Consensus, Inconsistency, Emergence: what's paraconsistency got to do with it?

TL;DR

This paper explores the implications of paraconsistency and inconsistency in distributed consensus, extending the FLP theorem, and investigates how complex systems theory can explain emergent behaviors and the potential for paraconsistent algorithms.

Contribution

It generalizes the FLP impossibility theorem using oracles and applies complex systems theory to analyze the emergence of inconsistency in consensus.

Findings

FLP theorem holds even with generalized computation models

Inconsistency can be an emergent property in distributed systems

Paraconsistent logics may prevent triviality despite inconsistency

Abstract

The consensus problem, briefly stated, consists of having processes in an asynchronous distributed system agree on a value. It is widely known that the consensus problem does not have a deterministic solution that ensures both termination and consistency, if there is at least one faulty process in the system. This result, known as the FLP impossibility theorem, led to several generalizations and developments in theoretical distributed computing. This paper argues that the FLP impossibility theorem holds even under a generalized definition of computation through oracles. Furthermore, using a theoretical machinery from complex systems, this paper also posits that inconsistency may be an emergent feature of consensus over distributed systems by examining how a system transitions phases. Under the same complex systems framework, this paper examines paraconsistent logics, arguing that while inconsistency is not an emergent feature for these logics, triviality may be. Lastly, some attention is given to the possibility of developing consensus algorithms capable of paraconsistent reasoning.