n a peer-to-peer inference system, there is no centralized control or hierarchical organization: each peer is equivalent in functionality and cooperates with other peers in order to solve a collective reasoning task. Since peer theories model possibly different viewpoints, even if each local theory is consistent, the global theory may be inconsistent. We exhibit a distributed algorithm detecting inconsistencies in a fully decentralized setting. We provide a fully distributed reasoning algorithm, which computes only well-founded consequences of a formula, i.e., with a consistent set of support.