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The Unified Modeling Language (UML) together with the Object Constraint Language (OCL) are the description means for modeling and specifying, e. g., software systems in early stages of the design. They allow to define components, their relations, and constraints of a system while, at the same time, hide precise implementation details. Despite providing a “blueprint” for the desired systems, UML/OCL descriptions also allow for an early validation and verification of the design. However, an often overseen feature of UML/OCL is that it explicitly allows for the consideration of irregular variables assignments such as null and invalid-yielding a four-valued logic in the current UML/OCL version. In this tutorial, we provide an overview on this feature and the resulting four-valued UML/OCL logic. More precisely, we are providing a review of the corresponding description means as well as existing methods that allow for a validation and verification of the corresponding models. By this, we are aiming to introduce those UML/OCL descriptions and methods to the MVL community in order to trigger new directions for research and application.

A modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC is introduced as a Gentzen-type sequent calculus. The completeness theorem with respect to a Kripke semantics for M4CC is proved. The finite model property for M4CC is shown by modifying the completeness proof. The decidability of M4CC is obtained as a corollary.

Four-valued semantics is applied to a deduction basis for granular reasoning with zooming operation. This enables the granular reasoning useful for the foundation of reasoning for incomplete and inconsistent information. We interpret the semantics of zooming operation with four-valued semantics based on partial interpretation and construct a deductive system with Belnap's four-valued logic. We also discuss an application with non-monotonic reasoning and paraconsistent logic using the zooming technique for frame problem.

Finding out the method of handling the missing information is essential for system efficiency and robustness in the field of the database. The sparsity of massive data in the big data environment makes the problem of missing information more prominent. The existing methods either have limited semantic expression ability or do not consider the influence of big data environment. Missing information in large-scale sparse data tends to have richer semantics, leading to more complex computational logic, as well as affecting operations such as data queries. To solve these problems, this paper proposes a novel missing information management method of logic operation definition and relational algebra expansion. Combining the practical case of big data environment, we summarize the missing information into two types: unknown value and nonexistent value, and define four-valued logic to support the logic operation. Based on the dynamic table model, we systematically extend the relational algebra to describe the data operations for massive sparse data. Our method is implemented in the self-developed big data management system Muldas. Experimental results on real large-scale sparse data set show the proposed four-valued logic and the relational algebra expansion of missing information have the good ability of semantic expression and computational efficiency.

In many-valued logic theories, the decision and construction for Sheffer functions is an important problem. The decision for Sheffer functions is interrelated to the decision for completeness of functions set, and the solution can be reduced to determining the minimal coverings of precomplete. It's well known that each precomplete set is a function set, T(G m ) , preserving the relation G m , therefore, the categorizing of this relation has provided the determination of precomplete set's minimal covering with more convenient ways. In this paper, preserving quaternary regularly separable relations in partial four-valued logic are categorized by similar relation.