A Specialized Set Theoretic Semantics for Acceptability Dynamics of Arguments.

Inspired by the standard set theoretic Tarskian semantics, we propose a novel interpretation structure for studying the acceptability dynamics of arguments (i.e., the eventual changes on their acceptability condition) for logic-based argumentation. Interpretation structures identify possible scenarios in which a given argument would be accepted, or not, according to some standard extension-based argumentation semantics. These scenarios are configured in accordance to the consideration or inconsideration of other arguments from the given argumentation framework. Thereafter, it would be possible to ensure the acceptability of an argument by handling the evolution of the argumentation framework throughout the use of argumentative change operations. Hence, an interpretation structure which is a model of a given argument specifies a possible epistemic state to which the argumentation framework could evolve towards the argument's positive acceptability. Moreover, the analysis of several models of a given argument brings the opportunity of satisfying additional restrictions towards the evolution of a framework. Finally, we propose a revision operator whose rationality is ensured through postulates and a corresponding representation theorem.