Many recent advances in complex domains such as Natural Language Processing (NLP) have taken a discriminative approach in conjunction with the global application of structural and domain specific constraints. We introduce LBJ, a new modeling language for specifying exact inference systems of this type, combining ideas from machine learning, optimization, First Order Logic (FOL), and Object Oriented Programming (OOP). Expressive constraints are specified declaratively as arbitrary FOL formulas over functions and objects. The language?s run-time library translates them to a mathematical programming representation from which an exact solution is computed. In addition, the compiler leverages an existing OOP language: objects and functions are grounded as the OOP objects and methods that encapsulate the user?s data.