The Collaborative International Dictionary of English v.0.48:

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:
         [1913 Webster] Every virtue is laudable; Kindness is a
         virtue; Therefore kindness is laudable.
         [1913 Webster] These propositions are denominated
         respectively the major premise, the minor premise, and
         the conclusion.
         [1913 Webster]

   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.
         [1913 Webster] Syllogistic

WordNet (r) 3.0 (2006):

syllogism
    n 1: deductive reasoning in which a conclusion is derived from
         two premises

Moby Thesaurus II by Grady Ward, 1.0:

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



The Free On-line Dictionary of Computing (30 December 2018):

syllogism

   /sil'oh-jiz`*m/  Deductive reasoning in which a
   conclusion is derived from two premises.  The conclusion
   necessarily follows from the premises so that, if these are
   true, the conclusion must be true, and the syllogism amounts
   to demonstration.  To put it another way, the premises imply
   the conclusion.

   For example, every virtue is laudable; kindness is a virtue;
   therefore kindness is laudable.

   Strangely, a syllogism can still be true if the premises are
   false.

   Compare inference rule.

   [Relationship between premises?]

   (2009-10-28)


The Devil's Dictionary (1881-1906):

SYLLOGISM, n.  A logical formula consisting of a major and a minor
assumption and an inconsequent.  (See LOGIC.)