(adv) lacking consequence, Syn. inconsequently, Ant. consequentially, Example:`You're so beautifully dressed, ' she said and added quite inconsequentially, `Can you stay the night?'
The Collaborative International Dictionary of English (GCIDE) v.0.53 Collaborative International Dictionary (GCIDE)
a. Not regularly following from the premises; hence, irrelevant; unimportant; of no consequence. Chesterfield. -- In*con`se*quen"tial*ly adv. [1913 Webster]