Formal argumentation frameworks traditionally emphasize constructing structural arguments from rules with well-supported deductive evidence. When part or the entire set of rules defining the support of an argument are interpreted through logic programming (LP) semantics (e.g., WFS, WFS+, or Stable), true atoms from its model are expected to be the argument’s conclusion. Differently from other approaches, this research emphasizes the crucial role of investigating frameworks that can also build arguments for unsuccessful interpretations, i.e., the conclusion atom interpretation is false. These “negative arguments” have been less explored in the formal argumentation theory, despite its potential use in practical applications for justifying atoms where no deductive evidence exists. Few current approaches disregard key characteristics of well-defined arguments, such as consistency (avoiding internal argument contradictions), relatedness (conclusions based on relevant information), and minimality (using the least amount of information necessary). This article introduces the so-called well-founded argumentation framework for building well-founded arguments guaranteeing these quality argumentation characteristics and the ability to justify both “positive” and “negative” conclusions. Well-founded arguments are defined in terms of Confluent LP Systems as rewriting systems on the set of all logic programs, making this approach a general framework. Additionally, we introduce a method for building such arguments using the program’s strata through partial interpretations, leading to a more efficient process compared to analyzing dependency graphs of atoms.