一阶混合线性规划
First-Order Mixed Integer Linear Programming
摘要：
混合整数线性规划（MILP）是一个强大的表示，经常用来制定决策问题的不确定性。然而，它缺乏一种自然的机制来推理对象、对象类和关系。另一方面，一阶逻辑（FOL）擅长于对对象类的推理，但缺乏对不确定性的丰富表示。虽然在MILP中表示命题逻辑已经被广泛探索，但还没有理论将FOL与MILP完全结合起来。我们提出了一个新的表示，称为一阶编程或FOP，其中包括FOL和MILP。建立了一阶规划的形式化推理方法，包括一个完整的整数一阶规划的提升推理过程。由于FOP可以提供指数级的节省表示和证明的大小相比，FOL，因为表示和证明从来没有显着长于FOP比FOL，我们预计，在FOP的推理将比在FOL推理相应的问题。
英文摘要：
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propositional logic in MILP has been extensively explored, no theory exists yet for fully combining FOL with MILP. We propose a new representation, called first-order programming or FOP, which subsumes both FOL and MILP. We establish formal methods for reasoning about first order programs, including a sound and complete lifted inference procedure for integer first order programs. Since FOP can offer exponential savings in representation and proof size compared to FOL, and since representations and proofs are never significantly longer in FOP than in FOL, we anticipate that inference in FOP will be more tractable than inference in FOL for corresponding problems.
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