Gradual evaluation methods in argumentation frameworks provide semantics for assessing the gradual acceptance of arguments, differing from the qualitative semantics that have been used in argument evaluation since argumentation’s conception. These methods and their semantics are wide-ranging; they comprise those for group acceptance, probabilistic measures and game-theoretical strength, amongst many others. This affords numerous application areas and so the requisite behaviour for each needs to be justified by theoretical proofs of useful properties for a specific application.
Our contributions to this field span three interweaving sub-categories, namely methods, properties and applications. For gradual evaluation methods, we develop a number of novel and useful methods themselves. For each method we detail the semantics’ and the frameworks’ definitions then undertake theoretical evaluations based on their properties, before applications targeting real-world problems are suggested for each method. As for gradual evaluation properties, we undertake a systematic analysis for this research landscape by first identifying groups of conceptually related properties in the literature and provide a simplifying and unifying perspective for these properties by showing that all the considered literature properties are implied by four, novel parametric principles. We then validate these principles by showing that they are satisfied by several quantitative argumentation formalisms in the literature. We also instantiate the extensive number of implied properties of these principles which are not present in the literature. These properties are also used to extract argumentation explanations for recommendations in recommender systems, a novel concept and application.