On the Incremental Union of Relations: A Key Property of General Systems Explained

Relations are one of the most important conceptual models and mathematical entities in logic, discrete mathematics, computer science, software science, system science, and formal semantics. However, some fundamental and indispensable operations on formal relations were overlooked in traditional studies. This paper presents an extended relation theory with a set of novel algebraic operators on relations beyond classic operations. The algebraic operators on formal relations known as the incremental union and decremental disunion are formally elaborated. The property of relational gains is mathematically modeled, which explains the dynamic mechanism of relations generated by associations of static sets of objects in physical or abstract systems.

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