We prove that there is a one to one correspondence between monadic finite quasi-modal operators on a distributive nearlattice and quantifiers on the distributive lattice of its finitely generated filters, extending the results given in ``Calomino I., Celani S., González L. J.: Quasi-modal operators on distributive nearlattices, Rev. Unión Mat. Argent. 61 (2020), 339--352".
Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.
The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is...
In this short paper we introduce the notion of -filter in the class of distributive nearlattices and we prove that the -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.
A topological duality for monadic -valued Łukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz -valente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of -distributive lattices and -homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets...
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a -MV algebra, and every observable is defined by a smearing of a sharp...