A formal background to unify triples and triple terms

[franconi]

Added at the end of Section 5.3:

• semantic properties relating triple terms and asserted triples, together with a general definition of (simple) satisfiability.

The terminology defined here should be used to support the unification of the terminology of triples, as per issue #158 in Concepts.

This closes #87

---

Preview | Diff

[pfps]

I would add "in an interpretation" after the introductory sentence of the first three definitions. That's pedantic, I know, but I think helpful here.

The third definition needs to be pedantic about whether A is included - A is missing from the "given" part.

The last definition reads as if blank node mappings are somehow part of graphs. Why not just use "..., ..., and ..."?

The last definition needs to have the blank node mapping everywhere it is required.

[franconi]

I would add "in an interpretation" after the introductory sentence of the first three definitions. That's pedantic, I know, but I think helpful here.

The third definition needs to be pedantic about whether A is included - A is missing from the "given" part.

The last definition reads as if blank node mappings are somehow part of graphs. Why not just use "..., ..., and ..."?

The last definition needs to have the blank node mapping everywhere it is required.

The latest commit should satisfy your comments, thanks.

[franconi]

@pfps, your requested change remains open, and I have no way to close it...

[pfps]

Better now.

[niklasl]

LGTM!

[franconi]

Ahah: https://letmegooglethat.com/?q=LGTM&l=1

[pfps]

It's a new initialism to get around the current political crackdown and still show that you are woke. I'll let you work out the expansion for yourself.

[afs]

Suggested change

	<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;&lt;x, y, z&gt;&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}; it is easy to see that the facts are the propositions which are true in the interpretation. </p>
	<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;&lt;x, y, z&gt;&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}. The set of facts is the set of propositions which are true in the interpretation. </p>

At a minimum

Suggested change

	<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;&lt;x, y, z&gt;&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}; it is easy to see that the facts are the propositions which are true in the interpretation. </p>
	<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;&lt;x, y, z&gt;&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}; it can be seen that the facts are the propositions which are true in the interpretation. </p>

[pchampin]

Suggested change

	<p class="fact">Given a blank node mapping A, the set of all facts asserted by a graph G in an interpretation I is FEXT(G, I, A) = {&nbsp;&lt;&nbsp;[I+A](s), I(p), [I+A](o)&nbsp;&gt;&#65372;`s p o.` is in G&nbsp;}; we observe that given a blank node mapping, the asserted facts of a graph in an interpretation may not necessarily be among the facts of the interpretation.</p>
	<p class="fact">Given a blank node mapping A, the set of all facts asserted by a graph G in an interpretation I is FEXT(G, I, A) = {&nbsp;&lt;&nbsp;[I+A](s), I(p), [I+A](o)&nbsp;&gt;&#65372;`s p o.` is in G&nbsp;}; we observe that given a blank node mapping, the asserted facts of a graph with respect to an interpretation may not necessarily be among the facts of the interpretation.</p>

I prefer this kind of wording. I don't see the graph doing anything in the interpretation.

[TallTed]

Good forward motion!

[niklasl]

Is the denotation of a triple term in the codomain of RE (i.e. the injectively mapped resource in IR)? If so, should the sets of propositions and facts also be defined using RE (e.g. IPR = { RE(x, y, z) | x ∈ IR, y ∈ IP, z ∈ IR })?

[doerthe]

I am not happy with that sentence because of the definition of "(simply) satisfies":
"we say that I (simply) satisfies E when I(E)=true"
and
"If E is an RDF graph then I(E) = true if [ I+A ](E) = true for some mapping A from the set of blank nodes in E to IR"

So, the "simply satisfies" includes that there EXISTS some A, so even with a given A, we could technically find an A' such that I(G)= true while FEXT(G, I, A)\notIn F(I).

[pchampin]

I totally agree with @doerthe here. This statement seems wrong.