A logical perspective on intending to keep a true secret

Abstract

Logical investigations of the notion of secrecy are typically concentrated on tools for deducing whether private information is well hidden from unauthorized, direct, or indirect access attempts. This paper proposes a multi-agent, normal multi-modal logic to capture salient features of secrecy's intentions. Specifically, we focus on the intentions, beliefs, and knowledge of secret keepers and, more generally, of all the actors involved in secret-keeping scenarios. In particular, we investigate intentions underlying the keeping of a true secret, namely a secret concerning information known (and so true) by the secret keeper. The resulting characterization of intending to keep a true secret provides valuable insights into conditions ensuring or undermining secrecy depending on agents' attitudes and links between secrets and their surrounding context. We present the proposed logical system's soundness, completeness, and decidability results. Furthermore, we outline some theorems with potential applications to several fields, e.g., computer science and the social sciences.