A Spatial Logic for Simplicial Models

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the distribution determines a space that can be either physical logical. The former is defined terms relation among components. latter depends on logical relations, such as being part same group. this context, specification and verification spatial properties play fundamental role supporting design systems predicting behaviour. For reason, different tools techniques have been proposed specify verify space, mainly described graphs. Therefore, approaches generally use model relations describe form proximity pairs entities. Unfortunately, graph-based models do not permit considering more than two may arise when one interested describing aspects involving interactions groups work, we propose logic interpreted simplicial complexes. are topological objects, able represent surfaces volumes efficiently generalise graphs higher-order edges. We discuss how satisfaction formulas verified correct complete checking algorithm, which linear dimension complex formula. expressiveness studied variants classical bisimulation branching over