Wikidata:Property proposal/symbol represents

symbol represents

Originally proposed at Wikidata:Property proposal/Natural science

Done: symbol represents (P9758) (Talk and documentation)

Description	qualifier for "in defining formula" (P7235) which indicates the quantity or operator represented by a symbol in the "defining formula" (P2534)
Data type	Item
Allowed values	instances or subclasses of individual quantity (Q71550118); mathematical operators
Example 1	magnetic flux density (Q30204)in defining formula (P7235) ${\boldsymbol {F}}$ symbol representsforce (Q11402)
Example 2	mass diffusivity (Q604008)in defining formula (P7235) $\operatorname {\mathbf {grad} }$ symbol representsgradient (Q173582)
Planned use	migrate descriptions of formula variables from the currently used calculated from (P4934) and has part(s) (P527)
See also	defining formula (P2534), in defining formula (P7235)

Motivation

defining formula (P2534) is used in two ways:

a) To define the main item. Example: magnetic flux density. The symbol representing the main item is indicated using in defining formula (P7235); other symbols are indicated with in defining formula (P7235) qualifiers on corresponding calculated from (P4934) statements.

b) Named formulas or laws. Example: mass-energy equivalence. Symbols are indicates using an inconsistent mix of qualifiers (P7235, P7973, P416, P2534 [!], ...) on has part(s) (P527).

Neither of the currently used approaches is satisfactory; main discussions:

My personal summary of the issue:

"has part": that does not sound right when defining a quantity. What, exactly, is a part of, say, the vector quantity velocity (Q11465)? Time is not a part of velocity like an arm is a part of a body. Going that route would encourage others to use "has part" for, say, its vector components and maybe other things. We should use well-scoped properties instead.
"calculated from": Not all formulas are of the form $x=f(a,b,...)$ where $x$ is being defined; nor are all relations "computational". Moreover, calculated from (P4934) is being used in contexts where no formula is presents.

The goal of this proposal is a unified way to describe the meaning of variables in formulas of both type a) and b). Toni 001 (talk) 06:09, 19 April 2021 (UTC)[reply]

Addendum 1: The unfortunate current situation has been noted in the literature: https://arxiv.org/abs/2104.05111. It's time we fix that. Toni 001 (talk) 06:19, 19 April 2021 (UTC)[reply]

Addendum 2: I also like as possible label simply "represents". Toni 001 (talk) 07:37, 19 April 2021 (UTC)[reply]

Discussion

Comment Maybe defining formula (P2534) should be split for these two different situations (and could there be others)? But I do see the concern here. ArthurPSmith (talk) 17:33, 19 April 2021 (UTC)[reply]

Hello Arthur. The label in German and various other languages for P2534 is simply "formula". And that's how it is being used: Either to define or to "illustrate" an item. In practice I don't see a need to split that aspect. There is no strong reason (that I'm aware of) for either case a) or b) to use "has part" or "calculated from", other than two groups of contributors sticking to their convention. For instance, I contributed most of the nearly 700 formulas using "calculated from", but never liked it; which is why I've been pondering about how to unify and improve those approaches. Toni 001 (talk) 06:32, 20 April 2021 (UTC)[reply]

Support, an important property for science.--Arbnos (talk) 17:33, 22 April 2021 (UTC)[reply]
Comment Thank you for starting this worthwile discussion. I have been contributing some of the "has part" properties but also understand the motivation for "calculated from". @Toni 001:, you say: "Time is not a part of velocity like an arm is a part of a body." Philosophically, I agree with you. However, I understand the "has part" referring to "formula" not the abstract concept at hand. So if the formula is, e.g., "v = s/t", then v,s,t are all parts of the formula. The property "calculated from" seems also correct to me if you say that v can be calculated from s or t. Yet, you could say that "v = s/t" is also a "defining formula" for "distance" or at least the equivalent form "s = v t". Here you calculate s from v and t. In case the formula contains operators (sin,exp,int,...) I would not add them to "calculated from" but they are parts of the formula, so "has part" I think is more general than "calculated from". Maybe we should somehow make it more clear that "has part" refers to the "defining formula" not the abstract item concept, which often does not make sense. What do you think? PhilMINT (talk) 15:32, 26 April 2021 (UTC)[reply]
The issue with making the property has part(s) (P527) more specific is that is it used in many (1.7 million) other places: Including in its description a phrase "variable or operator in the formula" would be confusing in those other contexts. The typical way to go in such a situation is to create a more specific property. Take for instance the property flag image (P41): We could have used image (P18) to illustrate administrative territories with a flag; by creating the more specific P41 we make clear which aspect of a country, city, ... is illustrated. This then allows placing tight constraints on P41 to ensure that it is not used on, say, an apple. Toni 001 (talk) 04:31, 27 April 2021 (UTC)[reply]

Another way to see it: This proposal wants to create a "has part" specifically for formulas. In that sense I'm not negating that a symbol is a part of a formula. Toni 001 (talk) 05:07, 27 April 2021 (UTC)[reply]
Comment while I like the idea, I think it would be good to have only one option. How is this property different from https://www.wikidata.org/wiki/Property:P7235? I think a better approach would be to rename P7235 in "symbol represents" and delete the other properties. On the other hand, to me, time is a part of velocity in the same way as the arm is part of the body. If I would present a picture with a body without an arm and ask what is missing people would normally answer arm. In the same way, if I presented the formula $v={\frac {dx}{d?}}$ people would usually say ${\textstyle ?\to t.}$ At least that is what I believe would happen.--Physikerwelt (talk) 16:24, 26 April 2021 (UTC)[reply]
The property in defining formula (P7235) has datatype Mathematical expression which means that it can only store expressions (symbols, operators, ...). Then we need an way to indicate what that symbol or operator represents, which is what this proposal is about. (I'm slightly confused about the idea of renaming P7235, so maybe I'm missing something.) Toni 001 (talk) 04:19, 27 April 2021 (UTC)[reply]
Comment I’m slightly concerned that this will be confused with symbolizes (P4878). Can we put tight constraints on it to prevent that? - PKM (talk) 19:27, 26 April 2021 (UTC)[reply]
Yes, we should use constraints, different from (P1889) and a clear description to avoid confusion. Toni 001 (talk) 04:33, 27 April 2021 (UTC)[reply]
Comment we already have represents (P1268) and several other properties with “represents” as aliases. Perhaps this could be “variable represents” or something similar? - PKM (talk) 19:33, 26 April 2021 (UTC)[reply]
We should definitely add "variable represents" as alias. We might want to describe other things appearing in a formula - things which are not variables. That's why I propose the more general term "symbol" in the name. Toni 001 (talk) 04:35, 27 April 2021 (UTC)[reply]
Support, I think we should use "symbol represents" to include operators and constants. PhilMINT (talk) 08:21, 28 April 2021 (UTC)[reply]
Support, I think it's useful in particular where certain symbols are common in a field, or where constants are used in a defining formula (P2534). Ari T. Benchaim ^(talk) 01:27, 19 June 2021 (UTC)[reply]
Comment in the proposal, it seems to me you are adding properties to an item which do not directly relate to that item. In example 1 you are recording that F stands for Force, but the item is actually about magnetic flux density. A better model might be: create a new item for the formula itself then add in defining formula (P7235) to this item. Just an idea ... — Martin (MSGJ · talk) 11:09, 19 July 2021 (UTC)[reply]
Hello. Note the difference between quantity symbol (LaTeX) (P7973) and in defining formula (P7235), both of which store symbols: The first one lists all symbols which are typically used for a quantity, on the item of that quantity. The second one, on the other hand, lists exactly one symbol with which a quantity is represented in the formula. Toni 001 (talk) 07:46, 20 July 2021 (UTC)[reply]

@Toni 001, ArthurPSmith, Arbnos, PhilMINT, Physikerwelt: @PKM, Ari T. Benchaim, MSGJ:

Done symbol represents (P9758) Pamputt (talk) 05:52, 23 July 2021 (UTC)[reply]

Thank you! Ari T. Benchaim ^(talk) 13:44, 23 July 2021 (UTC)[reply]

Oppose. I find existing (already past?) system as logical and intuitive: we have main quantity (subj. of the item) which "is calculated from" other quantities (we can adjust this label to smth. like "derived from") by some relation (which can be non-formula if you like). Now after changes like these we have all quantities symmetrically in one property (in defining formula (P7235)) which doesn't make sense and make it harder to query. --Infovarius (talk) 21:41, 23 July 2021 (UTC)[reply]
For example, we can't see in https://reasonator.toolforge.org/?q=Q88865973 now which quantities are based upon this quantity. This what was made worse by changes. --Infovarius (talk) 21:44, 23 July 2021 (UTC)[reply]
Hello. The issues with calculated from (P4934) have been discussed before with various proposals to improve them, all of which failed for some (valid) reason. The way to understand the "new" system is the following: For each item with a formula, there are multiple in defining formula (P7235) statements; if one of them does not have a symbol represents (P9758) qualifier then that symbol can be understood as representing the "main" item. Toni 001 (talk) 10:23, 24 July 2021 (UTC)[reply]

Regarding external tools making use of formulas I'd say it would be good if they could be updated to make use of the new scheme. See for instance this query which lists in a very understandable form defining formulas for physical quantities and explains there variables. Toni 001 (talk) 10:28, 24 July 2021 (UTC)[reply]

Comment @Toni 001, Infovarius, ArthurPSmith, Physikerwelt: Unfortunately, with the new format, several systems do not work properly anymore. The Wikipedia Special page for formula information (e.g., https://en.wikipedia.org/w/index.php?title=Special:MathWikibase&qid=Q30006) does not display the identifiers anymore. The Mathematical Question Answering system MathQA (https://mathqa.wmflabs.org) cannot answer identifier relationship questions (e.g., 'relation between mass and energy' targeting Q35875) anymore. The responsible SPARQL query [1] does not work. @Toni 001: do you have an idea how to translate this query for the new format? Btw. your aforementioned query [2] does not work anymore either. PhilMINT (talk) 13:13, 27 December 2021 (UTC)[reply]
Supplement: The problem with the new format is that the hierarchy now has two additional intermediate layers. For example for Q35875 ('mass-energy equivalence') now {P7235 ('in defining formula'), 'E', P9758 ('symbol represents'), Q11379 ('energy')} instead of as earlier directly {P4934 ('calculated from'), Q11379 ('energy')}. So you first go over a symbol, which in turn has a property. Even if we found a SPARQL query, it would probably be very slow. PhilMINT (talk) 13:24, 27 December 2021 (UTC)[reply]
Hello @PhilMINT:
I maintain a query listing formulas (for physical quantities in this case) here.

Here's an query listing items with formula which connect two given quantities (mass and energy in this case):
select ?item ?itemLabel ?formula where { ?item p:P7235 / pq:P9758 wd:Q11423 . #mass ?item p:P7235 / pq:P9758 wd:Q11379 . #energy ?item wdt:P2534 ?formula . service wikibase:label { bd:serviceParam wikibase:language "en" } }
Try it!
Best wishes, Toni 001 (talk) 10:43, 28 December 2021 (UTC)[reply]
Thank you! PhilMINT (talk) 14:29, 28 December 2021 (UTC)[reply]