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Adverb: illogically  i'ló-ji-k(u-)lee
  1. In an illogical manner
    "she acted illogically under the pressure"

Antonym: logically

Nearest

illiterate
illiterate person
ill-judged
ill-mannered
ill-natured
illness
illocution
illogic
illogical
illogicality
illogically
illogicalness
ill-omened
ill-proportioned
ill-scented
ill-shapen
ill-smelling
ill-sorted
ill-starred
ill-tempered
ill-timed