Conversion of sentences

Identities

1. A < B = B > A
2. A | B = B | A
3. A <> B = B <> A
4. A |> B = B <| A

Likewise for the "dotted" variants:

1. A <. B = B .> A
2. A |. B = B .| A
3. A .|. B = B .|. A

Implications

1. A. implies I: A <. B => A <> B
2. .A* implies I: B .> A => B <> A
3. E. implies O: A |. B => A |> B
4. .E implies O*: B .| A => B <| A
5. .E. implies O and O*: A .|. B => A |> B, and A .|. B => A <| B

Such conversions from universal to particular sentences are not valid for the "undotted" A, A* and E relations.

References

[1]: Aristotle. Analytica Priora. Book 1, Chapter 2.