Common knowledge is a fundamental notion of group knowledge.

Common knowledge is a necessary and sufficient condition for reaching an agreement and for coordinating actions.

Three famous illustrations:

1. Coordinated attack.
2. Agreeing to disagree.
3. Simultaneous byzantine agreement.

Relation between common knowledge and agreement:

 

Formally capture the cognition:

 

Learning from book names the same by  Ronald Faigin, Joseph Y. Halpern, Yoram Moses, Moshe Y. Vardi.

Duration: Two Days,

Day 1: Chapters 1 to 6 and Day 2: Chapters 7 to 11

1. Introduction and Overview.
2. A Model for Knowledge.
3. Completeness and Complexity.
4. Knowledge in Multi-Agent Systems.
5. Protocols and Programs.
6. Common Knowledge and Agreement.
7. Knowledge-Based Programming.
8. Evolving Knowledge.
9. Logical Omniscience.
10. Knowledge and Computation.
11. Common Knowledge Revisited.

This course investigates reasoning about knowledge