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"This monograph deals with aspects of the computer programming process that involve techniques derived from mathematical logic. The author focuses on proving that a given program produces the intended result whenever it halts, that a given program will eventually halt, that a given program is partially correct and terminates, and that a system of rewriting rules always halts. Also, the author describes the intermediate behavior of a given program, and discusses constructing a program to meet a given specification."

"We specifically focus on the following issues: 1. An important question when modeling continuous optimization problems is how we should handle overconstrained problems, i.e. problems that have no solutions. 2. Users of a programming language often want a rich language that is easy to model in. 3. A well-known technique for solving ASP consists of translating a program P to a propositional theory whose models exactly correspond to the answer sets of P. "