Modeling Spatio-Temporal Topological Relationships

Time and space are main parts of any phenomena in the real world. In spatial Information Systems (GIS) modeling processes are the first step in analyzing phenomena. Therefore including temporal aspects as well as spatial capabilities in GIS is necessary. One of the most important requirements in spatio-temporal modeling of phenomena in GIS is the ability to investigate their spatial and temporal topological relationships. In this paper we first explain different aspects of time as well as space and then propose a novel approach to extract a full list of temporal and also spatio-temporal topological relationships. Time as a distinct part of any phenomena can be considered to be zero or one dimensional. A zero dimensional temporal space is referred to a phenomena with start and end time occurrence in one chronon which is named event. A one dimensional temporal space is referred to a phenomena with a duration of existence and is named state. Accordingly, different spatial dimensions are point, line, area and volume. The proposed approach in this paper extracts all the possible relationships between different temporal aspects. The approach is based on a Boolean comparison matrix with two rows and four columns. Each cell of the matrix is a comparison between start and end of one temporal phenomena and start and end of the other which results true or false. This matrix leads to 28=256 relations which all of them are not logically acceptable. Therefore we explain how to find unacceptable relations. Removing these relations we find 13 relations between two temporal states, 6 relations between a temporal state and a temporal event and finally 3 relations between two temporal events. Furthermore, in order to conflate spatial and temporal topological relationships two strategies are proposed. In the first one, we used logical AND and OR operators and in the second strategy we consider the time to be an orthogonal dimension added to 2D spatial space. Each of these strategies leads to a comprehensive list of spatio-temporal relationships. Finally in order to illustrate the applicability of the extracted relationships, we implement them in a land information management system. The system is used to response spatial, temporal and spatio-temporal queries regarding historical situation of any parcels. As an example for spatial topological queries, the system is able to find parcels which are overlap with newly designed green space. Similarly the system can for example find land parcels which their duration of existence has same start point in time. This is a "start" temporal topological relationships. Regarding spatio-temporal relationship, the system can for example find land parcels which are coincide with a land parcel and are also neighbor to it.