\input zb-basic \input zb-ioport \iteman{io-port 04217340} \itemau{Plisko, V.E.} \itemti{On arithmetic complexity of some constructive logics.} \itemso{Mat. Zametki 52, No.1, 94-104 (1992).} \itemab The paper continues former works of the author concerning the notion of constructive arithmetic theory as a set of arithmetic propositions, closed with respect to certain intuitionistic deducibility rules. Within this framework, complexity and completeness properties of certain logics are studied. \itemrv{P.Kruszy\'nski (Delft)} \itemcc{} \itemut{constructive logics; constructive arithmetic; intuitionistic deducibility rules; complexity; completeness} \itemli{} \end