This paper points out that the notion of non-conservative extension of a knowledge base (KB) is important to the distributed logical setting of peer-to-peer inference systems (P2PIS), a.k.a. peer-to-peer semantic systems. It is useful to a peer in order to detect/prevent that a P2PIS corrupts (part of) its knowledge or to learn more about its own application domain from the P2PIS. That notion is all the more important since it has connections with the privacy of a peer within a P2PIS and with the quality of service provided by a P2PIS. We therefore study the following tightly related problems from both the theoretical and decentralized algorithmic perspectives: (i) deciding whether a P2PIS is a conservative extension of a given peer and (ii) computing the witnesses to the corruption of a given peer's KB within a P2PIS so that we can forbid it. We consider here scalable P2PISs that have already proved useful to Artificial Intelligence and DataBases.