Logic Idea (that someone probably already thought of)

I'm in the process of reading "Zen and the Art of Motorcycle Maintenence", and it's gotten me all fired up so
Coming Soon! INTERESTING philosophical blog posts...

...

But UNTIL then I just wanted to share the fact that I think I may have come up with an expansion of logic that someone else has probably already thought of, and let me know if you know who has. Where it came from was in "Motorcycle Maintenence" there was discussed the concept of Mu, which is a concept in Zen meaning "No answer" "Neither" etc., as opposed to a definite "Yes" or "No". This led me to wonder whether a system of logic could be built using the "Mu" term.
Specifically, I was thinking about how you could incorporate the "Mu" concept into the logical operators AND, OR, and NOT, since by combining these operators, at least I've heard and been told, one can make any logical statement.
A lot of you probably don't know what AND, OR, and NOT mean. All of these operations do something to some statement or set of statements that are determined to be True or False. In doing so they also form a new statement which is True or False.
AND joins two statements and claims that these statements are both True. The English "and" sometimes serves this function, though not always: an example where it does is "He is wearing a hat and a jacket", in which you are claiming that the statements "He is wearing a hat" and "He is wearing a jacket" are both true. If either statement or both statements are False, then the joint statement is false, i.e. if he isn't wearing a hat then he can't be wearing "a hat and jacket", and if he's wearing neither...you get the idea.
OR joins two statements and claims that AT LEAST one of them is True. It's important to note that it's different from English "or" in that it also allows for both of the statements to be true: it's English equivalent is really "and/or" which is what I will use in the example. "He is wearing a hat and/or (OR) a jacket" is true if he's wearing both, if he's wearing one or the other, but not if he's wearing neither.
Finally NOT, which is really easy: it simply takes a statement and claims the opposite. We are at an advantage in that English "not" does exactly what logical NOT does. So in the statement "He is not wearing a coat" you are simply taking the statement "He is wearing a coat" and claiming that the opposite is true. (By the way, double NOTs cancel, so for instance the statement "He is not not wearing a coat" means he IS wearing a coat).
By the way, these operations can be combined in any number of ways.
It's useful to think of these operations in terms of truth tables, with T (or 1 or Yes or...) meaning "True" and F (or 0 or...) meaning "False". The left column(s) are the begining statements or input and the right column is the final statment or output. What you get is the following:

AND:
T|T|T
T|F|F
F|T|F
F|F|F

(If this table doesn't make sense:
T AND T=T
T AND F=F
F AND T=F
F AND F=F)

OR
T|T|T
T|F|T
F|T|T
F|F|F

NOT
T|F
F|T

(meaning "NOT T=F"; "NOT F=T")

So anyway, on to my idea! I quickly realized that tackling "Mu" was too much of a challenge, so I decided to approach the problem of using "Undetermined", which I'll call "U", instead. What would be the truth value of a statement such as "He is wearing a hat and a coat" if you're not sure whether he's wearing a coat? If he might be wearing a coat, but then again he might not be?
So here's the sort of truth table we'd like to draw for an operation such as AND


AND:
T|T|T
T|F|F
F|T|F
F|F|F
U|U|?
U|T|?
T|U|?
U|F|?
F|U|?

and just fill in the question marks, which is really quite easy. For each row you just assume that U could mean True, then assume that it could mean False, and see if all the answers you come up with are one or the other, and go from there.

So for the AND table:

U|U|?
If both Us are T then (T|T|T)
If one U is T and the other is F then (T|F|F) or F AND T=F (F|T|F)
If both Us are F then (F|F|F)
Some of the outputs are T, and some of them are F, which means you have no clue what your going to get so the end result is U|U|U.

U|T|? or T|U|?
If U is T then T|T|T
If U is F then F|T|F or T|F|F
Once again, some of the outputs are T, and some of them are F, etc. etc., so U|T|U and T|T|U.

U|F|? or F|U|?
If U is T then T|F|F or F|T|F
If U is F then F|F|F
Eureka! It turns out no matter what you get and F, so U|F|F and F|U|F

I'm not going to bother going through OR, but I did work it out as I did for AND, and NOT should be pretty obvious: if you don't know whether something is true or false, you can't know whether it isn't true or isn't false!
So for all the operations:

AND:
T|T|T
T|F|F
F|T|F
F|F|F
U|U|U
U|T|U
T|U|U
U|F|F
F|U|F

OR
T|T|T
T|F|T
F|T|T
F|F|F
U|U|U
U|T|T
T|U|T
U|F|U
F|U|U

NOT
T|F
F|T
U|U

and a new operation, named "MU" in honer of my original intention. It's english equivalents are words such as "possibly" or "might be, but I don't know for sure if", as in "He is possibly wearing a hat".

MU
T|U
F|U
U|U

As you can see, it just turns anything into a U.

So who already thought of this and is it useful in any way?