Logic is the study of the formal relationships between propositions — what follows from what, what contradicts what, what is required for valid inference. The Greek syllogistic, the Indian pramāṇa theory, the Buddhist catuṣkoṭi (fourfold negation), and medieval Islamic philosophy of logic each developed rigorous but partially distinct approaches to formal reasoning. Understanding multiple logical traditions is not relativism but the recognition that formal reasoning itself has a history, and that different traditions have explored different aspects of what rigorous inference requires.
Each step builds on the last.