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

2025-07-11

AI Summary

This paper addresses contrastive explanation queries of the form “Why P rather than Q?” by proposing the first unified logical framework based on propositional logic to explicitly model and compare the causal antecedents of P and Q. Methodologically, it introduces a minimal-cardinality semantics for contrastive explanations, provides a decidable logical characterization, and implements an efficient ASP-based solver for CNF formulas. Theoretically, it establishes the computational complexity of multiple contrastive explanation variants—e.g., proving Σ₂^P-completeness—and delineates their formal boundaries. Practically, it develops a scalable prototype system empirically validated on diverse benchmark instances, demonstrating both effectiveness and practical utility. This work furnishes a formal foundation and computational toolkit for counterfactual reasoning in explainable AI.

Technology Category

• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Defining canonical problems for contrastive explanations in logic
• Analyzing computational complexities of contrastive explanation problems
• Implementing CNF-formula solutions using answer set programming

Innovation

• Logic-based framework for contrastive explanations
• Computes causes for P and Q differences
• Uses answer set programming for CNF-formulas