# Solution Problem

## Solution Problem

(or decision problem), an important concept in logic. The problem of constructing an algorithm that recognizes by any object of a set *V* whether or not the object belongs to a set *A* is called the solution problem of the given set *A* of constructive objects (with respect to some convolute set *V* of constructive objects). The solution problem of a set of all provable formulas of a formal system (or calculus) with respect to the set of all the system’s formulas is called its solution problem, or more accurately, the solution problem for provability. The solution problem of the set of all true formulas of an interpreted formal system (a formalized language) with respect to the set of all the system’s formulas is called a semantic solution problem, or the solution problem for truth.