Design-theoretic encoding of deterministic hypotheses as constraints and correlations into U-relational databases

TL;DR

This paper introduces a novel method to encode deterministic scientific hypotheses as constraints and correlations into U-relational databases, enabling effective uncertain data management in data-driven science.

Contribution

It presents a design-theoretic approach to encode hypotheses as functional dependencies and correlations into U-relational databases, bridging deterministic models and uncertain data handling.

Findings

Effective algorithms for encoding hypotheses into U-relational databases.

Applicable to both quantitative and qualitative hypotheses.

Initial tests show practical viability in computational science use cases.

Abstract

In view of the paradigm shift that makes science ever more data-driven, in this paper we consider deterministic scientific hypotheses as uncertain data. In the form of mathematical equations, hypotheses symmetrically relate aspects of the studied phenomena. For computing predictions, however, deterministic hypotheses are used asymmetrically as functions. We refer to Simon's notion of structural equations in order to extract the (so-called) causal ordering embedded in a hypothesis. Then we encode it into a set of functional dependencies (fd's) that is basic input to a design-theoretic method for the synthesis of U-relational databases (DB's). The causal ordering captured from a formally-specified system of mathematical equations into fd's determines not only the constraints (structure), but also the correlations (uncertainty chaining) hidden in the hypothesis predictive data. We show how to process it effectively through original algorithms for encoding and reasoning on the given hypotheses as constraints and correlations into U-relational DB's. The method is applicable to both quantitative and qualitative hypotheses and has underwent initial tests in a realistic use case from computational science.