{"ID":2825484,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21137","arxiv_id":"2512.21137","title":"Declarative distributed algorithms as axiomatic theories in three-valued modal logic over semitopologies","abstract":"We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic, using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The methods scale well and have been used to find errors in a proposed industrial protocol. The key novelty is to use modal logic to capture a declarative, high-level representation of essential system properties -- the logical essence of the algorithm -- while abstracting away from explicit state transitions of an abstract machine that implements it. It is like the difference between specifying code in a functional or logic programming language, versus specifying code in an imperative one. Thus we present axiomatisations of Declarative Bracha Broacast and Declarative Crusader Agreement. A logical axiomatisation in the style we propose provides a precise, compact, human-readable specification that abstractly captures essential system properties, while eliding low-level implementation details; it is more precise than a natural language description, yet more abstract than source code or a logical specification thereof. This creates new opportunities for reasoning about correctness, resilience, and failure, and could serve as a foundation for human- and machine verification efforts, design improvements, and even alternative protocol implementations. The proofs in this paper have been formalised in Lean 4.","short_abstract":"We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic, using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The methods scale well and have been used to fin...","url_abs":"https://arxiv.org/abs/2512.21137","url_pdf":"https://arxiv.org/pdf/2512.21137v3","authors":"[\"Murdoch J. Gabbay\"]","published":"2025-12-24T12:07:25Z","proceeding":"cs.LO","tasks":"[\"cs.LO\",\"cs.DC\"]","methods":"[]","has_code":false}