1998 Volume 5 Issue 2 Pages 2_80-2_94
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 in the process where we identify these relations, and also they have to be comprehensive for us and usable in the analysis of the nature. The objectives of this paper are to discuss a mathematical foundation of measurement in terms of representational change, to provide extended characterization of scientific laws based on the foundation, and to propose a method to discover the laws. First, the conditions of a “scientific law” that must hold among measured quantities are analyzed. Second, the axiomatic foundation of measurement processes and cognitive scales of feature quantities are discussed. Third, the strong constraints on the admissible formulae of the laws are shown on the basis of the foundation. Forth, a method is proposed to discover laws by successively composing the constraints that are derived from the required conditions and the experimental data. Finally, the validity and the performance of the method are demonstrated and evaluated through computer simulations.
