In the last decade, defeasible argumentation has proven to be a confluence point for many approaches to formalizing commonsense reasoning. Different formalisms have been developed, many of them sharing common features. This paper presents a formalization of an LDS for defensible argumentation, in which the main issues concerning defeasible argumentation are captured within a unified logical framework. The proposed framework is defined in two stages. First, defeasible inference will be formalized by characterizing an argumentative LDS. That system will be then extended in order to capture conflict among arguments using a dialectical approach. We also present some logical properties emerging from the proposed framework, discussing also its semantical characterization.