Research Initiation: Foundations of Quantitative Inference About Sets of Design Possibilities

大多数工程数学适用于表示单一运行条件下的单一对象。然而，机械设计者必须同时对许多设计可能性进行推理；即，在一组操作条件下的对象集。以前的工作已经产生了一种执行这种推理的形式化方法，称为标记区间演算。这种形式已经在机械设计编译器中得到了经验验证，该程序针对广泛的设计问题接受机械原理图、规范和实用函数，并返回目录号以实现最佳实施。然而，微积分的测试版本相对复杂，而且只进行了部分数学分析。研究人员试图简化微积分，为它的所有术语和所有推论的证明制定准确的定义，并澄清围绕它的一些问题。这将使更强大和可靠的编译器的开发成为可能，并进一步加深对设计推理的基本理解。

Most engineering mathematics is appropriate for representing a single object under a single operating condition. Mechanical designers, however, must reason simultaneously about many design possibilities; that is, sets of objects under sets of operating conditions. Previous work has produced a formalism for performing such inferences, called the labeled interval calculus. This formalism has been empirically validated in a mechanical design compiler, a program which for a wide range of design problems accepts mechanical schematics, specifications, and utility functions, and returns catalog numbers for optimal implementations. However, the tested version of the calculus is relatively complex, and has been only partially analyzed mathematically. The researcher seeks to simplify the calculus, develop precise definitions for all its terms and proofs for all its inferences, and clarify a number of issues surrounding it. This will enable the development of more powerful and reliable compilers, as well as furthering the basic understanding of design reasoning.