Access Hoare Logic

2025-11-03

AI Summary

This paper addresses the lack of dedicated formal reasoning frameworks for security properties such as program access control. To bridge this gap, we propose Access Hoare Logic (AHL)—the first systematic extension of Hoare logic to the domain of access security. AHL comprises a fully developed syntax, operational semantics, and axiomatic system; we formally prove its soundness and relative completeness, and establish a semantic mapping to classical Hoare logic. By introducing access permission predicates, permission calculus rules, and context-sensitive pre- and postconditions, AHL enables precise modeling and end-to-end verification of access policies. We demonstrate its applicability in canonical access control scenarios, showing that AHL effectively supports formal verification of critical security properties—including policy consistency and the principle of least privilege.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Authentication, authorization, and access control
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Following Hoare's seminal invention, later called Hoare logic, to reason about correctness of computer programs, we advocate a related but fundamentally different approach to reason about access security of computer programs such as access control. We define the formalism, which we denote access Hoare logic, and present examples which demonstrate its usefulness and fundamental difference to Hoare logic. We prove soundness and completeness of access Hoare logic, and provide a link between access Hoare logic and standard Hoare logic.

Problem

• Develops a logic for verifying program access security
• Establishes formal foundations for access control verification
• Proves soundness and completeness of access Hoare logic

Innovation

• Introduces Access Hoare Logic for security reasoning
• Formalism differs fundamentally from standard Hoare logic
• Proves soundness and completeness of the logic