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

AbstractI 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