As sentence connectors, I don't believe these 'adverbs' carry the traditional adverbial meanings. Such connectors as accordingly, again, also, besides, consequently, finally, furthermore, however, indeed, moreover, nevertheless, otherwise, then, therefore, and thus (from an on-line list) serve to define the relationship between the two independent clauses, and are likely lumped in with the adverbs for want of a better idea-- many of them are also used as normal adverbs: 'She was accordingly cordial; I saw him again; I finally found it; however sad she may feel ' etc.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.