 Varying the properties of the accessibility relations \(R_{1},R_{2},\ldots,R_{n}\), as described above results in different epistemic logics. For instance system K with common knowledge is determined by all frames, while system S4 with common knowledge is determined by all reflexive and transitive frames. Similar results can be obtained for the remaining epistemic logics (Fagin et al. 1995). For more, consult  the entry on common knowledge.