Algebraic Predicates for Empirical Data

It is widely assumed that the assignment of truth values to non-trivial algebraic predicates containing numerical data is possible only if the data are exact and if exact computation is employed. But in many application areas the answers to questions like “Are all zeros of that (model) polynomial in the left half-plane?” are of principal importance. We develop a framework in which algebraic predicates with empirical data are assigned a positive real number in place of a truth value. This validity value permits an interpretation which is more informative that the classical “yes - no” answer. It depends continuously on the data and can thus be computed approximately by floating-point arithmetic. A number of non-trivial examples support the usefulness of our approach.