On Monadic Operators on Modal Pseudocomplemented De Morgan Algebras and Tetravalent Modal Algebras

Studia Logica - In our paper, monadic modal pseudocomplemented De Morgan algebras (or mmpM) are considered following Halmos’ studies on monadic Boolean algebras. Hence, their topological...     

Hilbert-style Presentations of Two Logics Associated to Tetravalent Modal Algebras

We analyze the variety of A. Monteiro’s tetravalent modal algebras under the perspective of two logic systems naturally associated to it. Taking profit of the contrapositive implication introduced by A. Figallo and P. Landini, sound and complete Hilbert-style calculi for these logics are presented.     

A Preliminary Study of MV-Algebras with Two Quantifiers Which Commute

In this paper we investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal-free two-dimensional cylindric algebras (see Henkin et al., in Cylindric algebras, 1985). In the 40s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two-dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia (Ann Pure Appl Logic 128(1-3):125–139, 2004) related to the characterization of a quantifier in terms of some special sub-algebra associated to it. On the other hand, we present a topological duality for this class of algebras and we apply it to characterize the congruences of one algebra via certain closed sets. Finally, we study the subvariety of this class generated by a chain of length n + 1 (n <  ω). We prove that the subvariety is semisimple and we characterize their simple algebras. Using a special functional algebra, we determine all the simple finite algebras of this subvariety.     

A Categorical Equivalence for Tense Nelson Algebras

Studia Logica - In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKt-congruence...