A modular multi-modal specification of real-timed, end-to-end voter-verifiable voting systems

We propose a modular multi-modal specification of real-timed, end-to-end voter-verifiable voting systems, i.e., a formal but intuitive specification of real-timed voting systems that are accountable (and thus trustworthy) to their users. Our specification is expressed as a single but well-compounded formula in a logical language of temporal, epistemic, and provability modalities. The intuitiveness of the specification is the fruit of its modular and multi-modal form. This means that the specification can be appreciated compound-wise, as a logical conjunction of separate sub-requirements, each of which achieving the ideal of a formal transcription of a suitable natural-language formulation, thanks to powerful descriptive idioms in the form of our multiple modalities. The modular form reduces our proof of the satisfiability (consistency) and thus implementability of the specification to a proof by inspection, and induces the parallelisability of implementation-correctness verifications. The specification also pinpoints the implementation-specific part of particular voting systems, reuses a generic definition of accountability inducing trust in a formal sense, and, last but not least, counter-balances by its implementability some previous results about the contradictory conjunction of certain desirable property pairs of voting systems. So in some sense, ideal voting systems do exist. Our specific formalisation principles are agent correctness, i.e., the behavioural correctness of the voting-system-constituting agents, and data adequacy, i.e., the soundness and (relative) completeness of the voting data processed by the system.