Can a Three-State Logic System Revolutionize Computing?

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The discussion explores the potential of a three-state logic system, which includes states represented as horizontal, vertical, and both, as opposed to traditional binary logic. The creator is focused on developing a new type of computer and is particularly interested in how this tri-valued logic would affect the design of logic gates, especially the 'and' gate. There is uncertainty about how to define a state that is both true and false simultaneously, which complicates the logic structure. The creator provides examples of 'not' and 'or' gates to illustrate the challenges of implementing this new logic system. The conversation suggests that more than the standard three basic gates will be necessary to accommodate this tri-valued logic.
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Normal boolean logic works with two states; true and false, which works fine with today's computer systems, which work with 1's and 0's.

However, I'm working on a new type of computer (Just need to figure out one last part about the 'and' gate), which will have three states (--,|,+).
I'm thinking this would be horizontal, vertical, and both.

What I'm wondering, is how this effects the logic of it. (true, false, or both?)
What would this system of logic look like, and what different or new types of logic gates would be required?

It wouldn't be too difficult, except for the fact that I can't seem to make sense of something being both true and false.

As an example, here's an IO chart for a 'not' gate:
In Out
--..|
|...--
+...+
And an 'or' gate:
InA InB Out
.--..--...--
.--...|...|
.--...+...|
..|...|...|
..|...+...|
..+...+...|

I'm thinking that I'll have to use more than the normal three basic gates (which all the others are made of), but what will the others be like?


If this should be in the computers section instead, forgive me, but I don't think so, as this project hasn't produced anything I'd call a 'computer' yet.
 
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Try Google with "tri-valued logic" or "triple-valued logic". You should get a lot of hits.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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