And so, for the third time, what is the series of logical operators?
The overall domain is the domain of thought.
There is no "overall" domain. If that existed, it would include plane geometry, and sub-nuke theory under one umbrella, and as we have discussed, that means things could be commutative, and non-commutive at the same time.
To speak sensibly about applying the discrete laws of logic, you must be addressing a set of related, well-formed sets of things--things you can clearly say are in either set A, or set B, or ...
To speak of an "overall" domain is to commit yourself to fallacies of the excluded middle. Like virtually ALL mathematicians, I don't think you are really talking about much of anything at all that logical axioms apply to, unless you specify, either implicitly or explicitly, a well-formed domain of discourse. Discrete logic ain't about big fuffy clouds of vaguely understood existence. Discrete Logic is about things you can unambiguously plop into sets because that's all discrete logic tells you about at base--what you know axiomatically about how things in overlapping sets can relate to each other.
Thought about football and thought about homicide do not use different sets of logical operators, only the sequences of operations and the terms operated upon differ.
That's not the germane question. The fact is that any logic you apply to football is not likely to be usefully related to any logic regarding homicide. If you don't guarantee a well-formed domain of discourse--about things related to each other in terms of football exclusively, or homicide exclusively, you haven't guaranteed that you are talking sense in applying logic.
And so, for the third time, what is the series of logical operators?
PaWP=Persons who advocate the will to power.
Definition of like in this domain of discourse: [(A<>B) and (A is a member of PaWP) and (B is a member of PaWP)] or [(A<>B) and (A is not a member of PaWP) and (B is not a member of PaWP)] ==> A is like B ==> B is like A.
Tubas
Lightning
Joseph Stalin
Ron Paul
Hillary Clinton
Choose two entities, substitute them for A and B above, and crank the logic. In this domain:
Tubas are like lightning. Lightning is like tubas.
Tubas are not like Joseph Stalin. Joseph Stalin is not like tubas.
Tubas are like Ron Paul. Ron Paul is like tubas.
Tubas are not like Hillary Clinton. Hillary Clinton is not like tubas.
Lightning is not like Joseph Stalin. Joseph Stalin is not like lightning.
Lightning is like Ron Paul. Ron Paul is like lightning.
Lightning is not like Hillary Clinton. Hillary Clinton is not like lightning.
Joseph Stalin is not like Ron Paul. Ron Paul is not like Joseph Stalin.
Joseph Stalin is like Hillary Clinton. Hillary Clinton is like Joseph Stalin.
Ron Paul is not like Hillary Clinton. Hillary Clinton is not like Ron Paul.
You can crank the logic on additional entities if you like.