Solving Hard XAI Queries Based on a Compiled Dual-Rail Encoding

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.

Interpretable machine learning aims to provide transparent models whose decision-making processes can be readily understood by humans. Recent advances in rule-based approaches, such as expressive Boolean formulas (BoolXAI), offer faithful and compact representations of model behavior. However, for non-technical stakeholders, main challenges remain in practice: (i) selecting semantically meaningful features and (ii) translating formal logical rules into accessible explanations. In this work, we propose BoolXLLM , as a hybrid framework that integrates Large Language Models (LLMs) into the end-to-end pipeline of Boolean rule learning. We augment BoolXAI , an expressive Boolean rule-based classifier, with LLMs at three critical stages: (1) feature selection, where LLMs guide the identification of domain-relevant variables; (2) threshold recommendation, where LLMs propose semantically meaningful discretization strategies for numerical features; and (3) rule compression and interpretation, where Boolean rules are translated into natural language explanations at both global and local levels. This integration bridges formal, faithful explanations with human-understandable narratives. This allows build an explainable AI system that is both theoretically grounded and accessible to non-experts. Early empirical results demonstrate that LLM-assisted pipelines improve interpretability while maintaining competitive predictive performance. Our work highlights the promise of combining symbolic reasoning with language-based models for human-centered explainability.

Explaining opaque Machine Learning (ML) models has become an increasingly important challenge. However, current eXplanation in AI (XAI) methods suffer several shortcomings, including insufficient abstraction, limited user interactivity, and inadequate integration of symbolic knowledge. We propose ReasonX, an explanation tool based on expressions (or, queries) in a closed algebra of operators over theories of linear constraints. ReasonX provides declarative and interactive explanations for decision trees, which may represent the ML models under analysis or serve as global or local surrogate models for any black-box predictor. Users can express background or common sense knowledge as linear constraints. This allows for reasoning at multiple levels of abstraction, ranging from fully specified examples to under-specified or partially constrained ones. ReasonX leverages Mixed-Integer Linear Programming (MILP) to reason over the features of factual and contrastive instances. We present here the architecture of ReasonX, which consists of a Python layer, closer to the user, and a Constraint Logic Programming (CLP) layer, which implements a meta-interpreter of the query algebra. The capabilities of ReasonX are demonstrated through qualitative examples, and compared to other XAI tools through quantitative experiments.