Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far the systems that LFIT handles were mainly restricted to synchronous deterministic dynamics. However, other dynamics exist in the field of logical modeling, in particular the asynchronous semantics which is widely used to model biological systems. In this paper, we focus on methods to model and learn the dynamics of the system independently of its update semantics. For this purpose, we propose a modeling of multi-valued systems as logic programs in which a rule represents what can occur rather than what will occur. This modeling allows us to represent non-determinism and to propose an extension of LFIT to learn from discrete multi-valued transitions, regardless of their update schemes. We also propose a second algorithm which is able to learn a whole system dynamics, including its semantics, in the form of a single propositional logic program with constraints. We show through theoretical results the correctness of our approaches. Practical evaluation is performed on benchmarks from biological literature.