Process model discovery has gained a lot of attention in recent years, to mine a process model from traces of process executions. In our recent work, we have proposed SIM (Semantic Interactive Miner), an innovative process mining tool able to discover the process model in an incremental way: first, a mining module builds an initial process model, called log-tree, from the available traces; then, such a model is refined interactively with domain experts, through merge and abstraction operations. However, in several contexts, traces are richer: they do not record only actions, but also states (i.e., values of parameters possibly affected by the actions). A typical example is the medical domain, where traces contain both actions and measurements of patients’ parameters. In this paper, we propose AS-SIM (Action-State SIM), the first approach aiming at discovering a comprehensive model, in which two distinct classes of nodes are considered, to capture both actions and states. We focus on the definition and on the discovery of the initial action-state process model (called action-state log-tree), while in our future work we will extend SIM’s merge and abstraction operations accordingly.