Paper III · Cnidarian Foundation
Paraconsensus
Paraconsistent four-valued logic for federated meta-learning on BlockDAG
Larry Klosowski · Kurt McKelvey
Citation
Larry Klosowski, Kurt McKelvey (2026.04). Paraconsensus: Paraconsistent four-valued logic for federated meta-learning on BlockDAG. Gradient Paper III, Cnidarian Foundation. cnidarian.org/papers/paraconsensus
Abstract
Standard consensus protocols treat disagreement as failure: when nodes produce contradictory outputs, the protocol picks one and discards the others. Paraconsensus extends consensus to a paraconsistent four-valued logic — true, false, both, neither — that preserves disagreement as information. The paper develops the formal model, proves liveness and safety in the BFT setting, and demonstrates the protocol's performance on a federated meta-learning workload where contradictory model outputs carry epistemic content. The Citrate Network's inference verification layer is the production implementation.
Authors
- Larry Klosowski
- Kurt McKelvey
Why this paper matters to the cooperative
Paraconsensus is the verification primitive that Citrate's "AI you can verify, instead of AI you have to trust" claim rests on. When the network records disagreement rather than discarding it, the audit surface is real.