Boolean algebras arising from information systems Original Research Article

Following the theory of Boolean algebras with modal (normal and additive) operators (BAO), in this paper we investigate Boolean algebras with sufficiency (co-normal, co-additive) operators (SUA) and mixed (modal + sufficiency) operators (MIA). We present results concerning representability, generation by finite members, first order axiomatisability, possession of a discriminator term etc. We generalise the classes BAO, SUA, and MIA to classes of algebras with the families of relative (indexed with subsets of a set) operators. We present examples of the discussed classes of algebras that arise in connection with reasoning with incomplete information.