Note1 – the scope of these definitions is limited to semantic web discipline.
Note2 – 05.10.2009 – updated thanks to a comment from Horst.
Note3 – 06.10.2009 – changed “inference” to an effect instead of process/action (thanks Horst as well). If it is an action, then it is part of the reasoning action. And reasoning action is part of the inference action. So, inference=reasoning, which is not ok.

There is a bunch of definitions about each of the terms, here I try to define with the purpose of marking the main differences and relations between “inference”, “reasoning” and “consistency check”.

inference – the effect of triples added to a model achieved via reasoning (using OWL / SWRL rules / etc.)

reasoning – process of calculating logical consequences from a set of asserted facts or axioms (from wiki). The goal of reasoning can be an inference or a consistency check.

consistency check – verify if there are no logical clashes (contradictions) in the given model