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.
