The list of philosophers who support the claim that cosmological arguments are wrong includes: Immanuel Kant, Alvin Plantinga, Elliott Sober, and many others.

Logical explanations are scientific explanations. However, cosmological arguments are excluded in logical explanations. Wrong arguments are excluded in logical explanations.

Cosmological arguments include scientific concepts such as 'causality'. However, it does not follow that cosmological arguments provide reasons for theism.

The list of logicians who support the claim that logic is part of science includes: Rudolf Carnap, Hans Reichenbach, Willard Van Orman Quine, and so many others.

You misunderstood.
The argument in OP is about 'reason to believe'. The conclusion is 'there is no reason to believe in God'.
'Reason to believe' is not the same matter as 'truth value'. Atheism is by definition not about the truth/falsity of the existence of God, but about the rationality/irrationality of belief in God.

Logic is a scientific discipline. Theism is not a scientific discipline.

Scientific explanations provide reasons to believe. Theists' claims about God do not provide reasons to believe the existence of God.
Suppose that there is a scientific explanation about unicorns, but actually unicorns don't exist. Then, although there is a reason to believe the existence of unicorns, the belief about the existence of unicorns is false.

Many logicians support the claim that logic is part of science.

I just claim that logic is part of science. You don't have to worship logic in Sunday school.

By 'logic' I meant formal logic with natural deduction, such as first-order predicate logic.

Many logicians support that logic is part of science. Philosophers of science do so.

I think logic is part of science. Logic is included in science.

Suppose that there is no scientific explanation about God, and actually God does not exist. Then, there is no reason to believe the existence of God, and belief about the existence of God is false.

Suppose that there are scientific explanations about atoms, and atoms actually exist. Then, there is a reason to believe the existence of atoms.
Suppose that there are scientific explanations about unicorns, and unicorns actually don't exist. Then, there is a reason to believe the existence of unicorns, but the belief is false.

What if I don't agree with your definition of belief???

Also you don't understand what beliefs and opinions are. — Noblosh

What makes you think so???

There is no scientific explanation about the OP, therefore there is no reason to believe in the OP. — Mariner

Maybe there is.

I don't think this holds. — Michael

That's your opinion. Go ahead!

Premise 4 begs the question. — Michael

You think so.

What about 'scientific atheism' or 'logical atheism'? Science leads us to which there is no God.