Connections Between MVn Algebras and n-valued Lukasiewicz-Moisil Algebras - IV

Afrodita Iorgulescu (Department of Computer Science, Academy of Economic Studies, Romania)

Abstract:

We introduce two chains of unary operations in the MV_n algebra of Revaz Grigolia; they will be used in establishing many connections between these algebras and n-valued Lukasiewicz-Moisil algebras (LM_n algebras for short). The study has four parts. It is by and large self-contained.

The main result of the first part is that MV₄ algebras coincide with LM₄ algebras. The larger class of ``relaxed''-MV_n algebras is also introduced and studied. This class is related to the class of generalized LM_n pre-algebras.

The main results of the second part are that, for n 5, any MV_n algebra is an LM_n algebra and that the canonical MV_n algebra can be identified with the canonical LM_n algebra.

In the third part, the class of good LM_n algebras is introduced and studied and it is proved that MV_n algebras coincide with good LM_n algebras.

In the present fourth part, the class of -proper LM_n algebras is introduced and studied. -proper LM_n algebras coincide (can be identified) with Cignoli's proper n-valued Lukasiewicz algebras. MV_n algebras coincide with -proper LM_n algebras (n 2). We also give the construction of an LM₃(LM₄) algebra from the odd (respectively even)-valued LM_n algebra (n 5), which proves that LM₄ algebras are as much important than LM₃ algebras; MV_n algebras help to see this point.

Keywords: MVn algebra, n-valued Lukasiewicz-Moisil algebra

Categories: F.4.1