Why this and not that? A Logic-based Framework for Contrastive Explanations

TL;DR

This paper introduces a logic-based framework for contrastive explanations, addressing questions like 'Why P but not Q?' by defining problems that compare causes for P and Q, analyzing their properties, complexity, and practical implementation.

Contribution

It formalizes contrastive explanations within propositional logic, captures minimal explanations, and provides computational analysis and implementation for CNF formulas.

Findings

Framework captures minimal contrastive explanations

Complexity analysis of contrastive explanation problems

Implementation using answer set programming

Abstract

We define several canonical problems related to contrastive explanations, each answering a question of the form ''Why P but not Q?''. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.