Connections between MVn algebras and n-valued Lukasiewicz-Moisil algebras Part I Original Research Article

I introduce in the MVn algebras of Revaz Grigolia two chains of unary operations, which are key in establishing many connections between these algebras and n-valued Lukasiewicz-Moisil algebras (LMn algebras for short). The study has three parts. It is self-contained as much as possible. The main result of the first part is that MV4 algebras coincide with LM4 algebras. The larger class of ‘relaxed’-MVn algebras is also introduced and studied. This class is related to the class of generalized LMn pre-algebras. The main result of the second part is that, for n ⩾ 5, any MVn algebra is an LMn algebra and the converse is not true. The main result of the third part is the construction of an LM3(LM4) algebra from the odd (even)-valued LMn algebra (n ⩾ 5). This proves that LM4 algebras are as important as LM3 algebras; MVn algebras helped us to see that.