syllogism

Concise Oxford English Dictionary © 2008 Oxford University Press:
syllogism /ˈsɪləˌdʒɪz(ə)m/

▶noun a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises); a common or middle term is present in the two premises but not in the conclusion, which may be invalid (e.g. all dogs are animals; all animals have four legs; therefore all dogs have four legs).

– derivatives
syllogistic adjective,
syllogistically adverb,
syllogize (or syllogise) verb.

– origin ME: via OFr. or L. from Gk sullogismos, from sullogizesthai, from sun- ‘with’ + logizesthai ‘to reason’ (from logos ‘reasoning’).