Approximate qualitative temporal reasoning

We partition the time-line in different ways, for example, into minutes, hours, days, etc. When reasoning about relations between events and processes we often reason about their location within such partitions. For example, x happened yesterday and y happened today, consequently x and y are disjoint. Reasoning about these temporal granularities so far has focussed on temporal units (relations between minute, hour slots). I shall argue in this paper that in our representations and reasoning procedures we need into account that events and processes often lie skew to the cells of our partitions. For example, 'happened yesterday' does not mean that x started at 12 a.m. and ended 0 p.m. This has the consequence that our descriptions of temporal location of events and processes are often approximate and rough in nature rather than exact and crisp. In this paper I describe representation and reasoning methods that take the approximate character of our descriptions and the resulting limits (granularity) of our knowledge explicitly into account.