(The "L"'s in the two names should have lines through them, sorry).(adsbygoogle = window.adsbygoogle || []).push({});

Slupencki expanded (in 1936) the three-valued Lukasiewicz calculus L_{3}

to L_{3}S in order to make it functionally complete. He did this by adding functor T(.), where T(x) = 1 for all x in {0,1,2}, and two axioms: Tx⇒~Tx and ~Tx⇒Tx. Since val(x)= val(~x) if val(x) = 1, these axioms would seem OK, but what I don't get is why we cannot say then that Tx⇔~Tx poses an unacceptable contradiction. :(

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# Lukasiewicz-Slupencki three-valued calculus

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