Hi,
I think you said the following do not need a conjunction because a semicolon establishes the connection.
She loved him with all her heart; she never told him. sounds OK
I took out the garbage; it was smelly. sounds stupid.
Can I write like these for those two examples of yours? Yes.
She loved him with all her heart; however, she never told him that.
I took out the garbage; as a result, the house is free from foul smells.
If I follow your explanations, 'however' and 'as a reult' would be unnecessary since a semicolon is providing the connection. Am I right? Generally speaking, yes, although the conjunction clarifies the nature of the connection, while a semi-colon by itself leaves the reader to think about what is being said and work out the connection for himself.
Also, the four words that you said is not conjunctions are from a list of conjunctive adverbs and I believe those words as many conjunctive adverbs do and can, if not all of them, function as simple adverbs.
Also, as to the fact that both a conjunction and a semicolon not being necessary, please tell me why many online help sources have examples that have both a semicolon and conjunction? Just because something is not necessary does not mean that you can't do it if you want to.
Nothing can be unconditional; consequently nothing can be free. (George Bernard Shaw) Would you say 'consequently' is not used as a conjunction here but as an adverb? I didn't say that 'consequently' was not a conjunction. My dictionary lists it as both a conjunction and an adverb. However, I personally see it as more of an adverb here. I would write it with a conjunction, thus. He loved her, and consequently he married her'. How would I know? My first reaction to ask why you need to know
as long as you understand the meaning of the sentence.
"Always go to other people's funeral; otherwise, they won't go to yours." (Yogi Berra) Would you say 'otherwise' is an adverb, not a conjunction? My dictionary lists it as an adverb. I would write it with a conjunction, thus. 'Give me your money, or otherwise I will kill you'. How would I know? My first reaction to ask why you need to know
as long as you understand the meaning of the sentence.
What do you say about this? Does it contradict any of the helpful points you brought out or do they fit right in? Can you tell me what it means here?
The conjunctive adverbs that connect two main clauses are usually separated (punctuated with) by a semicolon preceding the word or term. Except the one-syllable conjunctive adverbs and also, which is then have a comma after them. I don't agree. These words that you are calling conjunctive adverbs are used a lot. Semi-colons are not used a lot.
Here are a couple of closing comments.
First, I've said it before, but I would like to stress it. Semi-colons are not used as much as I think that you think they are.
Second, here is some advice. Try to think less about about where a semi-colon should be used, and more about why it should be used.
eg Why would you want to say
'She loved him with all her heart; however, she never told him.'
instead of 'She loved him with all her heart; she never told him.'
or 'She loved him with all her heart. However, she never told him.'
or 'She loved him with all her heart. She never told him.'
Best wishes, Clive