We are all familiar with Binary, or at least I hope we are. Binary is consisting of two parts or states- True or False, On or Off, 1 or 0. This is the basic unit of computers - bits and Boolean logic. All computer data breaks down into bits (see table) and all Boolean evaluations result in either true or false.
| Unit | Number of Bits | |
|---|---|---|
| bit | 1 bit | |
| crumb | 2 bits | |
| nybble | 4 bits | |
| nickle | 5 bits | |
| byte | 8 bits | |
| deckle | 10 bits | |
| word | 16, 32 or 64 bits | |
| Italics for really obscure. | ||
In the real world things are not always black and white (binary). This is where fuzzy logic comes in. In fuzzy logic could be simply described as giving things a possibility of being a certain state (now a fuzzy logic expert might disagree with me on that, so do some research of your own if you are stickler for the truth). So it has a 75% chance of being true, and a 53.7% chance of being false. This makes more sense in more complicated examples. Take color fuchsia. I might say it has a 75% chance of being red, a 50% chance of being blue and 0% chance of being green. The interesting thing is someone else might give it a different rating.
Now these variable ratings are nice, but what if I don't want something so complicated, but more flexible then true and false?
I got to thinking, what would you call three states? At first I thought Trinary, which is in fact a word, that means "Consisting of three parts", but it appears that Ternary is preferred. I personally prefer Trinary, but I guess I will use Ternary since it appears preferred. For those of you who do much database development this concept should be pretty straight forward since you have to deal with null values, where the value is unknown. So you have true, false and unknown.
How about four states? I guessed Quadranary, which Google finds hits for but no definition. It suggests Quaternary, which has the definition of "Consisting of four; in fours." That sounds like what I am looking for. So what would these four states be? How about Unknown, True, False and Maybe. You could argue that Unknown should be Unlikely since that would be opposite of Maybe, but I like Unknown better.
So if you want to include Unlikely then you need five states. First I tried Pentanary which returned 84 hits, but no definition. Looking at some of the hits it is used to mean five parts or elements. It is even used in conjunction with Ternary and Quaternary, which looks promising! Then I tried Quintenary which returned 126 hits and no definition. It is used with Tertiary and Quaternary to mean fifth level and there is also a reference to base-5. I like Pentanary better since it is less likely to be confused with Quaternary. I think 5 states is a very useful base system since you have Unknown, Likely, True, False and Unlikely. Any more levels then this and you would be very fuzy.To summarize:
| System | States | |
|---|---|---|
| Binary/Boolean | True & False | |
| Ternary | Unknown, True, False | |
| Quaternary | Unknown, True, False, Maybe | |
| Pentanary | Unknown, Likely, True, False, Unlikely |
Would you suggest a system for six or more states? What would those states be? I think odd numbered systems would be better then even numbered systems since you would have an Unknown state, but maybe you might argue against that. I am interested in your comments on this! If you know Latin and would like to extend this system feel free to do so.
2 comments:
I implemented a logic evaluation system that dealt with a very small subset of quaternary logic. The four states for evaluation were a) True b) false c) unknown d) "not applicable" (i.e. don't consider this logic evaluation point for the requested vaue...) I'll spare you the details as to why I needed to do this, but suffice it to say people prefer a "true & false" world because it's simpler, while less forgiving than the real ternary (n-ary) world we live in.
I agree, the more states the more useful, but also the more complicated.
Post a Comment