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Adjective: unlogical  ,ún'ló-ji-kul
Usage: rare (=illogical)
  1. Lacking in correct logical relation
    "His unlogical argument failed to convince the jury";
    - illogical

See also: absurd, incoherent, inconsequential, intuitive, irrational, logicality, logicalness, nonrational, unreasonable, visceral