ExplAIner: A Declarative Query Language for Explaining Classification Models

2026-07-07

AI Summary

This work addresses the lack of a unified declarative language in existing explainable AI (XAI) methods for expressing and composing diverse explanation queries, particularly those centered on optimality. To bridge this gap, the paper introduces ExplAIner—a declarative query language tailored for Boolean classification models. By extending its vocabulary and adopting a hierarchical structure, ExplAIner unifies support for multiple explanation types, including abductive, contrastive, feature-based, and distance-based explanations. Furthermore, it incorporates an optimization fragment, Opt-FOIL, to compute minimal explanations under a partial order. Theoretical analysis shows that ExplAIner queries can be reduced in polynomial time to a fixed number of SAT calls, and Opt-FOIL is solvable efficiently within the complexity class FP^NP. This framework thus offers a formally grounded, expressive, and scalable approach to XAI.

Abstract

The XAI community has studied a wide range of queries and scores for explaining predictions of ML models. From a data management perspective, this proliferation of explanation notions calls for declarative query languages in which such notions can be specified, combined, and analyzed uniformly. In this paper, we develop such a framework for Boolean models. We first revisit FOIL, an interpretability query language for black-box models, and show that it has two fundamental limitations: it cannot express central optimality-based explanation queries, and its evaluation problem over decision trees is hard for every level of the polynomial hierarchy. We then introduce ExplAIner, a query language based on FOIL with an extended vocabulary and a layered structure. We show that ExplAIner can express a broad family of explanation notions, including abductive, contrastive, feature-based, and distance-based queries. We also prove that the evaluation problem for each query in ExplAIner belongs to the Boolean hierarchy over every class of Boolean models for which some basic predicates can be evaluated in polynomial time. In particular, that property holds for deterministic and decomposable Boolean circuits. Finally, we introduce Opt-FOIL, an optimization-oriented fragment of ExplAIner for computing explanations that are minimal with respect to strict partial orders, and prove that its evaluation problem is in $\mathrm{FP}^{\mathrm{NP}}$ under the same tractability assumptions. These complexity results have a direct algorithmic consequence: a fixed ExplAIner query can be evaluated with a fixed number of calls to a SAT solver, while a notion of explanation specified in Opt-FOIL can be computed with a polynomial number of such calls. This is particularly relevant in formal XAI, where SAT solvers have been successfully used to compute explanations for several classes of ML models.

Problem

• Explainable AI
• Declarative Query Language
• Boolean Models
• Explanation Queries
• Computational Complexity

Innovation

• declarative query language
• Explainable AI (XAI)
• Boolean models
• complexity analysis
• SAT-based explanation