Separability, expressiveness, and decidability in the ambient logic

The Ambient Logic (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the descriptive and discriminating power of AL, focusing on the equivalence on processes induced by the logic (=(L)). We consider MA, and two Turing complete subsets of it, MA(IF) and MA(IF)(syn), respectively defined by imposing a semantic and a syntactic constraint on process prefixes. The main contributions include: coinductive and inductive operational characterisations of =(L); an axiomatisation IF; the construction of characteristic formulas for the processes in MAIF with respect to =L; the decidability of =(L) on MA(IF) and on MA(IF)(syn) and its undecidability on MA.