Meeting of the Minds

We analyze existing game solution procedures as steps in a process of iterated public announcement between two minds that meet either in reality or virtually. We provide technical background in dynamic epistemic fixed-point logic, draw some analogies with the work of Krzysztof Apt, and finally use our framework to discuss some new scenarios for rational (inter)action in extensive games.

We compare the relative strength of four widely used procedures on finite strategic games: iterated elimination of weakly/strictly dominated strategies by a pure/mixed strategy. A complication is that none of these procedures is based on a monotonic operator. To deal with this problem we use 'global' versions of these operators. The ones corresponding with strict dominance are monotonic which allows us to use them in the epistemic framework of game theory based on possibility correspondences as `a stand alone' concept of rationality.

We propose a dynamic epistemic framework for the verification of security protocols. We introduce a dynamic epistemic logic equipped with iteration and cryptographic supplements in which we can formalize and check (epistemic) requirements of security protocols. On top of this, we give a general guide how to go from a protocol specification to its representation in our framework. We do a case study on a simplified version of a protocol for confidential message comparison.

This is joint work with Francien Dechesne.

Many logical systems today were designed to describe behaviour of intelligent interacting agents over time. Frameworks with a certain following include Interpreted Systems (IS, Fagin et al.), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam), STIT (Belnap et al.) and one might even add Process Algebra and Game Semantics (Abramsky) to this list. The main purpose of this paper is to look at one particular interface, between two systems that both address the dynamics of knowledge and information flow in multi-agent systems. One is the IS/ETL paradigm and the other framework is that of Dynamic Epistemic Logic (DEL). It has long been unclear how to compare these approaches in the most fruitful manner. We systematize and strengthen the interface between IS/ETL and DEL to an extent where fruitful interaction becomes possible, including new research questions on both sides. Note that we are not reducing one framework to another, nor simply `applying' them. We show rather how ETL and DEL lead to interesting new issues when merged as accounts of intelligent agents.

This is joint work with Johan van Benthem and Jelle Gerbrandy