Argumentative Reasoning in ASPIC+ under Incomplete Information

Reasoning under incomplete information is an important research direction in AI argumentation. Most computational advances in this direction have so far focused on abstract argumentation frameworks. Development of computational approaches to reasoning under incomplete information in structured formalisms remains to date to a large extent a challenge. We address this challenge by studying the so-called stability and relevance problems---with the aim of analyzing aspects of resilience of acceptance statuses in light of new information---in the central structured formalism of ASPIC+. Focusing on the case of the grounded semantics and an ASPIC+ fragment motivated through application scenarios, we develop exact ASP-based algorithms for stability and relevance in incomplete ASPIC+ theories, and pinpoint the complexity of reasoning about stability (coNP-complete) and relevance (Sigma-P-2-complete), further justifying our ASP-based approaches. Empirically, the algorithms exhibit promising scalability, outperforming even a recent inexact approach to stability, with our ASP-based iterative approach being the first algorithm proposed for reasoning about relevance in ASPIC+.