A syllogism, or logical appeal, (Greek: συλλογισμός — "conclusion," "inference"), (usually the categorical syllogism) is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form.In Aristotle's Prior Analytics, he defines syllogism as "a discourse in which, certain things having been supposed, something different from the things' supposed results of necessity because these things are so." (24b18–20)Despite this very general definition, he limits himself first to categorical syllogisms (and later to modal syllogisms). The syllogism was at the core of traditional deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations. Syllogism was superseded by first-order predicate logic following the work of Frege, in particular 1879 Begriffsschrift (Concept Script) 1879.

A categorical syllogism consists of three parts: Each part of which is a categorical proposition, and each categorical proposition containing two categorical terms . In Aristotle, each of the premises is in the form "Some/all A belong to B," or "Some/all A is/are [not]B,"where "A" is one term and "B" is another, but more modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, it is the minor term (the subject) of the conclusion.

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