Recently there has been an increasing interest in frameworks extending Dung's\nabstract Argumentation Framework (AF). Popular extensions include bipolar AFs\nand AFs with recursive attacks and necessary supports. Although the\nrelationships between AF semantics and Partial Stable Models (PSMs) of logic\nprograms has been deeply investigated, this is not the case for more general\nframeworks extending AF.\n In this paper we explore the relationships between AF-based frameworks and\nPSMs. We show that every AF-based framework $\\Delta$ can be translated into a\nlogic program $P_\\Delta$ so that the extensions prescribed by different\nsemantics of $\\Delta$ coincide with subsets of the PSMs of $P_\\Delta$. We\nprovide a logic programming approach that characterizes, in an elegant and\nuniform way, the semantics of several AF-based frameworks. This result allows\nalso to define the semantics for new AF-based frameworks, such as AFs with\nrecursive attacks and recursive deductive supports.\n Under consideration for publication in Theory and Practice of Logic\nProgramming.\n