Declarative distributed broadcast using three-valued modal logic and semitopologies

We demonstrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic. We exhibit the method on a simple voting protocol, a simple broadcast protocol, and a simple agreement protocol. 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 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. 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.