The \it{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 discriminating power of AL, focusing on the equivalence on
processes induced by the logic (=L>). As underlying calculi besides MA we
consider a subcalculus in which an image-finiteness condition holds and that we
prove to be Turing complete. Synchronous variants of these calculi are studied
as well. In these calculi, we provide two operational characterisations of
=L: a coinductive one (as a form of bisimilarity) and an inductive one
(based on structual properties of processes). After showing =L to be stricly
finer than barbed congruence, we establish axiomatisations of =L on the
subcalculus of MA (both the asynchronous and the synchronous version), enabling
us to relate =L to structural congruence. We also present some
(un)decidability results that are related to the above separation properties
for AL: the undecidability of =L on MA and its decidability on the
subcalculus.Comment: logical methods in computer science, 44 page