Abstract
Building on our previous work in non-classical dynamic epistemic logic, we add common knowledge operators to a version of public announcement logic based on the relevant logic \(\mathsf {R}\). We prove a completeness result with respect to a relational semantics, and we show that an alternative semantics based on information states is dual to the relational one. We add a question-forming inquisitive disjunction operator to the language and prove a completeness result with respect to the information semantics. It is argued that relevant public announcements are particularly suitable for modelling public argumentation.
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