A Boolean model for conflict-freeness in argumentation frameworks

The Boolean models of argumentation semantics have been established in various ways. These models commonly translate the conditions of extension-based semantics into some constraints of the models. The goal of this work is to explore a simple method to build Boolean models for argumentation. In this paper, the attack relation is treated as an operator, and its value is calculated by the values of its target and source arguments. By examining the values of the attacks, a Boolean model of conflict-free sets is introduced. This novel method simplifies the existing ways by eliminating the various constraints. The conflict-free sets can be calculated by simply checking the values of the attacks.