Consequently, adv.
By consequence; by natural or logical sequence or connection.
Syn. -- See Accordingly.
Shades of meaning
Fernald has no entry of its own for consequently; he lists it under therefore.
Where he writes about it:
Therefore, signifying for that (or this) reason, is the most precise and formal word for expressing the direct conclusion of a chain of reasoning; then carries a similar but slighter sense of inference, which it gives incidentally rather than formally; as, "All men are mortal; Caesar is a man; therefore Caesar is mortal;" or, "The contract is awarded; then there is no more to be said." Consequently denotes a direct result, but more frequently of a practical than a theoretic kind; as, "Important matters demand my attention; consequently I shall not sail to-day." Consequently is rarely used in the formal conclusions of logic or mathematics, but marks rather the freer and looser style of rhetorical argument. — from therefore