On the Computational Complexity of Naive-Based Semantics for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) are a powerful generalization of Dung’s abstract argumentation frameworks. ADFs allow to model argumentation scenarios such that ADF semantics then provide interpretations of the scenarios. Among the considerable number of ADF semantics, the naivebased ones are built upon the fundamental concept of conflict-freeness. Intuitively, a three-valued interpretation of an ADF’s statements is conflict-free iff all true statements can possibly be accepted, and all false statements cannot possibly be accepted.dialectical frameworks (ADFs) are a powerful generalization of Dung’s abstract argumentation frameworks. ADFs allow to model argumentation scenarios such that ADF semantics then provide interpretations of the scenarios. Among the considerable number of ADF semantics, the naivebased ones are built upon the fundamental concept of conflict-freeness. Intuitively, a three-valued interpretation of an ADF’s statements is conflict-free iff all true statements can possibly be accepted, and all false statements cannot possibly be accepted. In this paper, we perform an exhaustive analysis of the computational complexity of naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.