Projective and inductive generation of abstract logics

An abstract logic 〈A, C〉 consists of a finitary algebra A and a closure system C on A. C induces two other closure systems on A, CP and CI, by projective and inductive generation respectively. The various relations among C, CP and CI are determined. The special case that C is the standard equational closure system on monadic terms is studied in detail. The behavior of Boolean logics with respect to projective and inductive generation is determined. © 1976 Warszawa.