In this talk, I shall introduce two mathematical programming models, viz., Quantified Linear Programming and Quantified Integer Programming. Quantified Linear Programming is a generalization of traditional linear programming from the logical perspective. In traditional linear programming, we are given a system of linear inequalities, say Ax ≤ b and asked whether the polyhedron defined by these inequalities is empty. In Quantified Linear Programming, you are given a polytope A[x, y] ≤ b and a quantifier specification Q(x, y). The question then is whether the specification has a model. Quantified Integer Programming extends Integer Programming similarly. Both these models have a number of applications, especially in capturing requirements in embedded systems. We shall present some of our results on these two topics.