TuringAI Posted November 21, 2008 Report Share Posted November 21, 2008 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? Quote Link to comment Share on other sites More sharing options...

Hodge'sPodges Posted November 21, 2008 Report Share Posted November 21, 2008 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? Quote Link to comment Share on other sites More sharing options...

Steve D'Ippolito Posted November 21, 2008 Report Share Posted November 21, 2008 XORing an indefinite number of variables will result in 1 or "true" if an odd number of the variables are true. Quote Link to comment Share on other sites More sharing options...

Hodge'sPodges Posted November 21, 2008 Report Share Posted November 21, 2008 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. Quote Link to comment Share on other sites More sharing options...

punk Posted November 21, 2008 Report Share Posted November 21, 2008 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? Quote Link to comment Share on other sites More sharing options...

Hodge'sPodges Posted November 21, 2008 Report Share Posted November 21, 2008 (edited) 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 Quote Link to comment Share on other sites More sharing options...

TuringAI Posted November 22, 2008 Author Report Share Posted November 22, 2008 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. Quote Link to comment Share on other sites More sharing options...

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