COMPARISON OF DEDUCTION THEOREMS IN DIVERSE LOGIC SYSTEMS

Deduction theorem and its weak forms in classical mathematical logic system, Łukasiewicz logic system, Gödel logic system, product logic system, and the fuzzy logic system ℒ* are discussed and compared. It is pointed out that the weak form of deduction theorem in ℒ* has a clear structure and can be employed to define the concept of consistency degrees of finite theories. Moreover, it is clarified that the negation operator of Gödel type is too strong and is therefore unsuitable for establishing fuzzy logic systems.