Some descending chains of incomplete modal logics (Q1177647)

An incomplete normal propositional modal logic is a logic not characterized by any class of frames and so, a fortiori, not characterized by the class of all its frames. It is known that there exist infinite classes of incomplete logics where all members of the class have exactly the same frames, though up to now few axiomatic descriptions of such classes have existed. This paper presents some descending chains of incomplete logics where each logic in the chain has exactly the same frames as the one below it.