Source : Webster's Revised Unabridged Dictionary (1913)

Syllogism \Syl"lo*gism\, n. [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.

Source : WordNet®

syllogism
     n : deductive reasoning in which a conclusion is derived from
         two premises