Abstract
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.
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