Reasoning in Structured Argumentation under Incomplete Information

Abstract: Reasoning under incomplete information is a research direction in the study of computational argumentation. Most advances in this direction so far have focused on abstract argumentation frameworks. In particular, development of computational approaches to reasoning under incomplete information in structured formalisms remains to a large extent a challenge. We address this challenge by studying the problems of determining stability and relevance—with the aim of analyzing aspects of resilience of acceptance statuses in light of new information—in the central structured formalism of ASPIC+. The specific ASPIC+ instantiation and grounded argumentation semantics we focus on are motivated by current applications in criminal investigation at the Netherlands Police. Our contributions consist of a theoretical analysis of the complexity of deciding stability and relevance as well as first exact algorithms for reasoning about stability and relevance in incomplete ASPIC+ theories based on the declarative paradigm of answer set programming (ASP). Furthermore, we provide an open-source implementation of the algorithms, and show empirically that the implementation exhibits promising scalability on both real-world and synthetic data. Our exact approach to stability is competitive with a previously proposed inexact approach, and the run times of our algorithms for both stability and relevance are sufficiently low on real-world data to be used in online settings. 

This is joint work with Daphne Odekerken, Tuomo Lehtonen, and Matti Järvisalo.