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I am searching for an algorithm (most likely already present in the literature) that could solve the following problem:

Instance: Properties of sets of elements and relations between sets of elements

Question: Find the closure of the properties and relations

Possible properties of a set of elements S:

1. S=∅

2. S≠∅

Possible relations between sets S, T:

1. S⊆T

2. S∩T=∅

3. S=T

4. S≠T

Example.

Instance: {S∩T=∅, S⊆R, R⊆T}

Solution: Closure C = {S∩T=∅, S⊆R, R⊆T, S⊆T, S=∅}

Hope the formulation of the question is clear enough.. If not I am happy to try to make it more precise. The solution could probably be somehow extracted from the Venn's diagram, but exact algorithm I have not yet found.

So if anybody came across such an algorithm and could write your suggestions here I would very much appreciate it.

Thanks in any case

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# Closure of relations betweens sets

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