# Three-valued logic

1. Jun 16, 2006

### EvLer

In addition to boolean T-F, they have an "undetermined" or "null" value N

The truth table in the book for this logic goes like this:

"OR"
T v N = T
F v N = N

"AND"
T ^ N = N
F ^ N = F

it does not make sence unless I assume N to be unknown in a sense of unknown whether N = T or F, i.e. N = (T v F).
If N is considered to be a null it does not make sense at all! Is my assumption correct? or if not, could someone shed clarity on this
Thanks.

2. Jun 16, 2006

### chroot

Staff Emeritus
In this context, the word "null" is synonymous with "undefined" or "unknown", as you indicated in the first sentence of your post.

- Warren

3. Jun 16, 2006

### NateTG

Things are more complicated than that. In trinary logic, there are $3^{3^2}=19683$ possible binary operations, instead of $2^{2^2}=16$.

4. Jun 17, 2006

### HallsofIvy

Staff Emeritus
A v B= True would be "one or both of A and B are true" while A v B= False would be "neither one is true". Now look at "T v N". I know A= T is true while I don't know about B= N. But one being true is enough: T v N= True.
Look at "F v N". I know A= F is False but I don't know whether B= N is true of false. If it happens to be true then F v T= T but if it happens to be false, then F v F= F. Since I don't know, that's N:
F v N= N.

It's the opposite, of course, for and: A ^ B is True if and only if both A and B are true. With F ^ N, B= N doesn't matter. Since A= F is false, it doesn't matter what B is: F ^ "anything"= False so F ^ N= False.
But with T ^ N, I don't know. T ^ T= True while T ^ F= False. If I don't know whether B is true or false, I don't know whether the compound A ^ B is true or false: T ^ N= N.

5. Jun 17, 2006

### EvLer

Thanks. I think I got it now. I was just not sure why unknown is considered a null....