In this paper we tackle the problem of extending the logic of nested graph conditions with paths. This means, for instance, that we may state properties about the existence of paths between some given nodes. As a main contribution, a sound and complete tableau method is defined for reasoning about this kind of properties.
Navarro, M., Orejas, F., Pino, E., Lambers, L. A logic of graph conditions extended with paths. A: International Workshop on Graph Computation Models. "GCM 2016: Electronic pre-proceedings". Vienna: 2016, p. 1-15.