Speaker: Sonja Smets
Date and Time: Thursday, September 16th 2021, 16:30-18:00, Amsterdam time.
Venue: online.
Title: Learning what Others Know
Abstract.
I will present recent work on modelling scenarios in which agents read or communicate (or somehow gain access to) all the information stored at specific sources, or possessed by some other agents (including information of a non-propositional nature, such as data, passwords etc). Modelling such scenarios requires us to extend the framework of epistemic logics to one in which we abstract away from the specific announcement and formalize directly the action of sharing ‘all you know’ (with some or all of the other agents). In order to do this, we introduce a general framework for such informational events, that subsumes actions such as “sharing all you know” with a group or individual, giving one access to some folder or database, hacking a database without the owner’s knowledge, etc. We formalize their effect, i.e. the state of affairs in which one agent (or group of agents) has ‘epistemic superiority’ over another agent (or group). Concretely, we express epistemic superiority using comparative epistemic assertions between individuals and groups (as such extending the comparison-types considered in [5]). Another ingredient is a new modal operator for ‘common distributed knowledge’, that combines features of both common knowledge and distributed knowledge, and characterizes situations in which common knowledge can be gained in a larger group of agents (formed of a number of subgroups) by communication only within each of the subgroups. We position this work in the context of other known work such as: the problem of converting distributed knowledge into common knowledge via acts of sharing [4]; the more semantic approach in [2] on communication protocols requiring agents to ‘tell everybody all they know’; the work on public sharing events with a version of common distributed knowledge in [3]; and the work on resolution actions in [6].
This presentation is based on joint work with Alexandru Baltag in [1], and it subsumes and extends the material presented by Alexandru in his LIRa presentation in February 2020.
[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020. https://doi.org/10.29007/plm4
[2] A. Baltag and S. Smets, Protocols for Belief Merge: Reaching Agreement via Communication, Logic Journal of the IGPL, 21(3):468-487, 2013. https://doi.org/10.1093/jigpal/jzs049
[3] A. Baltag, What is DEL good for? Lecture at the ESSLLI2010-Workshop on Logic, Rationality and Intelligent Interaction, 16 August 2010.
[4] J. van Benthem, One is a lonely number. In P. Koepke Z. Chatzidakis and W. Pohlers, (eds.) Logic Colloquium 2002, 96-129, ASL and A.K. Peters, Wellesley MA, 2002.
[5] H. van Ditmarsch, W. van der Hoek & B. Kooi, Knowing More – from Global to Local Correspondence, Proc. of IJCAI-09, 955–960, 2009.
[6] T. Agotnes and Y.N. Wang, Resolving Distributed Knowledge, Artificial Intelligence, 252: 1–21, 2017. https://doi.org/10.1016/j.artint.2017.07.002