Logic of Confidence

Pavel Naumov and  Jia Tao

The article studies knowledge in multiagent systems where data available to the agents may have small errors. To reason about such uncertain knowledge, a formal semantics is introduced in which indistinguishability relations, commonly used in the semantics for epistemic logic S5, are replaced with metrics to capture how much two epistemic worlds are different from an agent’s point of view. The main result is a logical system sound and complete with respect to the proposed semantics. [pdf]

The Ryoan-ji Axiom for Common Knowledge on Hypergraphs

Jeffrey Kane and Pavel Naumov

The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryoan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryoan-ji axiom and two additional axioms, is proven to be sound and complete. [pdf]

On Interchangeability of Nash Equilibria in Multi-Player Strategic Games

Pavel Naumov and Brittany Nicholls

The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory. [pdf]