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35
votes
10answers
2k views

Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the necessity of singling ...
2
votes
1answer
179 views

Why is a UNION operation independent in relational algebra?

Why is a set union operation independent in relational algebra? Why it cannot by expressed by the other four basic operations (selection, projection, cartesian product and difference)? What kind of ...
1
vote
0answers
118 views

Substitution semiring?

Let G be a [ CF ] grammar, and let elements of semiring be sets of rules. Define multiplication as: $$ x\otimes y = \{ t| \exists r \in x \exists s \in y (t=subst(r,s))\} $$ where $subst(r,s)$ ...
1
vote
2answers
353 views

Calculus of Binary Relations

I was reading "Origins of the Calculus of Binary Relations" by Vaughan Pratt where he says "it consists of two components, a logical or static component and a relative or dynamic component" but it ...