# Talk:Ternary logic

## test case

re: "Kudos (κῦδος) for actually thinking up a test case algorithm where ternary logic is intrinsically useful, optimises the test case algorithm and is preferable to binary logic".

I know that calculating Perfect numbers and Matrix-exponentiation_operator in *binary* has some algorithmic advantages. I imagine that there is some problem would benefit from *Ternary logic*. Any hints or suggestions?

NevilleDNZ 07:21, 26 August 2011 (UTC)

- On first reading, it seems like you are implementing an analogue of the cmp function from C and C based languages. Or am I completely misunderstanding? --Thundergnat 11:03, 26 August 2011 (UTC)

- It's entirely possible (and probably κῦδος-worthy) to produce a terminating solution of the Halting problem in ternary logic; anything where your code can't definitely figure it out within some reasonable bound on effort becomes a “maybe”. We know we can do this: we can exhibit examples with minimal effort. –Donal Fellows 12:45, 8 September 2011 (UTC)
- Certainly -- the simplest implementation would be code that always returns "maybe". Going deeper would require an implementation which handles code in the language being used (which would have greatly varying complexity, depending on the target language). --Rdm 12:49, 8 September 2011 (UTC)

## Task structure

How about adding a truth table for implementation and cutting the history/leaving a link to the history?--Paddy3118 08:29, 26 August 2011 (UTC)

Just added the *Logic Operators* in *Truth Tables*. NevilleDNZ 11:33, 26 August 2011 (UTC)

## C example

Could have been better (I could have bothered to do a table), but I hope the C example is sufficiently and approriately clear, fast and clever. Hopefully, I'll get around to implementing the C++ version using templates. --Michael Mol 17:23, 26 August 2011 (UTC)

## if a then b

What is if a then b condition? It's not a straightforward conditional like `if a then: b; else:a;`

. Looks more like if we define false < true, and "maybe" means "unknown state of either true or false", the "if a then b" condition is the same as a <= b. Some clarification? --Ledrug 01:07, 27 August 2011 (UTC)

**if a then b**is logically equivalent to**(not a) or b**. --Kernigh 01:27, 27 August 2011 (UTC)

- That's equivelant to a <= b, I was more curious where the "if then" notation came from. --Ledrug 01:29, 27 August 2011 (UTC)

I included the operator ⊃ and ≡ as (for some reason) they are part of the original ALGOL 60 specification. (Strange but true!) But in the case of binary the ⊃ operator does not seem so useful, AFAIK I have never used it (any got a nice/useful example of usage). But in the case of Ternary logic ⊃ seems to be useful in tautologies so I included it. Indeed @Kernigh is correct to say **a ⊃ b** is logically equivalent to **(not a) or b**.

(Said with my tongue firmly in my cheek: Maybe binary is the reason the computers are so black and white, and (at least on Star Trek and Dr. Who) is it the reason that tautologies make the front panels of computers spout smoke. c.f. http://www.youtube.com/watch?v=w3fyKChJrZw LOL :-^ )

Note: ⊃ is the same as → and ⇒ operations. c.f. List of logic symbols

Also ⇔, ≡ and ↔ are "equivalent", **and** equivalent to each other and to **if and only if** and **iff**.

BTW: the operators /\ and \/ were originally part of the C programming language, they appear to be borrowed from the ALGOL ∧ and ∨ operators. Indeed the character "\" was included in ASCII for this specific purpose.

NevilleDNZ 04:04, 27 August 2011 (UTC)

## Any need for this task to remain draft?

By example count, diversity and clarity, it seems like it's reasonably well-understood. --Michael Mol 19:19, 7 September 2011 (UTC)

## Variable_truthfulness

I feel the C Variable Truthfulness code warrants it's own Task Page. This is because the task:

- Is sufficiently different to warrant a different page.
- Is not
__Ternary logic__*per se*, rather it might actually be a**super set**of some form. - Would benefit from some citations and/or link to actual theory.
- Needs to go through "draft" phase to determine an appropriate test case.
- Is sufficiently interesting to warrant a different page.

NevilleDNZ 09:57, 10 October 2011 (UTC)

- Well, for now it doesn't have a good place to go to. As to not being ternary logic per se, it can be reduced to one pretty easily though: define 1 as TRUE, 0 as FALSE, and anything in between as MAYBE, then the operator tables can be reproduced exactly. Since the "variable truths" are just probabilities, I'm not sure what more refs are needed without making it appear more complicated than necessary.
- This C entry was sort of targeting the kudos part of the task. To me, the most interesting place to use a "maybe" would be at the control flows (
`if3`

), but that requires knowledge of*how*ambiguous such an ambiguity is, hence the numeric values. --Ledrug 14:51, 13 October 2011 (UTC)

~~I suggest: A good place for it to go to is as a "Draft Task" with appropriate details of what the task is rather then complicate Ternary_logic. Also: A brief description of "variable truths" (or even Qubits) might help the draft task.~~ On rethinking, your point about the *"C entry was sort of targeting the kudos"* is about right. Indeed I have yet to see a more pratical use for Ternary Logic. ¢ However - maybe - Balanced Ternary Arithmetic appears to have an advantage, as Binary Addition is takes 58% more iterations, and Binary Multiplication takes 150% more iterations then Balanced Ternary. ¢

NevilleDNZ 09:16, 14 October 2011 (UTC)

- Eh which C code are we talking about? This topic was about using floating point to represent probability (or so I thought), so the natural thing is using range 0 to 1. I don't see how -1 got in here? --Ledrug 11:56, 14 October 2011 (UTC)

## another ternary truth table

I found another ternary truth table that I used for validation of some of the other functions for the REXX example (which shows more functions) at:

- http://www.scribd.com/doc/78370674/31/A-6-2-AND-XOR-OR-XNOR-NAND
*Ternary Computing Testbed 3-Trit Computer Architecture*by Jeff Connelly- Computer Engineering Department August 29
^{th}, 2008 - which is on page 59: A.6.2. AND, XOR, OR, XNOR, NAND
- -- Gerard Schildberger 06:48, 3 March 2013 (UTC)

- http://www.scribd.com/doc/78370674/31/A-6-2-AND-XOR-OR-XNOR-NAND