# Generalization of many-values logic minimization

What approaches of ternary and many-valued logic minimization algorithms (for example, Quine–McCluskey or Karnaugh map) are exists?

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 I will think about this. – mick Oct 8 '12 at 22:03 Which many-valued logical system? – Doug Spoonwood Oct 8 '12 at 23:37 For start, I would suggest checking Petr Hajek's book "Metamathematics of Fuzzy Logic". Chapter 6 on complexity and undecidability might have the answer to your question. – Kaveh Oct 9 '12 at 0:56 @DougSpoonwood, propositional logic. I specially added link on the wikipedia article. – KvanTTT Oct 9 '12 at 6:01 @KvanTTT There exists an infinity of many-valued propositional logics. Even if you only have the operations of implication and negation, and 3 truth values, you have 5 entries open in the truth table for implication, specifically those where 1/2 appears in (p->q) or equivalently {(0->1/2), (1/2->1/2), (1->1/2), (1/2->0), (1/2->1)}, and one for negation (the negation of "1/2" can equal 0, 1/2, or 1... though of course not in the same logical system) for (3^6)=729 possible logics. So which logical system do you want to talk about? One of Kleene's logics? Lukaseiweicz logic? Something else? – Doug Spoonwood Oct 10 '12 at 1:55