In this paper, we present an online (incremental) algorithm for checking the satisfiability of qualitative spatio-temporal data, with direct implications to other fundamental knowledge representation and reasoning problems for such data, like the problems of deductive closure and redundancy removal. In particular, qualitative data come in the form of human-like, symbolic, descriptions such as "region x contains or overlaps region y", which are abundant in the Web of Data. Our approach is also able to maintain, to some extent, any sparse graph structure that may be inherent in the data, i.e., it acts parsimoniously and only tries to infer new information when needed for soundness and completeness. To this end, we complement our practical alg...