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Temporal Reference Resolution Rules

Figure 6 presents the main temporal resolution rules, one for each of the cases described in Sections 4.1 and 4.2. In the complete set of rules, given in Online Appendix 1, many are broken down into subcases involving, for example, the end times or starting times.

The rules apply to individual Temporal Units. They return a certainty factor, and either a more fully specified Temporal Unit or an empty structure indicating failure.

Many of the rules calculate temporal information with respect to a frame of reference, using a separate calendar utility. Following are functions and conventions used in Figure 6.

next(TimeValue, RF): returns the next timeValue that follows reference frame RF. For example, next(Monday, [$\ldots$Friday, 19th,$\ldots$]) = Monday, 22nd.

resolve_deictic(DT, RF): resolves the deictic term DT with respect to the reference frame RF.

merge(TU1, TU2): if Temporal Units TU1 and TU2 contain no conflicting fields, returns a Temporal Unit containing all of the information in the two units; otherwise returns $\{ \}$.

merge_upper(TU1, TU2): similar to the previous function, except that the only fields from TU1 that are included are those that are of the same or less specificity as the most specific field in TU2.

specificity(TU): returns the specificity of the most specific field in TU.

most_specific(TU): returns the most specific field in TU.

starting_fields(TU): returns a list of starting field names for those in TU having non-null values.

structure $\rightarrow$component: returns the named component of the structure.

conventions: Values are in bold face and variables are in italics. TU is the current Temporal Unit being resolved. TodaysDate is a representation of the dialog date. FocusList is the list of discourse entities from all previous utterances.

Figure 6: Main Temporal Resolution Rules
{\large\em Rules for deictic relations}
...$ , merge\_upper($TU_{fl}$ , $TU$ )$\rangle$\space \\

The algorithm does not cover some subcases of relations concerning the end times. For instance, rule D-frame-of-reference covers only the starting-time case of the frame of reference deictic relation. An example of an end-time case that is not handled is the utterance ``Let's meet until Thursday,'' under the meaning that they should meet from today through Thursday. This is an area for future work.

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