Discovery of First Principle Based on Data - Driven Reasoning

We propose a novel approach to automatically discover formulae of rst principles from the measurement data. Our approach lies in between the deductive approaches as represented by dimension-based and symmetry-based reasoning and the empirical approaches as represented by BACON. We try to use the knowledge of the target relation as little as possible, so that it can be applied to various domains which are not limited to physics problem. In spite of its data-driven feature, the formulae obtained by our approach are ensured to represent sound rst principles similarly to the dimensionbased approach. The basic idea is the combined use of deductive \scale-based reasoning " and data-driven reasoning. The features of our approach are demonstrated by discovering the basic formulae of the ideal gas law and Black's speci c heat law from a set of numeric data. This approach may provide a basis to discover qualitative rst principles of ambiguous domains such as biology, psychology, economics and social science.