The model of persuasion that primarily appeals to logic is the Elaboration Likelihood Model (ELM), particularly the central route to persuasion. In this model, individuals are persuaded by the logical arguments and the quality of the information presented. When people are motivated and able to process information deeply, they are more likely to engage with the content's logical aspects, critically evaluating the arguments based on evidence and reasoning.
Another common approach that emphasizes logical appeal is the use of logos, which is one of Aristotle's three modes of persuasion (the others being ethos, relating to credibility or ethics, and pathos, relating to emotions). Logos involves using facts, statistics, logical reasoning, and structured arguments to convince the audience.