We study deduction, captured by datalog-style rules, in the presence of contradictions, captured by functional depen- dency (FD) violation. We propose a simple non-deterministic semantics for datalog with FDs based on inferring facts one at a time, never violating the FDs. We present a novel proof theory for this semantics. We also discuss a set-at-a- time semantics, where at each iteration, all facts that can be inferred are added to the database, and then choices are made between contradicting facts. We then build upon a distributed datalog idiom, namely Webdamlog, to define a semantics for the distributed setting. Observe that contra- dictions naturally arise in such a setting, with different peers having conflicting information or opinions. We study differ- ent semantics for this setting.