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<Paper uid="W06-1307">
  <Title>DRT Representation of Degrees of Belief</Title>
  <Section position="4" start_page="46" end_page="47" type="metho">
    <SectionTitle>
2 Problems Facing Modelling Beliefs in
DRT
</SectionTitle>
    <Paragraph position="0"> According to Heydrich et al. (1998), paradigms of dynamic semantics (DRT, Situation Semantics and Dynamic Predicate Logic) face three obstacles in modelling dialogue. First, there is the problem of adapting the paradigm, originally made to model monological discourse, to the description of dialogue with different agents. The second problem is the description of mental states and the beliefs of the agents. The third problem is in explaining how the mental states are related to overt linguistic behaviour.</Paragraph>
    <Paragraph position="1"> With respect to the first problem, DRT has gradually attempted to address problems of belief representation in dialogue. For example, in Prolegomena, Kamp introduces a simple model of verbal communication (Kamp 1990: 71), which consists of two agents, A and B, and their mental states K(A) and K(B). Later work by Kamp et al. (2005) introduces agent modelling for single-sentence discourse, namely the hearer. The treatment presented in this paper allows the representation of dialogue with different agents, thus, addressing the first problem identified by Heydrich et al. (1998).</Paragraph>
    <Paragraph position="2"> With regard to the second problem, however, DRT has been primarily concerned with representing utterances containing propositional attitudes such as 'believe', rather than the beliefs and meta-beliefs of agents. Segmented-DRT (SDRT) has mainly focused on belief update and revision (Asher and Lascarides 2003). The treatment in this paper takes previous work on beliefs in dynamic semantics as a starting point and extends it to reach a richer representation of the interaction between mental states and the linguistic content of utterances. For example, both speaker and hearer mental states are represented and the beliefs and  meta-beliefs of agents are reviewed after each utterance. null As a semantic theory, DRT tells us which discourse referents are needed in context. However, DRT does not deal with planning, nor with pragmatic aspects of contexts rendered through relating the current utterance to agents' intentions. Kamp et al.'s (2005) expansion of the original, also known as 'vanilla', DRT (Poesio and Traum 1997a), deal minimally with intentions. To deal with the third problem mentioned by Heydrich et al., Al-Raheb (2005) has already outlined a pragmatic extension to DRT that makes it appropriate for linking the current utterance and agents' intentions. null The present paper aims to show how that link can be strengthened through modelling agents' intentions and relating them to the dialogue acts communicated via utterances. In relation to this link, the significance of degrees of belief is explained in the following section.</Paragraph>
  </Section>
  <Section position="5" start_page="47" end_page="48" type="metho">
    <SectionTitle>
3 Degrees of Belief
</SectionTitle>
    <Paragraph position="0"> To our knowledge, there is no account in DRT that accommodates strengths or degrees of belief of agents in dialogue. This section addresses this gap and proposes initially two strengths of belief involved in dialogue to be expanded in future research to include further degrees of belief. Modal expressions, including words such as 'possibly' and 'might', are evidence that there exist more degrees of belief than the ones discussed in this paper. null The beliefs of an agent are 'her model of how things are' (Traum 1994: 15). The notion of belief (or strong belief) is to be understood in relation to the agent: it is what the agent takes to be true. There is an important philosophical background to the discussion of 'belief' and 'knowledge'. It is outside the scope of this paper to review all the literature here. Quine (1960), Hintikka (1962), Lewis (1969, 1979), and Davidson (1983) are representative. The term 'belief' is understood in this paper to refer to propositions strongly held by the agent to be true and when making utterances relating to them, the speaker not only commits herself to their truth but also communicates to the hearer that she, the speaker, believes those proposition to be true.</Paragraph>
    <Paragraph position="1"> Another degree of belief called acceptance is accounted for in this model. Acceptance consists of the agent's weakly believed propositions. The agent may be going along with what the speaker is saying or has acquired a new proposition based on the speaker's utterance which has not yet been confirmed into a stronger belief.</Paragraph>
    <Paragraph position="2"> To illustrate what is meant by the distinction be- null tween belief and acceptance, let us look at: (4) S1: I need to buy new shoes for Mary's  party.</Paragraph>
    <Paragraph position="3"> H1: Try Next on Henry Street.</Paragraph>
    <Paragraph position="4"> The speaker tells the hearer that she has to buy new shoes for Mary's party. In this example, the hearer already (strongly) believes there is a party and he suggests a place where the speaker can buy them. Figure 1 demonstrates the hearer's mental state after hearing the speaker's utterance, S1. The hearer's mental state is represented by a Discourse Representation Structure (DRS), which contains three sub-DRSs, one for intention (referred to by 'attitude(you, 'INT', drs6)' and the label for the intention DRS, drs6), another for the belief DRS containing strong beliefs (referred to by 'attitude(i, 'BEL', drs4)' and the the label for the belief DRS, drs4), and finally the acceptance DRS containing weak beliefs (referred to by 'attitude(i, 'AC-CEPT', drs2)' and the the label for the acceptance  DRS, drs2).3 If we change example (4) so that the hearer does not actually hold the belief that there is a party, as in: (5) S1: I need to buy new shoes for Mary's party.</Paragraph>
    <Paragraph position="5"> H1: I didn't realize Mary is throwing a party.</Paragraph>
    <Paragraph position="6"> S2: Yeah she is. It's next Tuesday.</Paragraph>
    <Paragraph position="7"> H2: You can probably buy them at Next.</Paragraph>
    <Paragraph position="8"> The hearer does not necessarily need to strongly believe that Mary is throwing a party. He can 'go along with' or accept it and even suggest a place where the speaker can buy the shoes. The existence of a party does not affect the hearer personally or directly, i.e. he does not need to act on it. However, let us now consider the effect if we change the example again so that the hearer does not know about Mary's party, nor that he is required to buy new shoes, as in:  (6) S1: You need to buy new shoes for Mary's party.</Paragraph>
    <Paragraph position="9">  H1: I didn't realize Mary is throwing a party.</Paragraph>
    <Paragraph position="10"> S2: Yeah she is. You should try Next on Henry Street.</Paragraph>
    <Paragraph position="11"> H2: I will.</Paragraph>
    <Paragraph position="12"> This time, for the hearer to commit to buying something for a party (in H2) that he did not even know existed suggests a stronger degree of belief than that of 'going along with' the speaker having to buy it. The existence of the party affects the hearer personally and directly. Therefore, agreeing to buy new shoes justifies the inference that he believes rather than just accepts there is a party. This is what the paper describes as belief, or a strong degree of belief. Contrast Figure 1 with the figure representing the speaker's mental state after hearing H2 in example 6, Figure 2.</Paragraph>
  </Section>
  <Section position="6" start_page="48" end_page="49" type="metho">
    <SectionTitle>
4 Beliefs and Mutual Beliefs
</SectionTitle>
    <Paragraph position="0"> The treatment of beliefs that we are developing here requires an explicit account of how the be- null 'Mutual belief', also referred to as 'mutual knowledge', is the term used by Traum (1994) among others, where a group of individuals may believe X, where X may or may not be true. Stalnaker's (2002) 'common belief' is comparable to what others call mutual belief. For X to be a mutual belief, it has to be accessible to a group; all believe X and all believe that all believe X, and all believe that all believe that all believe X.</Paragraph>
    <Paragraph position="1"> In face-to-face communication, the hearer believes that the speaker believes what she, the speaker, is communicating. On the other hand, unless the hearer indicates doubt or objects to what the speaker is saying, the speaker assumes that the hearer believes what the speaker has said - which is consistent with expectations under Gricean cooperativeness assumptions (1989). The speaker also assumes that the hearer now has the belief that the speaker believes what she just said. This assumption is what leads to 'mutual' beliefs (Kamp 1990: 79).</Paragraph>
    <Paragraph position="2"> However, mutual belief can be viewed as the process of establishing that the speaker and the hearer hold the same belief. One way in which this process may occur is when the speaker holds a belief and communicates that belief to the hearer.  This belief may then be adopted by the hearer who can provide feedback to the speaker that the information communicated has now acquired the status of belief in an ideal situation with a cooperative hearer. When both participants reach the conclusion that S bel(ieves) X, H bel X, H bel S bel X, and S bel H bel X, then mutual belief is established. The speaker in example (7) believes her neighbour is a weirdo. Whether the utterance is informative (new) or not depends on the context.</Paragraph>
    <Paragraph position="3"> In this example, (7), the speaker may not already have the belief that the hearer believes her neigh- null bour is a weirdo.</Paragraph>
    <Paragraph position="4"> (7) Speaker: My neighbour is such a  weirdo.</Paragraph>
    <Paragraph position="5"> Hearer: Yeah, he is. I saw him peeping through your window the other day.</Paragraph>
    <Paragraph position="6"> However, after the hearer makes his utterance, the speaker can now strongly believe that the hearer believes her neighbour is a weirdo, that he believes she believes her neighbour is a weirdo, and now she believes he believes her neighbour is a weirdo. Figure 3 shows the level of nesting to accommodate the mutual belief that the speaker's neighbour is a weirdo. It is possible when this level of nesting is reached to have a separate DRS or space for mutual beliefs, called 'mutual belief DRS'. In which case, the propositions held in drs6, can now be removed from drs6 and added to the 'mutual belief DRS'. Figure 3 represents the speaker's mental state after the hearer makes his utterance. For the purposes of this example, the DRT represented in Figure 3 will mainly focus on the speaker's belief DRT.</Paragraph>
    <Paragraph position="7"> Achieving mutual belief is immensely helped by dialogue acts. For example, when a hearer provides strong feedback about a new proposition (cf. drs7 in Figure 3), the speaker can come to believe the hearer believes that proposition. Section 5 shows the importance of considering the dialogue acts expressed by an assertion (new information) and their relationship to degrees of belief and strengthening of beliefs.</Paragraph>
  </Section>
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