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In recent years, several authors have been investigating simplicial models, amodel of epistemic logic based on higher-dimensional structures calledsimplicial complexes. In the original formulation, simplicial models werealways assumed to be pure, meaning that all worlds have the same dimension.This is equivalent to the standard S5n semantics of epistemic logic, based onKripke models. By removing the assumption that models must be pure, we can gobeyond the usual Kripke semantics and study epistemic logics where the numberof agents participating in a world can vary. This approach has been developedin a number of papers, with applications in fault-tolerant distributedcomputing where processes may crash during the execution of a system. Adifficulty that arises is that subtle design choices in the definition ofimpure simplicial models can result in different axioms of the resulting logic.In this paper, we classify those design choices systematically, and axiomatizethe corresponding logics. We illustrate them via distributed computing examplesof synchronous systems where processes may crash.

Simplicial Models for the Epistemic Logic of Faulty Agents