syllogize

/ˈsɪləˌdʒaɪz/
verb
  1. To reason or argue by means of syllogisms; to use deductive reasoning in a formal way.
    • The logician taught his students how to syllogize correctly, starting with two true premises.
    • Instead of getting emotional, try to syllogize the problem and see where your assumptions lead.
    • In the debate, she syllogized her way to a convincing conclusion that even her opponents had to accept.
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