Finding new consequences of an observation in a system of agents

When a new observation is added to an existing logical theory, it is often necessary to compute new consequences of this observation together with the theory. This paper investigates whether this reasoning task can be performed incrementally in a distributed setting involving first-order theories. We propose a complete asynchronous algorithm for this non-trivial task, and illustrate it with a small example. As some produced consequences may not be new, we also propose a post-processing technique to remove them.