Data Dependencies on Inequalities

Numerical inequalities present new challenges to data-base systems that keep track of "dependencies," or reasons for beliefs. Care must be taken in interpreting an inequality as an assertion, since occasionally a "strong" interpretation is needed, that the inequality is best known bound on a quantity. Such inequalities often have many proofs, so that the proper response to their erasure is often to look for an alternative proof. Fortunately, abstraction techniques developed by data-dependency theorists are robust enough that they can be extended fairly easily to handle these problems. The key abstractions involved are the "ddnode," an abstract assertion as seen by the data-dependency system, and its associated "signal function," which performs indexing, re-deduction, and garbage-collection functions. Such signal functions must have priorities, so that they don’t clobber each other when they run.