Logical inference has three canonical forms: deductive, inductive, and abductive

Inference is defined in the logical tradition as "steps in logical reasoning, moving from premises to logical consequences" — either a conclusion reached on the basis of evidence and reasoning, or the process of reaching such a conclusion. The three canonical forms are:

Deductive inference

Deductive reasoning moves from general premises to a logically certain conclusion. The classic example: All humans are mortal. All Greeks are humans. Therefore, all Greeks are mortal. If the premises are true and the argument form is valid, the conclusion cannot be false. Aristotle's Prior Analytics (c. 350 BCE) formalized deduction via the syllogism, providing the first systematic account of valid inference.

Inductive inference

Inductive reasoning moves in the opposite direction: from particular observations to a general principle. No number of confirming instances logically guarantees the conclusion — the classic problem of induction. Induction is the backbone of empirical science and of most machine-learning generalization: a model trained on finite examples is expected to infer a pattern that holds for unseen inputs.

Abductive inference

Abductive reasoning was named and theorized by the American philosopher Charles Sanders Peirce. It "seeks neither logical certainty nor a universal conclusion but a 'best explanation' based on likelihood given the evidence." Abduction is inference to the most plausible hypothesis. Medical diagnosis, detective work, and LLM generation are all described as abductive in character — none can logically prove their outputs, but all aim at the most credible account of available evidence.

Fallacies and limits

Incorrect inferences constitute fallacies. Confirmation bias — "seeking information that confirms beliefs rather than information that may contradict them" — is among the most documented sources of systematic inferential error in human cognition.

Relation to AI

Wikipedia notes that "artificial intelligence researchers develop automated inference systems to emulate human inference," a tradition that runs from 1970s expert systems (see claim-inference-classic-ai-engines) through modern neural networks. The three-way typology remains analytically useful: training is an inductive process; chain-of-thought reasoning by an LLM might be understood as a blend of deductive steps and abductive leaps. See also claim-extended-thinking-as-serial-inference-compute.

See also: claim-inference-word-etymology, claim-inference-classic-ai-engines, claim-statistical-inference-meaning