Synergistic knowledge

Simplicial complexes are a successful model for distributed computing. They have recently been observed to provide an interesting model for epistemic multi-agent logic where the agents' local states are the main building blocks (instead of the global states). A natural generalization is to study epistemic logic on semi-simplicial sets. However, finding the appropriate modal logic for semi-simplicial models has been an open question. We answer this by introducing the logic of synergistic knowledge and establishing its soundness and completeness. •Exploring simplicial semantics for modal logic based on semi-simplicial sets.•New form of distributed knowledge: Synergistic Knowledge.•Sound and complete system Syn for the language of synergistic knowledge.