An important feature of our approach is that the system is forced to choose among possibilities only if the resulting interpretations would be inconsistent. If the results for two possibilities are consistent, the system merges the results together.
At a high level, the algorithm operates as follows. There is a set of rules for each of the relations presented in Section 4.2. The rules include constraints involving the current utterance and another Temporal Unit. In the anaphoric cases, the other Temporal Unit is a potential antecedent from the focus list. In the deictic cases, it is the dialog date or a later time. For the current temporal expression to be resolved, each rule is applied. For the anaphoric rules, the antecedent considered is the most recent one satisfying the constraints. All consistent maximal mergings of the results are formed, and the one with the highest score is the chosen interpretation.