The Logic of Data Access and Data Exchanges

We investigate a new logic that extends Dynamic Epistemic Logic (DEL), by combining standard epistemic modalities K a ϕ and K A ϕ for (individual and distributed) propositional knowledge with operators K ϕ a x, K ϕ A x denoting (conditional) non-propositional knowledge of a number (in which an agent a or a group A have knowledge of the value of some variable x, if given additional information ϕ).We also generalize these operators, by considering formulas |x| ϕ A ≤ N (for any natural number N), saying that: conditional on ϕ, A can narrow down the possible values of variable x to at most N possibilities.In order to name and compare such hypothetical values, we extend the logic further with definite descriptions based on minimization operators: µ N x ϕ A denotes the least of the N possible values of x (according to some fixed order ≤) that are considered possible by group A (given condition ϕ).On this static base, we consider DEL-style extensions with dynamic modalities for general 'dataexchange events' (covering private and public propositional announcements, but also secret hacking of a private database, or public sharing of one's data via open-source repositories, etc).In such scenarios, whole 'chunks' of information may be exchanged or modified: once access to a given source is gained, all the 'data' stored at that specific location becomes available.We give complete axiomatizations for the resulting logics, and prove their decidability and co-expressivity.