Speaker: Alexandru Baltag (ILLC, University of Amsterdam)
Date and Time: Thursday, February 26th 2026, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107 and online.
Title: The Logic of Data Access and Data Exchanges
Abstract. In recent years, multi-agent epistemic logic has been extended to deal with the possession of non-propositional data (such as passwords, keys, graphical information, etc) by individuals or groups: in addition to the standard propositional knowledge K_a P (by an agent a) and distributed knowledge K_A P (by a group A), one considers operators K_a x or K_A x for (individual or distributed) knowledge of (the value of) some variable x. However, in the view of applications e.g. to Secure Communication, it seems useful to generalize this by considering operators |x|_a <= N (or |x|_A <= N), saying that the agent or group can narrow down the possible values of variable x to at most N possibilities. Indeed, if N is `small enough’ and x is say another agent b’s communication key or private password, then any intruder a having the capability |x|_a <= N will be able to hack b’s communication (by simply trying out all the N possible values). We study these logics and their dynamic versions, endowed with dynamic modalities for arbitrary data-exchange events (e.g., public and semi-public announcements, changing the value of a private variable, public sharing of one’s data via open-source depositories, semi-public data-sharing within different subgroups, suspected hacking of a private database, private detection of such hacking, etc).
To deal with such dynamic contexts, one needs to consider a conditional version of the above operators: |x|_a^P <=N says that, if given some new information P, the agent/group would be able to narrow down the value of x to <= N possibilities. To obtain a complete axiomatization of data-exchange events, one needs to extend the static logic even further, by introducing definite descriptions based on minimization operators: μ_N x_A^P denotes the least of the N possible values of x (according to some fixed total order <=) that are considered possible by the agent/group A (given condition P).
I give examples, as well as complete axiomatizations for the static and dynamic logics obtained in this way, and prove their decidability and co-expressivity. This talk is based on joint work with S. Smets.