A logical system based on rules and its application in teaching mathematical logic

Abstract

As it is known, the contemporary formal logic has sufficient means to for? malize each proof, in particular each mathematical proof. But it is also known that the formalization of proofs by means of logical laws gives often very long and burdensome constructions even in the case of simple intuitive proofs. Thus some divergences arise between the theoretical and practical scope of logic in this domain. Hence there appears the tendency to introduce such logical means which would enable us to eliminate these divergences and to formalize proofs in a practically simple and didactically easy manner. To bring logic as near as possible to the practice of proofs was one of the aims of the authors of the logical systems based on rules.1 It seems however that the existing systems of logic based on rules are only to a small extent pra? ctically and didactically exploited. In the present article we shall describe a logical system based on rules2. For some years we were using it in the lectures of formal logic and in some branches of mathematics. The practice showed that students easily and quickly learn the rules of the system and ? without the help of the teachers ? perform