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The Collaborative International Dictionary of English v.0.48:

Syllogistic \Syl`lo*gis"tic\, Syllogistical \Syl`lo*gis"tic*al\, a. [L. syllogisticus, Gr. ?: cf. F. syllogistique.] Of or pertaining to a syllogism; consisting of a syllogism, or of the form of reasoning by syllogisms; as, syllogistic arguments or reasoning. [1913 Webster]