Residuation in non-associative MV-algebras

A Non-associative Generalization of Mv-algebras

We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices. c ©2007 Mathematical Institute Slovak Academy of Sciences 1. Non-associative MV-algebras As known, MV-algebras were introduced in the late-fifties by C . C . C h a n g as an algebraic semantics of the Lukasiewicz ma...

Continuous approximations of MV-algebras with product and product residuation

Recently, MV -algebras with product have been investigated from different points of view. In particular, in [EGM01], a variety resulting from the combination of MV -algebras and product algebras (see [H98]) has been introduced. The elements of this variety are called LΠ-algebras. Even though the language of LΠ-algebras is strong enough to describe the main properties of product and of Lukasiewi...

Non-canonicity of Mv-algebras

The varietyMV of all MV-algebras is shown to be non-canonical in a strong sense. Specifically it is shown that the canonical extension of the Chang algebra, K2, is not an MV-algebra. As a consequence, no non-finitely generated variety of MV-algebras is canonical.

Continuous approximations of MV-algebras with product and product residuation: a category-theoretic equivalence

In [9] a new class of MV -algebras with product, called LΠqalgebras, has been introduced. In these algebras, the discontinuous product residuation →π defined in [4] is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need of expressiveness and the need of continuity of connectives. Following a good tradition in many-valued logic (see e.g. [10...

Non Associative Linear Algebras