For given algebra ({0,1,X,Z}, . , +) which “.” represent “Logical And” and “+” represent “Logical Or”, Following lookup tables are given (image):

4-Valued Logic Lookup_Tables

I guess the Hasse Diagram of a 4-Valued logic should be something like this (image) :

4–valued logic Hasse

But, If this is truely Hasse Diagram of 4-valued logic, what is a Right arrengement for X and Z and their complements in this Lattice ?

  • $\begingroup$ How is $z$ different from $x$? $\endgroup$ – Théophile Nov 28 '17 at 18:54
  • $\begingroup$ @Théophile They look-like same, They should be, I guess It is not possible for single value like z, supremum and infimum be different, as you can see sup(z,z)=x and inf(z,z)=x therefore i think they are same. $\endgroup$ – DEopen Nov 28 '17 at 18:57

As @Théophile mentioned, It seems there is no difference between X and Z , So X=Z and we have a 3-valued Logic and It’s Hasse Diagram shape a Chain graph, as you can see in this image: Hasse Diagram for 3-valued Logic

And it’s Relation could be this:


P.S. However complements are not match with this Hasse diagram. i think multi-valued logic like this one, which i don’t know is a 3-value logic or not, could have another Hasse diagram which i don’t know. Please if anyone has a better answer share it with me, Thanks.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.