Using Certifying Constraint Solvers for Generating Step-wise Explanations

TL;DR

This paper presents a framework that leverages proofs from constraint solvers to efficiently generate step-wise explanations for unsatisfiability, improving speed while maintaining explanation quality.

Contribution

It introduces a novel proof-based approach for step-wise explanations in constraint solving, with methods for converting proofs into explanations and techniques for simplifying them.

Findings

Significantly faster explanation generation

Maintains high explanation quality

Effective proof trimming and simplification techniques

Abstract

In the field of Explainable Constraint Solving, it is common to explain to a user why a problem is unsatisfiable. A recently proposed method for this is to compute a sequence of explanation steps. Such a step-wise explanation shows individual reasoning steps involving constraints from the original specification, that in the end explain a conflict. However, computing a step-wise explanation is computationally expensive, limiting the scope of problems for which it can be used. We investigate how we can use proofs generated by a constraint solver as a starting point for computing step-wise explanations, instead of computing them step-by-step. More specifically, we define a framework of abstract proofs, in which both proofs and step-wise explanations can be represented. We then propose several methods for converting a proof to a step-wise explanation sequence, with special attention to trimming and simplification techniques to keep the sequence and its individual steps small. Our results show our method significantly speeds up the generation of step-wise explanation sequences, while the resulting step-wise explanation has a quality similar to the current state-of-the-art.