extends propositional logic with necessity ($\square$) and possibility ($\diamond$) operators
a statement is necessary if it holds in all accessible worlds; possible if it holds in at least one. Kripke semantics (1963) formalizes this via a graph of possible worlds connected by accessibility relations — the original knowledge graph.
in the cybergraph: possible worlds are neighborhoods of a particle. necessity is consensus across all linked neurons. possibility is any single neuron asserting a cyberlink. the graph topology itself defines accessibility — what each node can see and reach.
variants: epistemic (knowledge/belief), deontic (obligation/permission), doxastic (belief revision). each maps to a different type of edge in the cybergraph.