This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of over does not hold in lattices. Some properties rely law. Furthermore, we study relationship among law, lattice-valued relation.

This work extends the game-based framework of μ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. This problem has many applications in verification, such as handling abstract or partial models, analyzing systems in the presence o...

We deene the notion of meet-uniformity for closure operators on a complete lattice, which corresponds to co-additivity restricted to subsets mapped into the same element, and we study its properties. A class of closures given by principal lters and the downward closures are relevant examples of meet-uniform closures. Next, we introduce a lifting of a complete order by means of a meet-uniform cl...

Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neu...

Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present an implementation of a symbolic model checker for multi-valued temporal logics. The model checker...

Consider the square lattice Z with vertices at points with integer-valued coordinates in R = {(x1, x2)| xk ∈ R, k = 1, 2} and complex (or real) scalar fields u on the lattice Z, u : Z → C, that are defined by their values ui1i2 , ui1i2 ∈ C, at each vertex of the lattice with the coordinates (i1, i2), ik ∈ Z, k = 1, 2. Consider a class of two-dimensional discrete equations on the lattice Z for t...