Action models in inquisitive logic

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic (IDEL). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of IDEL is that it can only encode public announcements. IDEL can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic (IEL), with action model logic (AML). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both AML and IEL, and a sound and complete axiomatization is given for both.