  In Reasoning about Action and Planning, one synthesizes the agent plan by
taking advantage of the assumption on how the environment works (that is, one
exploits the environment's effects, its fairness, its trajectory constraints).
In this paper we study this form of synthesis in detail. We consider
assumptions as constraints on the possible strategies that the environment can
have in order to respond to the agent's actions. Such constraints may be given
in the form of a planning domain (or action theory), as linear-time formulas
over infinite or finite runs, or as a combination of the two. We argue though
that not all assumption specifications are meaningful: they need to be
consistent, which means that there must exist an environment strategy
fulfilling the assumption in spite of the agent actions. For such assumptions,
we study how to do synthesis/planning for agent goals, ranging from a classical
reachability to goal on traces specified in \LTL and \LTLf/\LDLf,
characterizing the problem both mathematically and algorithmically.
