axiomatic basis

The axiomatic method is a procedure in logic where an entire system is built through logical deduction from basic propositions called axioms or postulates. These axioms are fundamental, indemonstrable principles that are generally accepted. The oldest examples of this method are found in Aristotle's syllogistic logic and Euclid's geometry.12

Key principles in logic, traditionally known as the laws of thought, include the law of contradiction, the law of excluded middle, and the principle of identity. These laws form the basis for deductive reasoning, where conclusions must necessarily follow from premises. The axiomatic method provides a structured way to develop complex systems from these foundational truths.34