We begin by introducing the Computer Science branch of Natural Language Processing, then narrowing the attention on its subbranch of Information Extraction and particularly on Named Entity Recognition, discussing briefly its main methodological approaches. It follows an introduction to state-of-the-art Conditional Random Fields under the form of linear chains. Subsequently, the idea of constrained inference as a way to model long-distance relationships in a text is presented, based on an Integer Linear Programming representation of the problem. Adding such relationships to the problem as automatically inferred logical formulas, translatable into linear conditions, we propose to solve the resulting more complex problem with the aid of Lagrangian relaxation, of which some technical details are explained. Lastly, we give some experimental results.