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)
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 ⊃ and ≡ as (for some reason) they are part of the original ALGOL 60 specification. (Strange but true!) But in binary ⊃ does not seem to useful, AFAIK I have never used it. But in the case of Ternary logic ⊃ seems to be useful in tautologies so I included it. Indeed @Kernigh is correct to say it is logically equivalent to (not a) or b
Note: ⊃ is the same as → and ⇒ operations. c.f. List of logic symbols Also ⇔, ≡ and ↔ are equivalent.
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)