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Erschienen in:
26.12.2015 | Foundations
Orthogonal relational systems
Erschienen in: Soft Computing | Ausgabe 11/2016
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Abstract
In this paper, we discuss the concept of relational system with involution. This system is called orthogonal if, for every pair of non-zero orthogonal elements, there exists a supremal element in their upper cone and the upper cone of orthogonal elements \(x,x'\) is a singleton (i.e. x; \(x'\) are complements of each other). To every orthogonal relational system can be assigned a groupoid with involution. The conditions under which a groupoid is assigned to an orthogonal relational systems are investigated. We will see that many properties of the relational system can be captured by the associated groupoid. Moreover, these structures enjoy several desirable algebraic features such as, e.g. a direct decomposition representation and the strong amalgamation property.