Abstract

Logic is an old science. It had developed rather slowly over a very long period; in the last one hundred years, however, it has made swift progress. That part of logic which developed rapidly in the last one hundred years is usually called modern logic. The principal part of modern logic is mathematical logic. Mathematical logic, according to its properties, is both logic and mathematics. The establishment of mathematical logic is a leap in the history of logic. Its development is essential to the study of modern mathematics. It is one of the foundation theories of computer science. The development of mathematical logic has progressed in three different directions and may be classified into three aspects