Spatial Logics for Semistructured Resources

Spatial Logics have been recently proposed as modal logics inspecting the ‘spatial’ nature of models (as opposed to ‘temporal logics’ inspecting model behavior). Spatial Logics, essentially, lift constructors (and structural properties) of underlying models to the logical level, obtaining new ‘spatial’ logical connectives. The semantics of spatial logics is model dependant: different properties in the model turn into different spatial connectives. The main aim of this thesis is an in-depth understanding of Spatial Logics, in particular about the notion of separation and abstraction in different models and their influence in the decidability of the logic. The new meta-model of bigraphs (proposed by Milner recently) is more general and more extensible than the models studied for spatial logics so far. We propose a general meta-logical framework, BiLog, inspired by the bigraphical structure. BiLog is contextual and parametric wrt structure and congruence of the model. This framework is interesting for spatial logics comparison and is very promising being a primary step for a truly general logic for distributed calculi with semistructured resources. We instantiate BiLog to describe bigraphs and their components and we show that the resulting logics naturally embed Spatial Logics previously proposed in literature. We also study how the introduction of name abstraction in the model and of quantifiers in the logic influences the decidability problem in Spatial Logics. Finally, we hint how Spatial Logics can be applied to model, describe and reason about a particular kind of semistructured resource: Web data.