Rough Consequence and other Modal Logics

Abstract

Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, based on such an S, is theorem equivalent, but not necessarily equivalent, to the modal logic M-S. The paper also shows that rough consequence logic, which was designed to handle rough equality, is somewhat limited for that purpose.