If an argument is invalid, then it is possible for the conclusion to be false even if all the premises are true.

I have a more difficult time finding a concise definition of a fallacious argument.

Does this work?
A fallacious argument is an argument based on false or invalid inference.

But this suggests that all invalid arguments are also fallacious arguments which in other threads I have been told that this is not the case.

It could be a case made for invalidating an argument but it is not a universal cause for invalidating arguments.

I can see that not all fallacious arguments are invalid arguments.
But are all invalid arguments fallacious arguments?

No. Because the conclusion could still be true absent the premises thus it would not be fallacious. This usually only happens during long discourses of validating conclusions. Where a first conclusion (assumed true) is used as a premise to try and make the following conclusions true (assumed false). So in other words it doesn't invalidate the whole argument if one conclusion is false.

So fallaciousness is to the falseness of a premise
as invalidity is to ?

If an argument is invalid, then it is possible for the conclusion to be false even if all the premises are true.

I have a more difficult time finding a concise definition of a fallacious argument.

Does this work?
A fallacious argument is an argument based on false or invalid inference.

But this suggests that all invalid arguments are also fallacious arguments which in other threads I have been told that this is not the case.

Typically a logical fallacy is one where at least one of the premises and the conclusion are both determined to be false. The resultant conclusion doesn't necessarily need to be false for it to be considered a fallacy.

p1. Bricks are used to make buildings.
p2. Bricks make things tall.
c1. All Buildings are tall.

p4. Buildings are tall.
p5. Bricks make things tall.
c2. All buildings use bricks.

c2 is false, however c1 is true. So is it a logical fallacy? Yep, even though there are some true statements.

edit: Actually c1 is not always true if you consider buildings underground but I don't think they actually call them buildings.

A fallacious argument may have premises and conclusion all of which are true.

1. All dog are mammals
2. All German citizens are European citizens

3. All planets move around the Sun in elliptical orbits,

The argument is fallacious because the conclusion fails to follow from the premises. As you can tell by inspection.

But no one realistically argues a premise and concludes something different from that premise. It would be like protesting your innocents of a crime and then say well I am however guilty of this other thing, so I guess you should consider me guilty for the first thing.

I didn't kill the neighbors dog.
I did kill a fly once.
I guess I am guilty for killing the neighbors dog.

No one ever argues like that.

The point is that the premises may or may not be connected by subject matter. What is crucial is whether the conclusion follows from the premises.

Here is a more conventional argument which is also fallacious:

All Germans are Europeans.
All Berliners are Europeans

Therefore, all Berliners are German.

Premises and conclusion all true, argument is fallacious.

But logically speaking, there is no difference between the two arguments,

My only problem with it is that your conclusion is false.

It is? How come? All Berliners who are citizens of Berlin are Germans. So "Berliners"=Citizens of Berlin.

Surely debates can be allot more subtle than simply correct or incorrect. What if certain knowledge is questionable and you use it, is it fallacious or invalid?

Well now you are talking about ethics and ethics do not care about truths. Truths are not dependent upon ethics. If they are then all truths are subjective which they are not.

Surely debates can be allot more subtle than simply correct or incorrect. What if certain knowledge is questionable and you use it, is it fallacious or invalid?

How do we determine that an argument is "fallacious" (using for the moment a common sense definition of the word to mean incorrect or "wrong")?

There seem to be several criteria for rejecting an argument.

First, The assertions in the premises are either doubtful (without sufficient warrants for accepting them) or wrong (contrary to matters of fact---this does not mean contrary to what I want to believe---and might also include the aspect of credibility).
Second, words in the premises (and/or conclusion) are used in different senses (e.g. the word "bias").
Third, the argument employs informal fallacies. While this might not necessarily make the conclusion wrong, it does put it into question by not providing a sound argument.
Fourth, the formal structure of the argument from premises to conclusion fails to follow logical rules (this can be similar to step 3), or if premises do follow these rules, the logical conclusion may nevertheless be indeterminate.

From the list that of course could be expanded, it seems clear that we accept or reject arguments to a conclusion using more than (strictly speaking) logical tests.

All members of this forum lie
I lie
therefore........?

for the record, Im not calling the forum-members for liars.