What's the difference between illogicality and inconsequence?

Illogicality

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Definition:

Example Sentences:

Inconsequence

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Definition:

• (n.) The quality or state of being inconsequent; want of just or logical inference or argument; inconclusiveness.

Example Sentences:

• (1) Essential errors in practice are the technically insufficient and inconsequent use of the treatment capacities.
• (2) The diagnosis is easy in most cases, if not obscured by an inconsiderate and inconsequent approach.
• (3) Complications were one death from pulmonary embolism, one case of possible genital disturbance, four inconsequent infections and three vessel injuries.