He ran to catch the bus. He is carrying a suitcase. Inferences are not achieved with mathematical rigor. Inferences do not have the certainty obtained with deductive reasoning. Inferences tend to reflect prior knowledge and experience as well as personal beliefs and assumptions.
Inferences thus tend to reflect one's stake in a situation or one's interests in the outcome.
People may reason differently or bring different assumptions or premises to bear. Given evidence that PCB's cause cancer in people, and that PCB's are in a particular water system, all reasonable people would reach the conclusion that that water system is dangerous to people. But given evidence that there is an increase in skin cancer among people who sun bathe, not all people would conclude that sunbathing causes skin cancer. Sun bathing, they might argue, may be coincidental with exposure to other cancer causing factors. More often than not, disagreements are based not on differences in reasoning, but in the values, assumptions, or information brought to bear.