Redundancy in logic I: CNF propositional formulae

A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study some problems related to the redundancy of a CNF formula. In particular, any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset. We study the complexity of problems related to irredundant equivalent subsets: verification, checking existence of an irredundant equivalent subset with a given size, checking necessary and possible presence of clauses in irredundant equivalent subsets, and uniqueness. We also consider the problem of redundancy with different definitions of equivalence.