Undefined abbreviations

[sulivanShu]

I'm currently studying RDF semantics alongside formal logic.

From https://w3c.github.io/rdf-semantics/spec/#simple , the abbreviations IR, I, IP, IEXT, IS, IL, and RE are introduced without their expansions.

These abbreviations do not appear to be standard in description logic — for instance, they are not documented on Wikipedia.

While such abbreviations may be transparent to experts, they can be opaque to readers encountering the specification for the first time. For example, I'm not entirely certain of the intended meaning of IS and RE — perhaps "Interpretation of Symbols" and "Reification of Expressions."

It might be helpful to include the expanded forms of these abbreviations alongside their definitions. The box in https://w3c.github.io/rdf-semantics/spec/#simple could be reworded for greater clarity, perhaps along the following lines:

Definition of a Simple Interpretation

0. Simple Interpretation (abbr. I): a structure consisting of the following components:
1. Interpretation of Resources (abbr. IR): a non-empty set of resources, called the domain or universe of I.
2. Interpretation of Properties (abbr. IP): a set of properties in the interpretation I.
3. Interpretation of Extensions (abbr. IEXT): a mapping from IP into the powerset of IR × IR—that is, into the set of sets of pairs ⟨x, y⟩ with x and y in IR.
4. Interpretation of Symbols (abbr. IS): a mapping from IRIs into (IR ∪ IP).
5. Interpretation of Literals (abbr. IL): a partial mapping from literals into IR.
6. Reification of Expressions (abbr. RE): an injective mapping from IR × IP × IR into IR, representing the denotation of triple terms.

[niklasl]

I would support an improvement along these lines.

[franconi]

I also believe it is a good idea to explain the choice of the symbols, even if I am not sure that they were meant as abbreviations, nor that they can be explained as abbreviations. We have to discuss about that.

[pfps]

I strongly believe that the current definitions of these symbols are adequate, namely:

1. A non-empty set IR of resources, called the domain or universe of I.

2. A set IP, called the set of properties of I.

3. A mapping IEXT from IP into the powerset of IR x IR i.e. the set of sets of pairs < x, y > with x and y in IR .

4. A mapping IS from IRIs into (IR union IP)

5. A partial mapping IL from literals into IR

6. An injective mapping RE from IR x IP x IR into IR, called the denotation of triple terms.

To me, 'expansions' like "Interpretation of Resources" are not correct. In particular IR is just a set, and not the interpretation of anything.

[sulivanShu]

The definition of the symbols is adequate, but the choice of symbols is obscure. Why "IR", "IP", "IEXT"? It seems that "I" stands for interpretation, "R" for resource, "P" for property, "EXT" for extension... It seems that the chosen symbols are shortened versions of longer names. What are the long names behind these symbols?

[pfps]

The symbols are just that - symbols. If you want to intuit a longer name for IR it would be something like "Resources of the Interpretation", but that's what the definition says.

[TallTed]

1. A non-empty set IR of resources, called the domain or universe of I.

This definition does not say "Resources of the Interpretation", nor does it say that "I" is a symbol or abbreviation of "Interpretation". Similar issues are found in each of the numbered definitions in #148 (comment) by @pfps.

At the least, I think a rearrangement of the current "definitions" into a table with a first column of either the full-name or the abbreviation (yes, all abbreviations might be considered to be symbols, but they have a derivation which can be helpful to know), and a second column of the other, followed by a column of their "definitions" or "meanings".

We must remember that a broad audience will be consuming these documents, and we should present the information herein in a way that is most easily understood by as much of that audience as possible. @sulivanShu is clearly not uneducated, and is in fact increasing their education even now, and had difficulty consuming our current draft document(s). I had similar difficulty the first several times I read the sections which use these "symbols"/"abbreviations". (I would have had an easier time had they been more abstract "symbols" — like ∆, ∂, ß, π, ¥, ∑, °, [though each of those has a common interpretation in one or more special contexts, such as currency symbols, physics, calculus, etc.] or others drawn from Voynich and the like — which are likely, if not guaranteed, not to appear in our texts.)

Brief clusters of capital letters — like I, IR, IP, IEXT, IS, IL, RE — not to mention the specialized language like "powerset" or "∪" — cry out for at least an expansion, as they appear to be acronyms, even if they are not. I hope that it is obvious that the domain-specific cant that includes "powerset" and "∪" should likewise be explained for the reader who is unfamiliar with this domain, which familiarity is not strictly nor clearly announced as a prerequisite.

[sulivanShu]

This discussion illustrates the tension that can exist between the logical rigor of a specification and the educational needs of readers.

While the symbols considered are not acronyms, it nevertheless seems that the characters chosen serve a mnemonic function.

Explaining the mnemonics behind the chosen characters should facilitate memorization of the symbols, not only for the RDF specification, but also for the OWL specification, which uses them extensively.

This explanation is already found in the document for ICEXT: "The semantic conditions are stated in terms of a mapping ICEXT (for the Class Extension in I) from IC to the set of subsets of IR." (9. RDFS Interpretations)

[franconi]

Being more a logician :-) I never realised that the function names have a rationale behind them.
Along these lines, we’d rather change the name of the newly introduces function RE to something like:
IPROP ?
ITT ?
New ideas?

[franconi]

(I prefer ITT)

[pfps]

Something like

A mapping IS from IRIs into (IR union IP), the denotation mapping for symbols in I.

seems reasonable.

I created PR #149 to modify the descriptions of the components of simple interpretations.

It might be reasonable to change RE to IT. Note that this is not for triple terms, but for triples!

[franconi]

Changing RE to IT would be perfect.
I’m travelling, @pfps can you make a PR?

[pfps]

@sulivanShu Are you satisfied with the changes in #149, plus a change from RE to IT?