I suppose this is sarcasm but the results are quite intuitive to me. From my perspective, it's trivial to construct the truth tables for trivalent logic based on a sense of what "should" be in them. Maybe give it a try.
Well guess what. Your "sense" of what "should" be in them has no place in computer SCIENCE.
Computer SCIENCE is that ugly thing that tells us that three-valued logic gives rise to 19683 distinct binary logical operators, while two-valued has 16.
Computer SCIENCE is that ugly thing that tells us that if you want a computer language over a three-valued logic to be expressively complete, then you need to implement all of those 19683 logical binary operators one way or another. In the worst case, that's 19683 operator names for the programmer to remember. And you come here claiming that it's "trivial" because you have a "sense" of what the results ought to be ? That proves just one thing but site policy probably won't allow me to spell that out.
(In case you were wondering what the 16 names are in two-valued logic : they aren't needed because the system being two-valued gives rise to certain symmetries that gracefully allow us to reduce the set we need to remember to just {AND OR NOT} (or some such) which beautifully parallels the way we communicate in everyday life.)
Ah, you seem to be a bit nutters. So I'm not going to engage further but I do want to give you a serious response to the argument you seem to be making.
First, the same argument above is also an argument that, say, integers, are not "Computer SCIENCE".
More to the point, you might enjoy reading the work of Charles Pierce and other logicians of that era who began to explore many variations on formal logic. Note that just as many operations arise from trinary relations in bivalent logic. Are binary relations "Computer SCIENCE", but not trinary or higher relations? Before you answer, you might want to look into whether all possible relations can be expressed using only binary relations (hint: nope).
Look deeper into the concept of functional completeness (with respect to a subset of operators), which you reference above without naming. You might be able to understand how many of those many trivalent operators are actually necessary to reason with (hint: not very many, hardly more than for bivalent logic, where, as you note, we only tend to use a few, and need not worry about it).
Consider also the relationship between operators folks have identified as useful in bivalent vs trivalent logic (hint: they not picking at random).
Could it be that just as with the 16 binary operators, many of which have relations to one another (e.g. inverses and complements, among others) that the trinary operators could fall into similar groups, which, making the 3^9 number you mentioned seem a whole lot less complex? Could that be why it's neither necessary nor customary to work with all the operators in either sort of logic?
Once you've caught up to state of the art in formal logic as of the 1930's you might have a new perspective -- perhaps you might even begin to let us know when "Computer SCIENCE" will catch up!
If you wanted that to be a real argument then you should have done the maths yourself. Without those maths you are doing nothing but gratuitious handwaving. I've done them for you and they prove me right (and you wrong at least where you say "hardly more than for bivalent logic").
Oh, and if you want to know why people don't want to find more "useful" operators than what they're used to from good old two-valued logic then I have a hint for you too : it's because they all immediately sense that their brains are not up to it as soon as they actually try (and my actually doing the maths has very clearly shown me why - so as you suggested to me "perhaps give it a try").
Clearly you are a theorist and not a practitioner. Dealing with the real world is far more complex than simply a YES or NO. Take a look at something called 9 valued logic - it will blow your mind if you are unable to handle 3 valued logic.
Don’t get me wrong - theory is important. The models that you develop though are only an approximation of the real world.
Well FWIW the real theorists would be utterly offended if they knew I was being put in the same league as they.
The way I see it there are practitioners who care about theory (and take the bother to try and understand some of it, and even more so the consequences on their practical tasks) and there are those who don't.
(Aside : the world of fact-oriented modeling and especially FCO-IM - that's communication oriented modeling - has this stance that our databases are actually not modeled according to how the world is, they are modeled after how our comunications about the world are. An interesting distinction you might want to ponder a bit more deeply.)
