How did Peirce distinguish abduction from induction and deduction?

Charles Sanders Peirce distinguished abduction from deduction and induction by defining it as the process of forming and accepting a hypothesis on probation to explain surprising facts. While he made significant contributions to deductive logic, he viewed himself primarily as a student of the "logic of science," which encompasses both induction and abduction.1

Peirce sought to establish these three modes of reasoning as distinct yet positively related components of logic:1

• Deduction: Involves deriving conclusions that follow necessarily from general or universal premises. It is often associated with mathematical logic and does not produce information not already contained within the premises.231
• Induction: A method of reasoning that involves forming a generalization based on observed particular instances, inherently involving an element of probability.23
• Abduction (or "retroduction"): The process of inferring the best explanation for a surprising observation. Unlike deduction, which guarantees the truth of a conclusion if the premises are true, abduction involves accepting a hypothesis as a "working hypothesis" to guide further research.21

Peirce’s work on pragmatism was closely tied to this logic of science, as he viewed beliefs as habits of action and scientific inquiry as a method for fixing those beliefs.1