Communicability criteria of law equations discovery

Abstract

The "laws" in science are not the relations established by only the objective features of the nature. They have to be consistent with the assumptions and the operations commonly used in the study of scientists identifying these relations. Upon this consistency, they become communicable among the scientists. The objectives of this literature are to discuss a mathematical foundation of the communicability of the "scientific law equation" and to demonstrate "Smart Discovery System (SDS)" to discover the law equations based on the foundation. First, the studies of the scientific law equation discovery are briefly reviewed, and the need to introduce an important communicability criterion called "Mathematical Admissibility" is pointed out. Second, the axiomatic foundation of the mathematical admissibility in terms of measurement processes and quantity scale-types are discussed. Third, the strong constraints on the admissible formulae of the law equations are shown based on the criterion. Forth, the SDS is demonstrated to discover law equations by successively composing the relations that are derived from the criterion and the experimental data. Fifth, the generic criteria to discover communicable law equations for scientists are discussed in wider view, and the consideration of these criteria in the SDS is reviewed. © Springer-Verlag Berlin Heidelberg 2007.