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<Paper uid="W06-1307">
  <Title>DRT Representation of Degrees of Belief</Title>
  <Section position="3" start_page="0" end_page="46" type="intro">
    <SectionTitle>
1 Introduction
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    <Paragraph position="0"> Heydrich et al. remark that 'serious description of natural dialogue seems to necessitate that we consider the mental states of the speakers involved' (1998).2 This is a step that is by no means easy. It is the aim of this paper to integrate previous work on beliefs in DRT and dialogue theory in order to model the mental states of agents in dialogue.</Paragraph>
    <Paragraph position="1"> The connection between beliefs, intentions and speech or dialogue acts has been noted in the literature. Stalnaker notes, for instance, that [i]f we understand contexts, and the speech acts made in contexts, in terms of the speaker's beliefs and intentions, we have a better chance of giving simpler and more transparent explanations of linguistic behaviour (Stalnaker 2002: 720).</Paragraph>
    <Paragraph position="2"> The kind of agent beliefs we are concerned with here arises in dialogue interaction. The nature of  clude 'information state', 'conversational score', and 'discourse context' (Larsson and Traum 2000).</Paragraph>
    <Paragraph position="3"> interaction dictates that the strength or degree of belief varies depending on contextual factors. This can be seen from the following example:  (1) A: I want to make a booking for my wife.</Paragraph>
    <Paragraph position="4"> B: Yeah.</Paragraph>
    <Paragraph position="5">  A: What time is the Thailand flight on Monday? B: It's at 2 pm.</Paragraph>
    <Paragraph position="6"> In example (1) B does not necessarily need to believe the presupposition (given information) that A has a wife. For the purposes of the conversation, which is providing A with information, B can simply 'go along with' the presupposition and not have it as a member of his beliefs (i.e. his belief set) (Stalnaker 2002). Similarly, let us consider the following example, (2). The speaker is a customer in a clothing shop.</Paragraph>
    <Paragraph position="7">  (2) S1: I want to buy a dress for my wife. H1: Is it for a formal occasion? S2: Yes.</Paragraph>
    <Paragraph position="8"> H2: What is her favourite colour? S3: She doesn't like red anymore.</Paragraph>
    <Paragraph position="9"> H3: Does your wife like black? S4: Yes  As the speaker, S, introduces the presupposition that he has a wife, the hearer, H, can come to the conclusion that S believes S has a wife. However, when the hearer comes to refer to S's wife, H does not necessarily have to believe S has a wife. H can simply go along with the information that the speaker has a wife and use this form of acceptance in H2 without committing to 'strongly believing' it. Indeed, the speaker may be buying a dress for his mistress rather than his wife. By going along  with it, the hearer does not have to commit himself to believing that the speaker has a wife. What is more at stake than believing that the speaker indeed has a wife and not a mistress is closing the sale. Contrast examples (1) and (2) with example  (3): (3) S1: You have to get Peter's son a Christening present.</Paragraph>
    <Paragraph position="10"> H1: Peter has a son? S2: Sorry I forgot to mention that before. null H2: Ok, what sort of present should I get him? S3: A toy would be nice.</Paragraph>
    <Paragraph position="11">  In this context, the hearer, H, is required to commit more strongly to the presupposition of Peter having a son than simply going along with it, since H is being asked to buy a Christening present. The fact that H2 agrees to buying a present for Peter's son reflects more commitment to the presupposition than B shows in example (1). Considerations of this kind lead to the conclusion that different contexts call for varying strengths of beliefs and belief representation. We shall not attempt to describe all the contextual factors that can cause strength of belief to vary. The point is, rather, that we clearly need to model strength of belief and no current model of DRT incorporates such a proposal. This paper, thus, makes an original proposal for including a system for graded beliefs in the belief spaces (or sets) of both the speaker and the hearer.</Paragraph>
    <Paragraph position="12"> Bearing this in mind, there is a need in DRT for representing the differing beliefs of agents in dialogue and their beliefs (meta-beliefs) about other agents' beliefs or mental state. By focussing on the intentions of speakers and hearers and inferring agents' intentions in making an utterance, the approach presented in this paper aims at fulfilling this need. It follows that, to have a 'full' theory of beliefs and to have an insight into the mental states of agents in dialogue (the speaker and the hearer), it is necessary to have a representation of agents' beliefs, degrees of beliefs, and the dialogue acts expressed by their utterances (Asher 1986). This is also in order to strengthen the link between utterances and agents' intentions in dialogue. The dialogue act or function performed by the utterance tells us something about the speaker's beliefs. Furthermore, what is also needed is a representation of beliefs that are shared between, or are common to, the two agents.</Paragraph>
    <Paragraph position="13"> The question is: how can DRT best model beliefs? The following section, 2, outlines the problems facing modelling beliefs in DRT. Section 3 presents a graded view of agents' beliefs in dialogue as a solution to these problems. This is followed by a description of the relationship between belief and mutual belief, section 4, and then of the relationship between belief and dialogue acts, section 5.</Paragraph>
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