[talanum1 (OP)]

Yes. In Classical Logic Syllogism: (A -> B, B -> ~C) -> (A -> ~C) is provable. However I found an interpretation that makes the premises true and the conclusion false: take A = "Are mortal", B = "All men" and C = "are dogs", "~" = not. Thus it does not semantically follow.

[Colin2B]

Yes. In Classical Logic Syllogism: (A -> B, B -> ~C) -> (A -> ~C) is provable. However I found an interpretation that makes the premises true and the conclusion false: take A = "Are mortal", B = "All men" and C = "are dogs", "~" = not. Thus it does not semantically follow.

Why are you saying that the set of all mortal things is the same as the set of all things that are men? That is not a valid assumption.
The set of all mortal things includes the set of all men and the set of all dogs, but all men and all dogs do not overlap.

[talanum1 (OP)]

I didn't know A -> B needs to be the whole truth.

[Colin2B]

I didn't know A -> B needs to be the whole truth.

It does if you want this statement to be true:

I found an interpretation that makes the premises true and the conclusion false

The first premise is false.
Your lack of understanding of logic means you would make a good politician. I suggest you resign now before you get impeached.

By the way, it might be a good idea to learn logic before trying to invent a new one.

[alancalverd]

If I read the OP correctly, it states that all mortals are men, which is false;  and all men are not dogs, which is true. Using Boolean representation we have 0 x 1 = 0, so the conclusion is false. 

[Colin2B]

If I read the OP correctly, it states that all mortals are men, which is false;  and all men are not dogs, which is true. Using Boolean representation we have 0 x 1 = 0, so the conclusion is false. 

That’s the way I interpreted it. The logic is correct, but the first premise is false despite the OP’s claim that it is true. Typical politician, a right and a wrong do not make a right!