Is point-based semantics always adequate for temporal databases?

The analysis of the semantics of temporal data and queries plays a central role in the area of temporal relational databases. Although many different models and algebra have been proposed, almost all of them are based on a point-based (snapshot) semantics of the association of time to tuples/attributes. On the other hand, in the areas of linguistics, philosophy, and recently, artificial intelligence, a very debated issue concerns the use of an interval-based vs. a point-based semantics. We consider a slight adaptation of TSQL2's "consensus" algebra and model, discuss its semantics, and show some critical aspects arisen by the adoption of a point-based semantics.