Capability Safety as Datalog: A Foundational Equivalence
Summary: arXiv:2603.26725v1 Announce Type: cross
Abstract: We prove that capability safety admits an exact representation as propositional Datalog evaluation (Datalogprop: the monadic, ground, function-free fragment of first-order logic), enabling the transfer of algorithmic and structural results unavailable in the native formulation. This addresses two structural limitations of the capability hypergraph framework of Spera [2026]: the absence of efficient incremental maintenance, and the absence of a decision procedure for audit surface containment. The equivalence is tight: capability hypergraphs correspond to exactly this fragment, no more.
Introduction
In recent years, the concept of capability safety has gained prominence in discussions surrounding secure computing and system integrity. This article explores a groundbreaking perspective on capability safety through its representation in Datalog, a declarative logic programming language.
Understanding Capability Safety
Capability safety refers to the assurance that a system’s capabilities are correctly managed to prevent unauthorized access or actions. The traditional framework for analyzing capability safety has been based on hypergraphs, which visually represent the relationships between different capabilities.
Limitations of the Traditional Framework
Despite its usefulness, the hypergraph framework introduced by Spera in 2026 has notable limitations:
- Lack of Efficient Incremental Maintenance: The traditional hypergraph approach struggles to adapt efficiently when changes occur in the underlying capability structure, making it cumbersome for dynamic environments.
- Absence of a Decision Procedure: The existing framework lacks a robust decision procedure for audit surface containment, which is critical for ensuring that all necessary capabilities are accounted for during audits.
Datalog as a Solution
In this paper, we introduce an innovative solution by demonstrating that capability safety can be represented as propositional Datalog evaluation (Datalogprop). This fragment of first-order logic is monadic, ground, and function-free, making it particularly suited for the task.
Benefits of the Datalog Representation
The adoption of Datalog to represent capability safety offers several significant advantages:
- Algorithmic Enhancements: By utilizing Datalog, researchers and practitioners can leverage existing algorithmic techniques that are otherwise unavailable in the traditional hypergraph framework.
- Structural Clarity: Datalog provides a clearer structural representation of capability safety, enhancing understanding and facilitating better analysis.
- Efficient Maintenance: The Datalog representation allows for efficient incremental maintenance, enabling systems to adapt seamlessly to changes in capabilities.
- Decision Procedures: Implementing Datalog introduces decision procedures for audit surface containment, addressing a significant gap in the previous framework.
Conclusion
This work establishes a foundational equivalence between capability safety and Datalog, revealing a powerful tool for advancing the field of secure computing. The tight correspondence between capability hypergraphs and the Datalog fragment underscores the potential for significant progress in capability management and safety auditing. As this research unfolds, it promises to enhance the security posture of systems relying on capability-based access controls.