This paper presents a formal approach to design of a solver of an intelligent managementinformation system and its implementation. The approach implies set theoretic modeling based on thegeneral systems concepts and implementation in the extProlog. There are research efforts which attack(optimization)problems using the set theory and logics.Furthermore, they use logic programming languages for their implementation. Although their methodslook quite similar to the approach of this paper, there are clear differences between them. This paper isinterested in exploration of the solving system rather than algorithms. The paper first presents a design and implementation procedure of a solver. Then, classificationof problems is discussed. The least structured class of the classification is the target of this paper. Adata mining system is an example of the class. Formal theories are derived for the design procedure assuming the least structured case. A solvingstrategy,which is called a hill climbing method with a The paper presents a formal approach to design of a solver of an intelligent management information system and its implementation. The approach implies set theoretic modeling based on the general systems concepts and implementation in the extProlog. There are research efforts which attack (optimization) problems using the set theory and logics.Furthermore, they use logic programming languages ​​for their implementation. The paper methods are quite similar to the approach of this paper, there are clear differences between them. This paper isinterested in exploration of the solving system rather than algorithms. The paper first presents a design and implementation procedure of a solver. Then, the least of class classification of the target of this paper. Formal theories are derived for the design of the class. the least structured case. A solvingstrategy, which is called a hill clim bing method with a