Fuzzy times on space-time volumes

This paper is a study on the formal representation of the temporal extent of periods, as defined in CIDOC CRM. Our proposal exploits positive and negative evidence, gained by observations, to approximate the definite and indefinite bounds of a period, stating whether it is considered as active or possibly active. We contribute to the modeling of imprecise temporal information by proposing a generalized definition of time intervals which allows the representation of fuzziness that characterizes archaeological findings and historical data. Moreover, we provide an alternative to Allen's operators, based on fuzzy time intervals. Finally, we extend our fuzzy interval model to represent four-dimensional volumes, which are associated with the spatiotemporal nature of periods; we also provide a spatiotemporal version of the basic temporal relations to approximate the temporal topology of periods. Our study has a crucial impact to fields associated with reality modeling, especially observation-based sciences.