The Collaborative International Dictionary
Syllogized
Syllogize \Syl"lo*gize\, v. i. [imp. & p. p. Syllogized; p. pr. & vb. n. Syllogizing.] [Gr. ?: cf. F. syllogiser.] To reason by means of syllogisms.
Men have endeavored . . . to teach boys to syllogize,
or frame arguments and refute them, without any real
inward knowledge of the question.
--I. Watts.
Wiktionary
syllogized
vb. (en-past of: syllogize)