Conditions of Law Equations and the Approach of their Discovery

| This paper discusses the criteria to judge if a given equation represents a set of rst principle-based laws or a super cial relation. Based on the criteria, the approach of scienti c discovery to automatically discover law equations from data is presented. The state of the art of the scienti c law equation discovery has remained to derive candidate law equations without taking into account the criteria of generic mathematical admissibility, and thus many super cial relations can be resulted under the high computational complexity. The principles and the approach presented in this paper overcome these drawbacks. The performance of the presented approach is demonstrated and evaluated through some applications to physics and sociology, and their abilities to derive candidate law equations with high con dence and high e ciency have been con rmed. Keywords| Scienti c Discovery, Law Equation, Scale-