This paper presents the first systematic study of how similarity between arguments affects their evaluation under extension semantics. We define a set of principles that govern how similarity should be taken into account by a semantics, and introduce a broad family of parameterized extension semantics that adhere to these principles. Each member of this family generalizes a classical extension semantics (such as preferred semantics) while disregarding redundant attacks. We identify classes of argumentation graphs in which similarity has no effect on the acceptability status of arguments, and we characterize the conditions under which a family instance either improves an argument’s acceptability or coincides with the semantics it generalizes. Finally, we discuss different types of selection functions, which specify the subset of attacks to disregard.