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Set logic

Relational classifications in Minyu operate on sets of rows, not on individual values.
Set logic defines how multiple result sets are combined, filtered, or compared to produce a final outcome.

In Minyu, all set operations work on row identity. Attribute values are not compared directly.

What a set is

A set is a collection of row identities (id) originating from the same table.

  • Each row can appear at most once in a set.
  • Sets do not preserve order.
  • All operations are type-safe: sets must originate from the same table.

Sets are produced by relation traversal, classification evaluation, and filtering.

Core properties

All set operations in Minyu share these properties:

  • No duplicates
    Membership is based on row identity. A row cannot appear more than once.

  • Type safety
    Set operations are only valid between sets from the same table.
    Cross-table combinations are not allowed.

These constraints are enforced by the system.

Union (A ∪ B)

The union contains all rows that exist in either set A or set B.

  • Minyu meaning: rows that match Classification A OR Classification B.
Set Result
Set A {1, 2, 3, 4}
Set B {3, 4, 5, 6}
Union (A ∪ B) {1, 2, 3, 4, 5, 6}

If a row appears in both sets, it still appears only once in the result.

Intersection (A ∩ B)

The intersection contains only rows that exist in both sets.

  • Minyu meaning: rows that match Classification A AND Classification B.
Set Result
Set A {1, 2, 3, 4}
Set B {3, 4, 5, 6}
Intersection (A ∩ B) {3, 4}

If either input set is empty, the result is empty.

Difference (A − B and B − A)

The difference contains rows that exist in one set but not the other.

  • Minyu meaning: exclusion-based filtering.

This operation is directional.

Operation Result
Difference (A − B) {1, 2}
Difference (B − A) {5, 6}

Reversing the operands changes the result.

Identity selection (single-set selection)

Identity selection is not a mathematical set operation.

It represents selecting exactly one set without combining it with another.
This exists because Minyu allows selecting a single region in the set-selection model.

  • Minyu meaning: pass-through of one classification result set without modification.
Selection Result
All in A {1, 2, 3, 4}
All in B {3, 4, 5, 6}

No filtering or comparison occurs.

Symmetric difference (A Δ B)

The symmetric difference contains rows that exist in either A or B, but not both.

  • Minyu meaning: exclusive classification matching.
Operation Result
Symmetric difference (A Δ B) {1, 2, 5, 6}

Rows present in both sets are excluded.

Usage in Minyu

Set operations are used when combining results from:

  • relational classifications
  • logical classifications
  • multi-path evaluations

They determine how multiple classification result sets are merged into a final evaluated set.
Evaluation always operates on row identity, ensuring stable behavior even when attribute values change.

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