Wanted Dead or Alive: Epistemic Logic for Impure Simplicial Complexes

We propose a logic of knowledge for impure simplicial complexes. Impure complexes represent distributed systems under uncertainty over which processes are still active (are alive) and have failed or crashed dead). Our work generalizes the pure complexes, where all alive, by Goubault et al. logical semantics has satisfaction relation defined simultaneously with definability relation. The latter restricts formulas allowed to truth value: dead cannot know be uncertain about any proposition, live propositions involving they dead. satisfies some but not axioms rules modal S5. correspond Kripke models each agent’s accessibility is an equivalence on subset domain only. also notion bisimulation show correspondence.