Allen operators rendered through equivalences

In the 57th CIDOC CRM & 50th FRBR/LRMoo SIG Meeting, upon discussing issue 622, the SIG appointed WS to review the temporal primitive properties that are listed as superpreoperties to the Allen Operators that have been introduced in CRMarchaeo, and see how they can be represented as equivalences rather than material implications. 

Nb. Any changes that may result in CRMarchaeo, will go to the next draft release 

Marseille, October 2023

Post by Wolfgang Schmidle (8 November 2024)

Dear All,

I have checked the relationships between the Allen operators and the Temporal Primitives.

CRMarchaeo: The stated implications are indeed equivalences.

AP22(x,y) ⇔ P175(x,y) ∧ P175i(x,y) ∧ P184(x,y) ∧ P184i(x,y)
AP23(x,y) ⇔ P176i(x,y) ∧ P184(x,y) ∧ P184i(x,y)
AP24(x,y) ⇔ P175(x,y) ∧ P175i(x,y) ∧ P185(x,y)
AP25(x,y) ⇔ P176i(x,y) ∧ P185(x,y)
AP26(x,y) ⇔ P176(x,y) ∧ P174i(x,y) ∧ P185(x,y)
AP27(x,y) ⇔ P182(x,y) ∧ P173i(x,y)
AP28(x,y) ⇔ P183(x,y)

In particular, AP28 is not (only) a subproperty of P183 but in fact equivalent.

CRMbase: I have assumed that the Allen operators are exhaustive, i.e. any pair of Temporal Entities satisfies exactly one Allen relationship, regardless of our knowledge about it, even if the Temporal Entities are still ongoing. Then what is called "corresponds to" in the scope notes, for example in P175:

> This property corresponds to a disjunction (logical OR) of the following Allen temporal relations (Allen, 1983): {before, meets, overlaps, starts, started-by, contains, finished-by, equals}

are equivalences as well. For the example P175:

P175(x,y) ⇔ AP22(x,y) ∨ AP23i(x,y) ∨ AP24(x,y) ∨ AP24i(x,y) ∨ AP25i(x,y) ∨ AP26(x,y) ∨ AP27(x,y) ∨ AP28(x,y)

The full list, leaving out the x and y for better readability:

P173 ⇔ AP22 ∨ AP23 ∨ AP23i ∨ AP24 ∨ AP24i ∨ AP25 ∨ AP25i ∨ AP26 ∨ AP26i ∨ AP27 ∨ AP27i ∨ AP28
P174 ⇔ AP22 ∨ AP23 ∨ AP23i ∨ AP24 ∨ AP24i ∨ AP25 ∨ AP25i ∨ AP26 ∨ AP26i ∨ AP27 ∨ AP28
P175 ⇔ AP22 ∨ AP23i ∨ AP24 ∨ AP24i ∨ AP25i ∨ AP26 ∨ AP27 ∨ AP28
P176 ⇔ AP23i ∨ AP25i ∨ AP26 ∨ AP27 ∨ AP28
P182 ⇔ AP27 ∨ AP28
P183 ⇔ AP28
P184 ⇔ AP22 ∨ AP23 ∨ AP23i ∨ AP24 ∨ AP25 ∨ AP26 ∨ AP27 ∨ AP28
P185 ⇔ AP24 ∨ AP25 ∨ AP26 ∨ AP27 ∨ AP28

However, this list and its textual counterparts feel like a dramatic reading of a database dump to me. Perhaps a single table in the introduction for all Temporal Primitives, with simple yes-or-no entries, would be a more efficient way of conveying the same information?

Best,
Wolfgang

Post by Martin Doerr (8 November 2024)

Dear Wolfgang,

Thank you for checking this again!

I think putting this in a digestible initial list is not a bad idea.
Since CRMbase does not rely on Allen, this has the character of a
reference, but als a migration instruction from older CRMbase versions.
Since the Allen relations appear now in CRMarcheo, we should make sure
the way all temporal relations are presented is in the same style in
CRMarchaeo and CRMbase.

Of course, complete equivalence was intended, and Allens as
conjunction-only from ur primitives, and our primitives as disjunction
only from Allens.

All the best,

Martin