I'm Such a Dick

For context.

So, I thought about what he'd said for a while. I tried to come up with the essential flaw in his argument. Just now, I sent a message approximated here:

Subject: Laws of Logic

Since you've apparently figured out how to reason about the absence of logic, I have a few questions for you.

A=A

A is either true or false. (Logic is binary)

A != !A (Noncontradiction.)

What would a universe where A!=A or A=!A look like?

What would trinary (or continuous!) logic look like?

I have no faith that he will even attempt to answer these questions. So, I'm a dick. Nevertheless, if you, dear reader, can answer them, I would greatly appreciate it. I strongly suspect that our brains will find it literally impossible to property conceive of such situations, but a counterexample would quickly disprove me.

Update: Yup. Got a link to ternary logic. You'll notice that the third value is 'unknown' which is impossible with respect to physics. I responded by outlining why I don't accept this, and mentioning that it was flippant at best, but probably an insult. Again, unfortunately, this simply proves that I'm a dick.

2nd Update: "...design purposes." Yup, definitely an insult. Does this actually mean anything? Can it mean anything?