntax and its support for both default and abductive reasoning. Within Theorist, we represent linguistic knowledge and the discourse context, and also model how speakers reason about their actions and misunderstandings.</Paragraph>
    <Paragraph position="1"> We have used Poole's implementation of Theorist, extended to incorporate preferences among defaults as suggested by Van Arragon \[1990\]. Poole's Theorist implements a full first-order clausal theorem prover in Prolog. It extends Prolog with a true negation symbol and the contrapositive forms of each clause. Thus, a Theorist clause a D/3 is interpreted as {/3 *-- a,-~a 4-- -~/3}. A Prioritized Theorist reasoner can also assume any default d that the programmer has designated as a potential hypothesis, unless it can prove -~d from some fact or overriding hypothesis.</Paragraph>
    <Paragraph position="2"> The reasoning algorithm uses model elimination \[Loveland, 1978; Stickel, 1989; Umrigar and Pitchumani, 1985\] as its proof strategy. Like Prolog, it is a resolution-based procedure that chains backward from goals to subgoals, using rules of the form goal 4-- subgoall A... A subgoaln, to reduce the goals to their subgoals. However, unlike Prolog, it records each subgoal that occurs in the proof tree leading to the current one and checks this list before searching the knowledge base for a relevant clause; this permits it to reason by cases.</Paragraph>
  </Section>
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