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

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…
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Taxonomy
TopicsPhilosophy and Theoretical Science
