Hmm... I am possibly misremembering something from a dicrete maths course about 13 years ago. I must admit that the details are a bit hazy now -- it's possible that the 3-value logic might have been something homegrown used as a means of explaining the ideas behind intuitionistic logic, and I may have picked up on that rather than the proof system (which definitely did have the properties you mentioned).
Anyway, if you forgive my previous incorrect use of terminology, the 3-value logic idea goes like this:
which allows 'don't know' or 'unknown' states to be handled easily. This is used quite a lot in the EE world -- most logic synthesis systems can use these * states to generate less logic than would otherwise be required. That's the good news -- the bad news is that logic minimisation based on this logic (or classical logic, for that matter) is only really safe for pure synchronous circuits. Minimisation strategies for more general classes of circuit need to take switching behaviour into account, which is where the 5 and 16 value 'logics' become useful.
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
(no subject)
Date: 2003-10-13 06:26 am (UTC)Anyway, if you forgive my previous incorrect use of terminology, the 3-value logic idea goes like this:
/\ 0 1 *
---+---+---+---
0 | 0 | 0 | 0
1 | 0 | 1 | *
* | 0 | * | *
\/ 0 1 *
---+---+---+---
0 | 0 | 1 | *
1 | 1 | 1 | 1
* | * | 1 | *
!
---+---
0 | 1
1 | 0
* | *
which allows 'don't know' or 'unknown' states to be handled easily. This is used quite a lot in the EE world -- most logic synthesis systems can use these * states to generate less logic than would otherwise be required. That's the good news -- the bad news is that logic minimisation based on this logic (or classical logic, for that matter) is only really safe for pure synchronous circuits. Minimisation strategies for more general classes of circuit need to take switching behaviour into account, which is where the 5 and 16 value 'logics' become useful.
Mea culpa.