INCONSEQUENTLY
inconsequently, inconsequentially
(adverb) lacking consequence; “‘You’re so beautifully dressed,’ she said and added quite inconsequentially, ‘Can you stay the night?’”
Source: WordNet® 3.1
Etymology
Adverb
inconsequently (comparative more inconsequently, superlative most inconsequently)
In an inconsequential way, or a way that suggests a lack of consequence
Source: Wiktionary
INCONSEQUENT
In*con"se*quent, a. Etym: [L. inconsequens: cf. F. inconséquent. See
In- not, and Consequent.]
Definition: Not following from the premises; not regularly inferred;
invalid; not characterized by logical method; illogical; arbitrary;
inconsistent; of no consequence.
Loose and inconsequent conjectures. Sir T. Browne.
Source: Webster’s Unabridged Dictionary 1913 Edition