Both semantic web applications and individuals are in need of knowledge infrastructures that can be used in dynamic and distributed environments where different autonomous entities create knowledge and build their own view of a domain. Our framework represents this using evolving simple contextual ontologies and mappings between them, at the same time as incremental logical coherence is maintained. The definition of semantic autonomy includes these aspects. Our earlier research has shown that a knowledge infrastructure can have semantic autonomy that maintains global consistency, if the knowledge representation is kept simple. We generalize that research by investigating what happens if the consistency of a knowledge infrastructure is bounded 1) within certain regions called spheres of consistency, and 2) by allowing a limited variable degree of inconsistency. Our experiments show that a phase transition can occur in this kind of system, beyond which constant-time and constant-memory c...