Abstract Conventional database systems function as static data repositories, storing vast amounts of facts and offering efficient query processing capabilities. The sheer volume of data these systems store has a direct impact on their scalability, both in terms of storage space and query processing time. Deductive database systems, on the other hand, require far less storage space since they derive new knowledge by applying inference rules. The challenge is how to efficiently obtain the required derivations, compared to having them in explicit form. In this study, we concentrate on a set of predefined inference rules for subsumption and disjointness relations, including their negations. We use compact data structures to store the facts and provide algorithms to support each type of relation, minimizing even further the storage space requirements. Our experimental findings demonstrate the feasibility of this approach, which not only saves space but is often faster than a baseline that uses well‐known graph traversal algorithms implemented on top of a traditional adjacency list representation to derive the relations.

The topological model for spatial objects identifies common boundaries between regions, explicitly storing adjacency relations, which not only improves the efficiency of topologyrelated queries, but also provides advantages such as avoiding data duplication and facilitating data consistency. Recently, a compact representation of the topological model based on planar graph embeddings was proposed. In this article, we provide an elegant generalization of such a representation to support hierarchies of vector objects, which better fits the multi-granular nature of spatial data, such as the political and administrative partition of a country. This representation adds a small space on top of the succinct base representation of each granularity, while efficiently answering new topology-related queries between objects not necessarily at the same level of granularity.