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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 ?

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  • $\begingroup$ 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
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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:

R={(0,x),(0,1),(x,1),(0,0),(x,x),(1,1)}

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.

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