Speaker: Alexandru Baltag
Date and Time: Thursday, February 27th 2020, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Tell Us All You Know
I analyze the notion of “epistemic superiority” between agents or groups (e.g. “She knows all they know”), by adding epistemic comparison statements to standard epistemic logic. I show the connection of this notion with the logic of local dependence between variables (as axiomatized in my joint paper with van Benthem, recently presented at LIRa). On the dynamic side, I introduce actions by which epistemic superiority can be acquired: “sharing all one knows” (by e.g. giving access to one’s information database to all or some of the other agents), or “reading a knowledge base” (i.e. gaining such access to another’s information database, regardless of whether or not gave permission). I show that distributed knowledge is necessary to `pre-encode’ what happens to individual knowledge after such actions. As for dealing with common knowledge after these actions, we need to introduce a further generalization: the concept of “common distributed knowledge” (described for the first time in my student’s Suzanne van Wijk’s MoL thesis). I give an axiomatization of the logic of epistemic comparisons and common distributed knowledge, and I use it as a static base to axiomatize the dynamic logic of public and semi-public sharing/reading events. I move on to more complex such events involving privacy (e.g. hacking), and use an analogue of event models to describe and axiomatize them. I end with some related open questions. This is joint work with Sonja Smets.