Logic applied to integer programming and integer programming applied to logic

The many connections between the methods of Computational Logic and Integer Programming (IP) are surveyed. It is shown how computational problems arising in formal logic can be solved by IP. Also it is shown how the methods of logic are applicable both to modelling and solving IP models. It is shown how Fourier–Motzkin elimination for Linear Programming, when specialised to 0–1 IP models, gives rise to the logic method of Resolution. Finally conventional IP methods are applied to solving logical inference problems.