3 valued logic.

[TuringAI]

I have a problem with 2 valued logic involving the xor problem, which is simpyl that AxorBxorC cannot be construed in such a way that it's incorrect when A, B, and C are all true. So I'm trying to invent a new one.

So far I've gotten an xor function that returns different values based on which problem occurs: Too many variables or too few.

x OTU

O OOO

T OOT

U OTU

The problem is now a proper construction of the original & and |, and of a not table, along with equivalence, which is probably only valid for 2-valued-logic.

Any help?

[Hodge'sPodges]

I have a problem with 2 valued logic involving the xor problem, which is simpyl that AxorBxorC cannot be construed in such a way that it's incorrect when A, B, and C are all true.

I take it that by xor, you mean exclusive or, which has this truth table:

A B AxorB

T T F

T F T

F T T

F F F

By the way, this is equivalent to ~(P<->Q).

The operation is associative, and you're correct that AxorBxorC evaluates as true when A, B, and C are all true.

So I'm trying to invent a new one.

So far I've gotten an xor function that returns different values based on which problem occurs: Too many variables or too few.

x OTU

O OOO

T OOT

U OTU

I don't understand. Are you seeking to define a binary operation (an operation on A and that has among three different values (O, T, U)? A truth table for that would like this (fill in your column below 'AxB'):

A B AxB

T T

T O

T U

O T

O O

O U

U T

U O

U U

/

P.S. You've not responded for a long time to my post in the thread in which I gave a proof that there is no function from a set onto its power set. May I take it that your qualms about that matter were thus satisfied as consistent with my last post?

[Steve D'Ippolito]

XORing an indefinite number of variables will result in 1 or "true" if an odd number of the variables are true.

[Hodge'sPodges]

XORing an indefinite number of variables will result in 1 or "true" if an odd number of the variables are true.

Right, and easily provable by induction on the number of variables.

[punk]

I have a problem with 2 valued logic involving the xor problem, which is simpyl that AxorBxorC cannot be construed in such a way that it's incorrect when A, B, and C are all true. So I'm trying to invent a new one.

So far I've gotten an xor function that returns different values based on which problem occurs: Too many variables or too few.

x OTU

O OOO

T OOT

U OTU

The problem is now a proper construction of the original & and |, and of a not table, along with equivalence, which is probably only valid for 2-valued-logic.

Any help?

The closest thing to a natural 3-valued logic is intuitionistic logic.

Have you tried that?

[Hodge'sPodges]

The closest thing to a natural 3-valued logic is intuitionistic logic.

Intuitionistic logic cannot be 3-valued, nor n-valued for any natural number n. I do not personally know all the details of the proof, but it is a famous result of Godel's.

However, there are different 3-valued logics that one can look up in the literature.

Edited November 21, 2008 by Hodge'sPodges

[TuringAI]

P.S. You've not responded for a long time to my post in the thread in which I gave a proof that there is no function from a set onto its power set. May I take it that your qualms about that matter were thus satisfied as consistent with my last post?

Yeah I figured it out. I had to read a math book but it explained the process.

And yeah, I'll have to read more about n valued logic.

My interest now is in trying to see if there exists a method to explain in detail how to derive a concept from a given set of particulars, something that formalizes induction akin to how mathematics formalizes deduction.