Abstract : Modelling and specifying distributed systems require an adaptation of logical model habitually used to represent those systems. Notions of location and resource is one of the key points for representing such systems.
We begin with a first proposition of logic, the Distributed and Concurrent Linear Logic (DMLL), which integrates notion of distribution and of mobility. We also propose a Kripke's semantic and a sequent calculus that supports cut-elimination.
This first study emphasize the central role of semantics in the modelling of distributed systems. We propose then a new structure, the resource trees, which are labelled trees containing resources from a partial monoid inside their nodes and a new logic, BI-Loc, to reason about these trees. We also propose a language to transform these trees and its correct and complete logical axiomatisation using Hoare's triples. Concerning BI-Loc, we determine sufficient condition to decide satisfaction and validity and we develop a correct and complete proof-search method using semantic labelled tableaux. This method is inspired of the one developed for BI.
Then we show some application of the partial tree model. Firstly, we show how the resource trees can be used to reason about the heap of pointers and a refinement of this model, the permission model. Then, we focus on semi-structured data, and show how we can represent and specify such data using resource trees.