# User:StarTower/Structure Notes/Also known as

## Lexicon $\subseteq$ Terms $\times$ Concepts

Loosely, a term of mathematics is an expression or label that practitioners of mathematics use to refer to mathematical objects.

Denote the set of all terms as $\mathcal T$.

Loosely, let the set of all definiens found in mathematical literature be denoted as $\mathcal D$.

A concept of mathematics is an equivalence class of $\mathcal D / \equiv$, where $\equiv$ denotes the equivalence relation of logical equivalence (under the most widely accepted and used proof system).

(This idea is not new and is formalised inside mathematics by provable equivalence. A rough overview only is intended here.)

Denote the set of all concepts $\mathcal D / \equiv$ as $\mathcal C$.

Ideally, and possibly even naively, it might be hoped that a lexicon for mathematics (in a particular natural language) would be a one-to-one relation on $\mathcal T \times \mathcal C$.

There are many reasons why this is not so (this would not be so even if mathematicians agreed to start from scratch right now) and why any contemporary lexicon $\mathcal L$ (a lexicon which would attempt to encompass all the literature) is better modeled as a many to many relation on $\mathcal T \times \mathcal C$.

$\mathsf{Pr} \infty \mathsf{fWiki}$ has divided and addressed this problem:

### $\mathcal L$ is One-to-Many: Disambiguation Pages

A term, such as zero, may refer to a number of concepts in separate contexts.

The prevailing way to address this on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to have title the pages structured as so:

• Definition:Zero (Context One)
• Definition:Zero (Context Two)
• Etc.

and to have Definition:Zero itself be a disambiguation page with a nested bullet point structure:

• Field 1
• Usage 1 in Field 1
• Usage 2 in Field 1
• Etc.
• Field 2
• Usage 1 in Field 2
• Usage 2 in Field 2
• Etc.
• Etc.

### $\mathcal L$ is Many-to-One: "Also known as" Sections

#### Synonyms with no conflict

Sometimes a term $A$ has a synonym $A '$ such that $A$ and $A '$ point to the exact same concept and nothing else (as far as the editors of $\mathsf{Pr} \infty \mathsf{fWiki}$ that are aware of the page know).

E.g. "Path-connected" and "path connected"

For a definition page of a term $A$, let these be referred to as its synonyms with no conflict.

#### Synonyms with external conflict

Sometimes a term $A$ (pointing to the concept $C$ on $\mathsf{Pr} \infty \mathsf{fWiki}$) has a synonym $A '$ such that $A '$ may point to either the concept $C$ or a distinct concept $C '$ in the literature.

E.g. "Irreflexive" for "antireflexive"

For a definition page of a term $A$, let these be referred to as its synonyms with external conflict.

#### Synonyms with internal conflict

Sometimes a term $A$ (pointing to the concept $C$ on $\mathsf{Pr} \infty \mathsf{fWiki}$) has a synonym $A '$ such that $A '$ may point to the concept $C$, but is used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to point to another concept.

E.g. "Sentence" and "string" for "word"

For a definition page of a term $A$, let these be referred to as its synonyms with internal conflict.

Synonyms with no conflict may be useful to a future advancement of the site's search function and allowing viewers to find the pages they are after more readily.

The other two types of synonyms, identified thus far, will likely not be as straightforward.

To facilitate the parsing of $\mathsf{Pr} \infty \mathsf{fWiki}$ that would occur when this does happen, there should be a regular structure to the Also known as sections (implemented for new terms from here on out perhaps).

A possible template to this may be:

== Also known as ==

(Possible leading line (such as, "Some sources use the terms:"))

* '''Synonym with no conflict 1''' - (Optional note 1).
* '''Synonym with no conflict 2''' - (Optional note 2).
* Etc.

* '''Synonym with external conflict 1''' - (Mandatory note 1).
* '''Synonym with external conflict 2''' - (Mandatory note 2).
* Etc.

* '''Synonym with internal conflict 1''' - (Mandatory note 1).
* '''Synonym with internal conflict 2''' - (Mandatory note 2).
* Etc.

Additional synonym-related information that is not so simply accommodated to the above bullet point lists.


For the benefit of the parser, the mandatory notes of the external conflict subsection could contain a key word or phrase such as:

[[ProofWiki:Books|literature]]


and the mandatory notes of the internal conflict subsection could contain a key word or phrase such as:

{{ProofWiki}}


--StarTower (talk) 16:02, 27 January 2014 (UTC)