A Commonsense Theory of Secrets

With the advent of social robots, precise accounts of an increasing number of social phenomena are called for. Although the phenomenon of secrets is an important part of everyday social situations, logical accounts of it can only be found, in a rather strict sense, within logical investigations of systems security. This paper is an attempt to formalize the logic of a commonsense notion of secrets as a contribution to ontologies of social and epistemological phenomena. We take a secret to be a five-way relation between a proposition, a group of secret-keepers, a group of nescients, a condition of secrecy, and a time point. A bare-bones notion of secrets is defined by providing necessary and sufficient conditions for said relation to hold. Special classes of secrets are then identified by considering an assortment of extra conditions. The logical language employed formalizes a classical account of belief and intention, a theory of groups, and a novel notion of revealing. In such a rich theory, interesting properties of secrets are proved.