Complexity of Faceted Explanations in Propositional Abduction
This work addresses the need for more fine-grained analysis of explanation heterogeneity in AI applications like diagnosis and planning, though it is incremental as it builds on existing complexity studies in propositional abduction.
The paper tackled the problem of understanding variability in explanations for propositional abduction by introducing facets (literals that are relevant but not indispensable) and analyzing distances between explanations, resulting in a comprehensive complexity characterization, including an almost complete classification in Post's framework.
Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional abduction, we focus on specifying knowledge by a propositional formula. The computational complexity of tasks in propositional abduction has been systematically characterized - even with detailed classifications for Boolean fragments. Unsurprisingly, the most insightful reasoning problems (counting and enumeration) are computationally highly challenging. Therefore, we consider reasoning between decisions and counting, allowing us to understand explanations better while maintaining favorable complexity. We introduce facets to propositional abductions, which are literals that occur in some explanation (relevant) but not all explanations (dispensable). Reasoning with facets provides a more fine-grained understanding of variability in explanations (heterogeneous). In addition, we consider the distance between two explanations, enabling a better understanding of heterogeneity/homogeneity. We comprehensively analyze facets of propositional abduction in various settings, including an almost complete characterization in Post's framework.