Logic of confidence

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.