In this SNSF-funded project, we plan to develop and investigate new notions of group knowledge in multi-agent systems. The two classic forms of group knowledge are common knowledge and distributed knowledge. We will devise novel variants of these notions, which are important for distributed computing, and study their logical and mathematical properties.

One part of our project deals with eventual common knowledge (ECK), which is a form of common knowledge that is relevant for the epistemic analysis of many applications. However, ECK needs to be better understood from a mathematical and logical perspective.
We will develop axiomatic systems for ECK and investigate its meta-logical properties, such as compactness, finite model property, etc. We will then study the relationship between task solvability and the properties of the corresponding form of ECK. In particular, we will establish the precise connection of ECK and the Firing Rebels with Relay problem, which is a particularly interesting case in distributed computing.

The second part of the project is concerned with novel variants of distributed knowledge. Simplicial models are an essential tool in the area of distributed computing. Recently, it has been observed that simplicial models also provide an interesting semantics for multi-agent epistemic logic. These models focus on the local states of the agents instead of the global state of the system (represented as a possible world). This simplicial semantics makes it possible to represent new forms of distributed knowledge.
Current simplicial models support notions of knowledge. However, in the presence of Byzantine agents, only forms of belief can be obtained, but not knowledge. We will adapt simplicial models to support belief and belief dynamics. Further, we will develop and study an epistemic logic for simplicial sets. This is the most general form of simplicial models. Yet, their logical analysis is still missing.