Analytical Approach to Problem Solving

Abstract

The work is devoted to the logical analysis of the problem solving. Typically, in each task we highlight the conditions and goals that we have to find or build. In this case the solution of the problem is seen as a kind of deduction from goals to the conditions. This representation of problems and their solutions is too narrow. In actual practice, a task or goal is often formulated in quite general terms as a wish. For example, the task to build a railway between the two cities. Sufficient conditions for the solution of this problem are initially unclear and should be found. For this kind of problems their solution can be represented as a gradual refinement of goals and their reduction to a simpler sub-goals. The methods by which we produce clarification of goals, we took from the theory of definitions. In this paper we construct a calculus in the form of analytical tables, which allows us to represent the whole process algorithmically.