<?xml version="1.0" standalone="yes"?>
<Paper uid="W98-1410">
  <Title>Macroplanning with a Cognitive Architecture for the Adaptive Explanation of Proofs</Title>
  <Section position="2" start_page="0" end_page="88" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> A )erson who explains to another person a technical device or a logical line of reasoning adapts his explanations to the addressee's knowledge. A computer program designed to take over the explaining part should also adopt this principle.</Paragraph>
    <Paragraph position="1"> Assorted systems take into account the intended audience's knowledge in the generation of explanations (see e.g. \[Cawsey, 1990, Paris, 1991, Wahlster et al., 1993\]). Most of them adapt to the addressee by choosing between different discourse strategies: Since proofs areinherently rich in infer ences, their explanation must also consider which inferences the audience can make \[Hora~ek, 1997, Zukerman and McConachy, 1993\]. However, because of the constraints of the human memory, inferences are not chainable without costs. The explicit representation of the addressee's cognitive states proves to be useful in choosing the information to convey \[Walker and Rambow, 1994\].</Paragraph>
    <Paragraph position="2"> While a mathematician communicates a proof on a level of abstraction that is tailored to the audience, state-of-the-art proof presentation systems such as PROVERB \[Huang and Fiedler, 1997\] verbalize proofs in a nearly textbook'like style on a fixed degree of abstraction given by the initial representatio n of the proof. Nevertheless, PROVERB is not restricted to the presentation on a certain level of abstraction. Adaptation to the reader's knowledge may still take place by providing the appropriate level of abstraction in the initial representation of the proof.</Paragraph>
    <Paragraph position="3"> Drawing on results from cognitive science, we are Currently developing an interactive proof explanation system~ called P. rez (for proof explainer). In this paper, we propose an architecture for its dialog planner based on the theory of human cognition AcT-R \[Anderson, 1993\]. The latter explicitly represents the addressee's knowledge in a declarative memory and his cognitive</Paragraph>
    <Paragraph position="5"> skills in procedural production rules. This cognitive model enables the dialog planner to trace the addressee's cognitive states during the explanation. Hence, it can choose for each proof step as an appropriate explanation its most abstract justification known by the addressee.</Paragraph>
    <Paragraph position="6"> The architecture of P. rex, which is sketched in Section 3, is designed to allow for multimodal generation. The dialog planner is described in detail in Section 4. Since it is necessary to know some of the concepts in ACT-R to understand the macroplanning process, the cognitive architecture is *first introduced in the next section.</Paragraph>
  </Section>
class="xml-element"></Paper>