From expert systems to those developing theories of subject domains

The present paper deals with expert systems of the second generation characterized by the formula: Domain Theory + Problem Solving Knowledge = Heuristic Rules. Tendencies of further expert systems development are considered. The results of philosophical logic, measurement theory and axiomatic theory of decision making are noted to give more precise definition of the first component--Domain Theory, and the idea of "natural" classification of knowledge makes more precise definition of the second one. The above results show that the aim of constructing expert systems is to produce systems developing theories of subject domains. There is a short description of project for instrumental expert system of developing empirical (experimentally proved) theories in various subject domains. The project is based on the following main results and methods. The results obtained in philosophical logic, measurement theory and axiomatic theory of making decisions show that the empirical theory of subject domain is a system of quantities connected (with each other) by laws. The quantities and laws are closely connected with each other. A functional form of the laws is simple because the numerical representation of quantities embodied in the law and the functional form of the law are often produced from the same system of axioms. The functional form of the laws and a set of mathematical operations having sense for numeric values of a certain quantity are determined at a theoretical-model level by systems of axioms and empirical systems (algebraic systems in which the main set of quantity (quantities) values and a set of relationships, operations and constants are interpreted in terms of subject domain). For determination feasibility of particular system of axioms on a partially-determined empirical system a method of detecting the regularities in the first order language has been elaborated. Thus, the empirical theory of subject domain should contain the three complementary empirical theories--qualitative, logical, and quantitative ones. Transition of theory from a qualitative state to quantitative one is possible only through logical empirical theory. Logical theory performs axiomatic analysis of subject domain. Transition from logical theory to quantitative one takes place by means of the results of both the measurement theory and axiomatic theory of decision making. The qualitative empirical theory is a description of subject domain and that knowledge (if any) which is already available in this subject domain. Description of subject domain is setting a system of notions and class of objects to be studied as well as quantities, data and measuring devices (including an expert) interpreted in the system of notions. Making more precise definition of the component "Problem Solving Knowledge" is performed by the methods of "natural" classification of knowledge based on the principle: objects, events, phenomena of the same class are described by identical regularities, of different class by different ones. The original method of "natural" classification of objects is considered in the paper.