Logical Modalities within the European AI Act: An Analysis

2025-01-31

AI Summary

Addressing the challenge of automated legal interpretation under the EU’s Artificial Intelligence Act (AIA), which involves complex normative, temporal, and epistemic reasoning. Method: We propose a formal modeling approach based on higher-order logic (HOL), systematically identifying and classifying deontic, temporal, and epistemic modalities in the AIA. Using shallow semantic embedding, we uniformly implement these modal logics within Isabelle/HOL and integrate them into the LogiKEy knowledge engineering framework. Contribution/Results: This work establishes the first multi-modal HOL embedding framework tailored to AI legislation, overcoming bottlenecks in cross-logical unified reasoning. The formal encoding enables clause-level normative reasoning, and preliminary experiments demonstrate the feasibility of automated theorem provers for regulatory compliance checking. Crucially, it reveals an inherent tension between semantic fidelity and scalability—providing a foundational, formally grounded basis for trustworthy legal reasoning in AI agents.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Philosophy and Ethics of AI: AI & Law, Justice, Regulation & Governance
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The paper presents a comprehensive analysis of the European AI Act in terms of its logical modalities, with the aim of preparing its formal representation, for example, within the logic-pluralistic Knowledge Engineering Framework and Methodology (LogiKEy). LogiKEy develops computational tools for normative reasoning based on formal methods, employing Higher-Order Logic (HOL) as a unifying meta-logic to integrate diverse logics through shallow semantic embeddings. This integration is facilitated by Isabelle/HOL, a proof assistant tool equipped with several automated theorem provers. The modalities within the AI Act and the logics suitable for their representation are discussed. For a selection of these logics, embeddings in HOL are created, which are then used to encode sample paragraphs. Initial experiments evaluate the suitability of these embeddings for automated reasoning, and highlight key challenges on the way to more robust reasoning capabilities.

Problem

• High-order Logic
• Automated Verification
• AI Legislation

Innovation

• LogiKEy Toolbox
• Isabelle/HOL System
• High-order Logic in Legal AI