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From The Collaborative International Dictionary of English v.0.44 [gcide]:
Syllogism \Syl"lo*gism\, noun [OE. silogisme, OF. silogime, sillogisme, F. syllogisme, L. syllogismus, Gr. syllogismo's a reckoning all together, a reasoning, syllogism, fr. syllogi'zesqai to reckon all together, to bring at once before the mind, to infer, conclude; sy'n with, together + logi'zesqai to reckon, to conclude by reasoning. See {Syn-}, and {Logistic}, {Logic}.] (Logic) The regular logical form of every argument, consisting of three propositions, of which the first two are called the premises, and the last, the conclusion. The conclusion necessarily follows from the premises; so that, if these are true, the conclusion must be true, and the argument amounts to demonstration;
Note: as in the following example: Every virtue is laudable; Kindness is a virtue; Therefore kindness is laudable. These propositions are denominated respectively the major premise, the minor premise, and the conclusion.
Note: If the premises are not true and the syllogism is regular, the reasoning is valid, and the conclusion, whether true or false, is correctly derived.
From WordNet (r) 2.0 [wn]:
syllogism
noun: deductive reasoning in which a conclusion is derived from two premises
From Moby Thesaurus II by Grady Ward, 1.0 [moby-thes]:
32 Moby Thesaurus words for "syllogism": Aristotelian sorites, Baconian method, Goclenian sorites, a fortiori reasoning, a posteriori reasoning, a priori reasoning, analysis, categorical syllogism, deduction, deductive reasoning, dilemma, enthymeme, epagoge, figure, generalization, hypothesis and verification, induction, inductive reasoning, inference, mode, modus tollens, mood, paralogism, particularization, philosophical induction, prosyllogism, pseudosyllogism, rule, rule of deduction, sorites, syllogistic reasoning, synthesis
From THE DEVIL'S DICTIONARY ((C)1911 Released April 15 1993) [devils]:
SYLLOGISM, noun A logical formula consisting of a major and a minor assumption and an inconsequent. (See LOGIC.)
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