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 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. Keywords: Approximate Reasoning, Qualitative Reasoning, Temporal Relations, Granularity, Ontology 1. Introduction Formal systems that support reasoning about calendar units and clock units are called temporal granularities [3]. Such systems have been the subject of intensive research in recent years, e.g., [2,27,12]. These systems provide foundations for task and process management [19,13,18], for work on database systems [20], on (geographic) information systems [23], and they are relevant also in many other domains. Essentially, temporal granularities describe ways of partitioning the time-line and methods for reasoning about cells within the partitions which result. Examples of partitions are: the partition of the time-line into fifteen minute slots produced by your favorite calendar application, or the partition of the time-line created by the succession of update operations of some data-base system. Partitions of the time-line can be rough. Consider, for example, the partition with cells labeled `before World War 2', `during World War 2', 2 T. Bittner / Approximate Qualitative Temporal Reasoning `after World War 2'. (In what follows I use the terms calendar-par...

We define a family of qualitative spatio-temporal relations such as sameplace -same-time and same-path-different-time, which describe the relative location of spatio-temporal objects within places or along paths. The relations in question are approximate, and this means that some of them are context-dependent. We explore the relationships between context, judgments that are made in certain contexts, and the spatio-temporal relations that do occur in those judgments. Understanding these relationships is important for understanding human judgments about spatio-temporal configurations as well as for the interaction of humans with spatio-temporal databases.

Existing spatiotemporal data models and query languages offer only basic support to query changes of data. In particular, although these systems often allow the formulation of queries that ask for changes at particular time points, they fall short of expressing queries for sequences of such changes. In this chapter we propose the concept of spatiotemporal patterns as a systematic and scalable concept to query developments of objects and their relationships. Based on our previous work on spatiotemporal predicates, we outline the design of spatiotemporal patterns as a query mechanism to characterize complex object behaviors in space and time. We will not present a fully-fledged design. Instead, we will focus on deriving constraints that will allow spatiotemporal patterns to become well-designed composable abstractions that can be smoothly integrated into spatiotemporal query languages. Spatiotemporal patterns can be applied in many different areas of science, for example, in geosciences, geophysics, meteorology, ecology, and environmental studies. Since users in these areas typically do not have extended formal computer training, it is often difficult for them to use advanced query languages. A visual notation for spatiotemporal patterns can help solving this problem. In particular, since spatial objects and their relationships have a natural graphical representation, a visual notation can express relationships in many cases implicitly where textual notations require the explicit application of operations and predicates. Based on our work on the visualization of spatiotemporal predicates, we will sketch the design of a visual language to formulate spatiotemporal patterns.