Logic. an argument the conclusion of which is supported by two premises, of which one (major premise) contains the term (major term) that is the predicate of the conclusion, and the other (minor premise) contains the term (minor term) that is the subject of the conclusion; common to both premises is a term (middle term) that is excluded from the conclusion. A typical form is “All A is C; all B is A; therefore all B is C.”
deductive reasoning.
an extremely subtle, sophisticated, or deceptive argument.

1350–1400; < Latin syllogismus < Greek syllogismós, equivalent to syllog- (see syllogize) + -ismos -ism; replacing Middle English silogime < Old French < Latin, as above Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
syllogism (ˈsɪləˌdʒɪzəm)
1.  a deductive inference consisting of two premises and a conclusion, all of which are categorial propositions. The subject of the conclusion is the minor term and its predicate the major term; the middle term occurs in both premises but not the conclusion. There are 256 such arguments but only 24 are valid. Some men are mortal; some men are angelic; so some mortals are angelic is invalid, while some temples are in ruins; all ruins are fascinating; so some temples are fascinating is valid. Here fascinating, in ruins, and temples are respectively major, middle, and minor terms
2.  a deductive inference of certain other forms with two premises, such as the hypothetical syllogism,if P then Q; if Q then R; so if P then R
3.  a piece of deductive reasoning from the general to the particular
4.  a subtle or deceptive piece of reasoning
[C14: via Latin from Greek sullogismos, from sullogizesthai to reckon together, from sul-syn- + logizesthai to calculate, from logos a discourse]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

late 14c., from O.Fr. silogisme "a syllogism," from L. syllogismus, from Gk. syllogismos "a syllogism," originally "inference, conclusion, computation, calculation," from syllogizesthai "bring together, premise, conclude," lit. "think together," from syn- "together" + logizesthai "to reason, count,"
from logos "a reckoning, reason."
Online Etymology Dictionary, © 2010 Douglas Harper
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Computing Dictionary

syllogism definition

/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?]

The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
His reasoning is based upon an unconvincing syllogism.
How people act and how they are influenced should be deduced from observation of their behavior and not by the use of a syllogism.
The fire officer of this age is one of management, performance, syllogism.
The provost, in his letter of invitation, puts forth an intriguing syllogism.
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