On the Complexity of Finding Second-Best Abductive Explanations

TL;DR

This paper investigates the computational complexity of identifying second-best abductive explanations under various orderings and definitions, extending existing knowledge on the difficulty of finding optimal solutions.

Contribution

It analyzes the complexity of computing second-best abductive explanations for different orderings and definitions, providing new insights into their computational challenges.

Findings

Complexity results vary depending on the ordering used.

Some definitions of second-best solutions are computationally hard to find.

The work extends understanding of abductive reasoning beyond the best solutions.

Abstract

While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the computational complexity of finding second-best solutions. We consider different orderings, and consider also different possible definitions of what a second-best solution is.