Rosé et al. [31, p. 31] describe dialogs composed of multiple threads as ``negotiation dialogues in which multiple propositions are negotiated in parallel.'' According to Rosé et al., dialogs with such multiple threads pose challenges to a stack-based discourse model on both the intentional and attentional levels. They posit a more complex representation of attentional state to meet these challenges, and improve their results on speech act resolution in a corpus of scheduling dialogs by using their model of attentional state.5
The case represented by row three in Figure 10, whose structure is depicted above in 13, is the instance in our data that is most closely related to the situations addressed by Rosé et al. This is a type of structure that Grosz and Sidner's model addresses, but it is not a multiple thread case, since TU2 is not needed to interpret a Temporal Unit mentioned after TU3.
Rosé et al.'s examples of dialogs containing multiple threads are shown in Figures 16 and 17, which are Rosé et al.'s Figures 1 and 2, respectively. Figure 16 is an extended example, and Figure 17 contains a simplified example which they analyze in greater detail.
The passage in Figure 16 would be processed by our algorithm as follows. The dialog date is not given in . For concreteness, let us suppose that the dialog date is Friday 11 April. Then, next week is Monday 14 April through Friday 18 April (the dialog does not mention weekend days, so we exclude them for ease of discussion). Utterance 2 is deictic, introducing next week into the discourse. Utterances 3-6 all have both deictic and anaphoric readings, all of which yield the correct results.
The deictic relation for all of them is the frame of reference deictic relation, under which the interpretations are forward references from the dialog date:
|3||Monday 14 April & Tuesday 15 April|
|4||Wednesday 16 April|
|5||Thursday 17 April|
|6||Friday 18 April|
The correct interpretations of (3)-(6) are also established with the co-reference anaphoric relation, with antecedent next week in utterance 2: they each can be interpreted as specifying a more specific time than next week, that is, as a particular day of next week.
Finally, the frame of reference anaphoric relation yields the correct result for ``Tuesday'' in (3)6 and for the times specified in utterances (4)-(6). The interpretation is the day calculated forward from the most recently mentioned Temporal Unit:
|3||Monday 14 April, Utterance 3||Tuesday 15 April|
|4||Tuesday 15 April, Utterance 3||Wednesday 16 April|
|5||Wednesday 16 April, Utterance 4||Thursday 17 April|
|6||Thursday 17 April, Utterance 5||Friday 18 April|
Utterances (7) and (10) are potential challenges for our algorithm, representing instances of the situation depicted in Figure 13: Thursday 24 April is a possible incorrect interpretation of ``Thursday'' in these utterances, yielded by the frame of reference anaphoric relation. The correct interpretation is also a candidate, yielded by multiple relations: the frame of reference deictic relation and the co-reference anaphoric relation, with Thursday 17 April in utterance (5) as antecedent. The relative magnitude of the certainty factors of the co-reference and frame of reference anaphoric relations means that the correct interpretation is likely to be chosen in practice, as mentioned in Section 8.1.1. If the incorrect interpretation were chosen for utterances (7) and (10), then incorrect interpretations of ``Friday'' in each of (8) and (11) would be possible: the Friday after the incorrect date of Thursday 24 April, yielded by the frame of reference anaphoric relation. However, the correct interpretations would be possible too, yielded by the frame of reference deictic relation and the co-reference anaphoric relation.
Utterances (12) through (16) have analogous interpretations, except that the deictic interpretations yield incorrect results (that is, due to utterance 12, ``How is the next week?'', the days are actually of the week Monday 21 April through Friday 25 April; the deictic interpretations are of the week Monday 14 April through Friday 18 April). Thus, there are one correct and two incorrect interpretations for some of the utterances, making it less likely in practice that the correct interpretation would be chosen. Note that, generally speaking, which focus model is used does not directly address the deictic/anaphoric ambiguity, so, for the purposes of this section, the two parts of the dialog pose the same challenge to the focus model.
The dialog in Figure 17 is analogous. However, ``The other day'' in (5) brings up other issues. There is a special case of the co-reference anaphoric relation for such expressions (i.e., ``the other'' ``day''``month''``year''; see Anaphoric Rule 7 in Online Appendix 1). In this case, the second most recent day, month, or year, as appropriate, is the candidate antecedent. Presumably, neither the most recently mentioned day nor a day mentioned before two or more others would be referred to as ``the other day''; thus, we anticipate that this is a good heuristic. Nevertheless, if (5) explicitly mentioned ``Wednesday,'' our algorithm would have a correct and an incorrect interpretation to choose between.
In summary, there were no instances of temporal multiple threads of the type addressed by Rosé et al., either in the CMU training data upon which the algorithm was developed, or in the NMSU training data to which the algorithm was later applied. If segments such as those illustrated in Rosé et al. were to appear, an incorrect interpretation by our algorithm would be possible, but, under our model, the correct antecedent would also be available. For the examples they present, the algorithm faces the same choice: establish a co-reference relation to a time before the last one (the correct interpretation), or establish a frame of reference relation with the immediately preceding time (an incorrect interpretation). If performing temporal reference resolution is the goal, and if one is faced with an application in which such temporal multiple threads do occur, our investigation of the problem suggests that this specific situation should be investigated before assuming that a more complex focus model is needed. Adding a new modify anaphoric relation could be investigated. Or, as implemented in our system, a specific preference could be defined for the co-reference relation over the frame of reference relation when both are possible in a local context. Statistical techniques could be used to establish preferences appropriate for the particular application.
The different findings between Rosé et al. and our work might be due to the fact that different problems are being addressed. Having no intentional state, our model does not distinguish between times being negotiated and other times. It is possible that another structure is relevant for the intentional level. Rosé et al. do not specify whether or not this is so. The different findings may also be due to differences in the data: their protocol is like a radio conversation in which a button must be pressed in order to transmit a message, and the other participant cannot transmit a message until the speaker releases the button. This results in less dynamic interaction and longer turns . In the dialogs used here, the participants have free control over turn-taking.