We propose a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks/supports whose targets are arguments or other attacks/supports) with an evidential meaning for supports. Our purpose is to separate the logical expression of the meaning of an attack or an evidential support (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks/supports) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung’s argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung’s frameworks, enabling to recover standard extensions.