Complexity of Faceted Explanations in Propositional Abduction

TL;DR

This paper explores the complexity of explanations in propositional abduction, introducing facets to analyze variability and heterogeneity of explanations, with comprehensive complexity characterizations across different logical frameworks.

Contribution

It introduces the concept of facets in propositional abduction to analyze explanation variability and provides a detailed complexity analysis across various logical settings.

Findings

Facets help distinguish relevant and dispensable literals in explanations.

Complexity results vary across different propositional fragments.

The framework offers a nuanced understanding of explanation heterogeneity.

Abstract

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.