On Some Logics Intermediate Between S4.2 and S4.3 Defined by the Notion of Independence

Hamkins and Löwe described modal logic S4.2 through the notion of sets of independent buttonsstatements that are possibly necessary -and switches -necessarily contingent statements.In this article we investigate logics intermediate between S4.2 and S4.3 that are defined through a different notion of independence.We provide an axiomatic description of such logics, state some basic facts and prove various completeness and decidability results.