Abduction, Argumentation and Bi-Disjunctive Logic Programs

We study the relationship between argumentation (abduction) and disjunctive logic programming. Based on the paradigm of argumentation, an abductive semantic framework for disjunctive logic programming is presented, in which the disjunctions of negative literals are taken as possible assumptions rather than only negative literals as the case of non-disjunctive logic programming. In our framework, three semantics PDH, CDH and WFDH are defined by three kinds of acceptable hypotheses to represent credulous reasoning, moderate reasoning and skeptical reasoning in AI, respectively. On the other hand, our semantic framework could be established in a broader class than that of disjunctive programs (called bi-disjunctive logic programs) and, hence, the corresponding abductive framework is abbreviated as BDAS (Bi-Disjunctive Argumentation-theoretic Semantics). Besides its rich expressive power and nondeterminism, BDAS integrates and naturally extends many key semantics, such as the minimal models, EGCWA, the well-founded model, and the stable models. In particular, a novel and interesting argumentation-theoretic characterization of EGCWA is shown. Thus the framework in this paper does not only provides a new way of performing argumentation (abduction) in disjunctive logic programming, but also is a simple, intuitive and unifying semantic framework for disjunctive logic programming.