The recently proposed (Güney and Hillery in Phys Rev A 90:062121, 2014; Phys Rev A 91:052110, 2015) group theoretical approach to the problem of violating the Bell inequalities is applied to S 4 group. The Bell inequalities based on the choice of three orbits in the representation space corresponding to standard representation of S 4 are derived and their violation is described. The corresponding nonlocal games are analyzed.
Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us to transparently use alternative logical frameworks, such as fuzzy relations. Mathematically, our work demonstrates how to enrich with modal operators and to give a many world semantics to an abstract algebraic logic framework. We also give some examples of applications of the modal extension.
We demonstrate how one can use the formal concept analysis (FCA) to obtain the role hierarchy for the role based access control from the existing access control matrix. We also discuss assesed by means of FCA the quality of security system and finding users with excess permissions.
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