Distributed knowing whether: (Extended abstract)

Abstract

Standard epistemic logic studies reasoning patterns about ‘knowing that’, where interesting group notions of ‘knowing that’ arise naturally, such as distributed knowledge and common knowledge. In recent research, other notions of knowledge are also studied, such as ‘knowing whether’, ‘knowing how’, and so on. It is natural to ask what are the group notions of these non-standard knowledge expressions. This paper makes an initial attempt in this line, by looking at the notion corresponding to distributed knowledge in the setting of ‘knowing whether’. We introduce the distributed know-whether operator, and give complete axiomatizations of the resulting logics over arbitrary or S 5 frames, based on the corresponding axiomatizations of ‘knowing whether’.