However, all of the other systems perform temporal reference resolution as part of their overall processing, in service of solving another problem such as speech act resolution. None of them lays out a detailed approach or model for temporal reference resolution, and none gives results of system performance on any temporal interpretation tasks.
Kamp and Reyle  address representational and processing issues in the interpretation of temporal expressions. However, they do not implement their ideas or present the results of a working system. They do not attempt coverage of a data set, or present a comprehensive set of relations, as we do, but consider only specific cases that are interesting for their Discourse Representation Theory. In addition, they do not address the issues of discourse structure and attentional state focused on here. For example, they recognize that references such as ``on Sunday'' may have to be understood with respect to a frame of reference. But they do not address how the frame of reference is chosen in context, so do not address the question of what type of focus model is required.
Note that temporal reference resolution is a different problem from tense and aspect interpretation in discourse (as addressed in, for example, [41,36,15,19,17]). These tasks are briefly reviewed here to clarify the differences. Temporal reference resolution is determining what time is being explicitly specified by noun phrases that are temporal referring expressions (e.g., ``Monday'' resolved to Monday 19 August). Tense and aspect interpretation involves determining implicit information about the states and events specified by verb phrases (e.g., that the kissing event specified in ``He had kissed her'' happened before some reference time in the past). While it could aid in performing temporal reference resolution, we are not addressing tense and aspect interpretation itself.
Scheduling dialogs, or scheduling subdialogs of other kinds of dialogs, predominantly employ the present and future tenses, due to the nature of the task. As discussed further below in Section 8.1, a primary way that tracking the tense and aspect would aid in temporal reference resolution would be to recognize discourse segments that depart from the scheduling dialog or subdialog. In addition, Kamp and Reyle  address some cases in which tense and aspect, temporal nouns, and temporal adverbs interact to affect the temporal interpretation. We intend to pursue these ideas in future work.