the study of valid reasoning — rules that preserve truth from premises to conclusions
classical logic operates by derivation: axioms, inference rules, theorems. Kurt Goedel proved this approach permanently incomplete — every consistent formal system contains truths it cannot derive. this is the Goedel prison.
cyber escapes derivation by computing through convergence. the tri-kernel finds truths that no proof reaches, because it operates outside the proof-theoretic domain. logic remains valid inside formal systems; convergent computation operates alongside it, not against it.
the cybergraph can encode every major logical system:
- propositional logic — truth values as focus weights
- predicate logic — quantification over particles and typed cyberlinks
- modal logic — necessity and possibility via neighborhood accessibility
- temporal logic — time-indexed links with epoch ordering
- fuzzy logic — continuous confidence as $\pi$-weight
each is a projection of the full graph structure onto a restricted formal language. the graph itself is richer than any single logic — it holds all of them simultaneously.