Introducing Real Variables and Integer Objective Functions to Answer Set Programming

Answer set programming languages have been extended to support linear constraints and objective functions. However, the variables allowed in the constraints and functions are restricted to integer and Boolean domains, respectively. In this paper, we generalize the domain of linear constraints to real numbers and that of objective functions to integers. Since these extensions are based on a translation from logic programs to mixed integer programs, we compare the translation-based answer set programming approach with the native mixed integer programming approach using a number of benchmark problems.