Wikidata:Property proposal/implies (2)
implies
[edit]Originally proposed at Wikidata:Property proposal/Natural science
| Description | axiom or conjecture that this axiom or conjecture implies |
|---|---|
| Represents | logical consequence (Q374182) |
| Data type | Item |
| Domain | item, conjecture (Q319141), axiom (Q17736) |
| Allowed values | item, conjecture (Q319141), axiom (Q17736) |
| Example 1 | Riemann hypothesis (Q205966)→Lindelöf hypothesis (Q911528) |
| Example 2 | Generalized Riemann hypothesis (Q685140)→Artin's conjecture on primitive roots (Q2319635) |
| Example 3 | Schanuel's conjecture (Q1579982)→Four exponentials conjecture (Q5475668) |
| Example 4 | generalized continuum hypothesis (Q45412229)→axiom of choice (Q179692) |
| Example 5 | axiom of constructibility (Q1151112)→generalized continuum hypothesis (Q45412229) |
| Example 6 | continuum hypothesis (Q208416)→Martin's axiom (Q622185) |
Motivation
[edit]A property to model logical consequence (Q374182). For details of this notion one can refer to a Wikipedia article in their language or their favorirte mathematical logic literature. Some aspects regarding its Wikidata modeling:
- generalization of (P7719) was proposed to have "implies" as label and, nevertheless, to model an informal relation different from logical consequence (Q374182).
- Every statement implies a true statement and is implied by a false statement. So for this to be useful, one whould only consider the case in which either the two statements are both independent of a given theory (ZFC by default) or their truth is unknown.
- This is better modeled as a transitive Wikidata property, therefore a statement should be made as sharp as possible.
- One may want to state an implication result within a theory different from Zermelo–Fraenkel set theory with choice (Q10856991). In this case I'd suggest specifying the theory as value of the qualifier relative to (P2210).
慈居 (talk) 22:11, 20 August 2025 (UTC)
Discussion
[edit]
Notified participants of WikiProject Mathematics --Dexxor (talk) 21:25, 25 August 2025 (UTC)- Comment I think generalization of (P7719) is still good enough for now. It seems weird to use the "implies" property for the relation between Generalized Riemann hypothesis (Q685140) and Riemann hypothesis (Q205966) (the former contains the latter as a special case) and then switch to generalization of (P7719) once the hypothesis is proven. Dexxor (talk) 21:25, 25 August 2025 (UTC)
- I believe GRH and RH have both relationships and both are worth noting. Generalized Riemann hypothesis (Q685140)generalization of (P7719)Riemann hypothesis (Q205966) means that GRH covers RH, in whatever sense. This is informal and subjective matter but useful even if some of them are (dis)proved. Generalized Riemann hypothesis (Q685140)impliesRiemann hypothesis (Q205966) will be equivalent to , which does not depend on people's point of view, but will become useless if some of them are (dis)proved.
- I expect there to be some but only small overlaps between the two properties because a statement is not usually seen as a generalization of its implication if they differ in contents (see Examples 2 and 4–6 above). 慈居 (talk) 03:03, 26 August 2025 (UTC)
Support I agree. Dexxor (talk) 08:01, 26 August 2025 (UTC)
- @慈居, Dexxor:
Done --Tinker Bell ★ ♥ 01:47, 26 December 2025 (UTC)