Argumentation has become an essential tool in AI, allowing the representation of knowledge with only a set of arguments and a binary relation between arguments, the attack relation. Since the seminal work presented in 1995 by Dung, many extensions have been proposed in order to enrich this very simple framework by the addition of a second type of interaction, the support relation, and by the use of higher-order or collective interactions. In parallel, several links have been exhibited and studied between Logics and Abstract Argumentation, showing that these two domains are closely interrelated. Among these works, one can find several logical encodings of abstract argumentation frameworks. Nevertheless, these encodings are very often built ad hoc and only for some given frameworks. The aim of this paper is to propose a generic logical encoding covering several families of abstract argumentation frameworks, from Dung’s framework to the most enriched framework using higher-order and collective evidential supports and attacks.