From e69a6b33ae3c8627c9744e564c26a23bf7f36aeb Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 14:19:14 +0200 Subject: [PATCH 01/13] Better text in Section 5.3 on propositions, facts, and asserted facts. --- spec/index.html | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/spec/index.html b/spec/index.html index 0f44e08..5a0c596 100644 --- a/spec/index.html +++ b/spec/index.html @@ -722,17 +722,23 @@

Properties of simple entailment and satisfiability

We define the set of propositions in an interpretation as follows:

-

The set of propositions in an interpretation I is IPR(I) = { IT(x, y, z)｜x is in IR, y is in IP, z is in IR }; we observe that a proposition is in the extension of rdfs:Proposition.

+

The set of propositions in an interpretation I is IPR(I) = { IT(x, y, z)｜x is in IR, y is in IP, z is in IR }.

+ +

The denotation of a triple, being it a triple term or an asserted triple, is a proposition. Given the semantics of RDFS Interpretations, a proposition is in the extension of the class rdfs:Proposition.

We define the set of facts in an interpretation as follows:

-

The set F of facts in an interpretation I is F(I) = { IT(x, y, z)｜<x, z> is in IEXT(y) }. The set of facts is the set of propositions which are true in the interpretation.

+

The set F of facts in an interpretation I is F(I) = { IT(x, y, z)｜<x, z> is in IEXT(y) }.

+ +

A fact in an interpretation is a proposition which is true in the interpretation. In other words, a fact in an interpretation is the proposition corresponding to the denotation of an asserted triple in the interpretation.

Given a blank node mapping, we define the set of facts asserted by a graph in an interpretation as follows:

-

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) = { IT( [I+A](s), I(p), [I+A](o) )｜`s p o.` is in G }. We then 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.

+

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) = { IT( [I+A](s), I(p), [I+A](o) )｜`s p o.` is in G }.

+ +

Given a blank node mapping and an interpretation, an asserted fact in a graph is the proposition corresponding to the denotation of a triple in the graph. These asserted facts may not necessarily be among the facts in the interpretation.

-

We introduce a general definition of satisfiability of a graph in an interpretation as follows:

+

We introduce a general definition of satisfiability of a graph in an interpretation, based on the intuition that a graph is satisfied by an interpretation if the asserted facts by the graph are among the facts of the interpretation.:

An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.

From 1a6a1675e8590986bacae167752f0ad8ec039b36 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 14:43:31 +0200 Subject: [PATCH 02/13] Added rdfs:Proposition explanation in RDFS Section --- spec/index.html | 2 ++ 1 file changed, 2 insertions(+) diff --git a/spec/index.html b/spec/index.html index 5a0c596..8fd2e22 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1249,6 +1249,8 @@

RDFS Interpretations

Extension in I) from IC to the set of subsets of IR.

A class may have an empty class extension. Two different classes can have the same class extension. The class extension of rdfs:Class contains the class rdfs:Class.

+ +

RDFS introduces also the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in Section 5.3.

An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.

From 0a01814f01d3a36fa02b2f8d6e00dd6ea8e90f15 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 14:56:01 +0200 Subject: [PATCH 03/13] Added comment on rdf:reifies having no semantic condition in RDF --- spec/index.html | 2 ++ 1 file changed, 2 insertions(+) diff --git a/spec/index.html b/spec/index.html index 8fd2e22..ab0f98b 100644 --- a/spec/index.html +++ b/spec/index.html @@ -504,6 +504,8 @@

Simple Interpretations

the referent of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.

+ +

We observe that the rdf:reifies property does not have any special semantic condition in RDF. Its intended meaning is thoroughly explained in Section 1.5 of the RDF Concepts document.

Semantic extensions may impose further constraints upon interpretation mappings by requiring some IRIs to denote in particular ways. From b5784f4d3a4a65a9bace1eabe0d9716bb329ba69 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 16:25:49 +0200 Subject: [PATCH 04/13] accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin --- spec/index.html | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index ab0f98b..75e7337 100644 --- a/spec/index.html +++ b/spec/index.html @@ -504,8 +504,7 @@

Simple Interpretations

the referent of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.

- -

We observe that the rdf:reifies property does not have any special semantic condition in RDF. Its intended meaning is thoroughly explained in Section 1.5 of the RDF Concepts document.

+

We observe no IRI, not even those in the rdf:, has any special semantic condition associated to it in a simple interpretation.

Semantic extensions may impose further constraints upon interpretation mappings by requiring some IRIs to denote in particular ways. From 4ee6775bf26ba76f4f207a925b30e0a738a205f7 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 16:26:01 +0200 Subject: [PATCH 05/13] accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin --- spec/index.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/spec/index.html b/spec/index.html index 75e7337..8f0ea57 100644 --- a/spec/index.html +++ b/spec/index.html @@ -737,9 +737,9 @@

Properties of simple entailment and satisfiability

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) = { IT( [I+A](s), I(p), [I+A](o) )｜`s p o.` is in G }.

-

Given a blank node mapping and an interpretation, an asserted fact in a graph is the proposition corresponding to the denotation of a triple in the graph. These asserted facts may not necessarily be among the facts in the interpretation.

- -

We introduce a general definition of satisfiability of a graph in an interpretation, based on the intuition that a graph is satisfied by an interpretation if the asserted facts by the graph are among the facts of the interpretation.:

+

Given a blank node mapping and an interpretation, an asserted fact in a graph is the proposition corresponding to the denotation of a triple in the graph. These asserted facts may not necessarily be among the facts in the interpretation. + Intuitively, this would only be the case if the interpretation satisfies the graph. +

An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.

From 8a59587aa3609a587643aa6d335e14ae16acf4e9 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 16:26:12 +0200 Subject: [PATCH 06/13] accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 8f0ea57..b4c9c50 100644 --- a/spec/index.html +++ b/spec/index.html @@ -741,7 +741,7 @@

Properties of simple entailment and satisfiability

Intuitively, this would only be the case if the interpretation satisfies the graph.

-

An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.

+

An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.

From 1b9648265bb8a06999ed36af8bdc7b04ae80968b Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 16:26:22 +0200 Subject: [PATCH 07/13] accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index b4c9c50..c297c0a 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1251,7 +1251,7 @@

RDFS Interpretations

empty class extension. Two different classes can have the same class extension. The class extension of rdfs:Class contains the class rdfs:Class.

-

RDFS introduces also the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in Section 5.3.

+

RDFS introduces also the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in Section 5.3.

An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.

From 625c537cf0c18422ba5b02ac26d8128e8f4be937 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 17:11:50 +0200 Subject: [PATCH 08/13] accepted Niklas text improvement MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Niklas Lindström --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index c297c0a..fa9639c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -725,7 +725,7 @@

Properties of simple entailment and satisfiability

The set of propositions in an interpretation I is IPR(I) = { IT(x, y, z)｜x is in IR, y is in IP, z is in IR }.

-

The denotation of a triple, being it a triple term or an asserted triple, is a proposition. Given the semantics of RDFS Interpretations, a proposition is in the extension of the class rdfs:Proposition.

+

The denotation of a triple is a proposition, regardless of whether it is used as a triple term or an asserted triple. Given the semantics of RDFS Interpretations, a proposition is in the extension of the class rdfs:Proposition.

We define the set of facts in an interpretation as follows:

From 19009afd8832a8b868149c1efa25307d5c777665 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 17:25:55 +0200 Subject: [PATCH 09/13] accepting Niklas amended text MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Niklas Lindström --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index fa9639c..a453c36 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1251,7 +1251,7 @@

RDFS Interpretations

empty class extension. Two different classes can have the same class extension. The class extension of rdfs:Class contains the class rdfs:Class.

-

RDFS introduces also the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in Section 5.3.

+

RDFS also introduces the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in [[[#simple_entailment_properties]]].

An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.

From 974080fd8c4dd2a9f870cf3dad4390e6b61c2df9 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 17:35:23 +0200 Subject: [PATCH 10/13] accepted Andy's suggestion Co-authored-by: Andy Seaborne --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index a453c36..f1cd33f 100644 --- a/spec/index.html +++ b/spec/index.html @@ -504,7 +504,7 @@

Simple Interpretations

the referent of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.

-

We observe no IRI, not even those in the rdf:, has any special semantic condition associated to it in a simple interpretation.

+

We observe that no IRI, not even those in the rdf: namespace, has any special semantic condition associated with it in a simple interpretation.

Semantic extensions may impose further constraints upon interpretation mappings by requiring some IRIs to denote in particular ways. From 39cde88de798f74462249de588a9c0141271a713 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 4 Sep 2025 18:53:09 +0200 Subject: [PATCH 11/13] Added a brief intro on rdf:reifies --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index f1cd33f..9f37cd1 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1251,7 +1251,7 @@

RDFS Interpretations

empty class extension. Two different classes can have the same class extension. The class extension of rdfs:Class contains the class rdfs:Class.

-

RDFS also introduces the special class rdfs:Proposition, i.e. a resource whose extension is the set of propositions as defined in [[[#simple_entailment_properties]]].

+

RDFS also introduces the class rdfs:Proposition, which denotes a resource whose extension is exactly the set of propositions as defined in [[[#simple_entailment_properties]]]. The denotation of rdfs:Proposition also includes the range of the rdf:reifies property. A triple where the predicate is rdf:reifies and the object is therefore a proposition, is a reifying triple, and its subject is called a reifier.

An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.

From fabf0e11f91b05c9dac10e8bcc719f2f854f4cce Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 11 Sep 2025 16:43:39 +0200 Subject: [PATCH 12/13] Block commit of all the suggestion until 10 September --- spec/index.html | 37 ++++++++++++++++++++++++++++--------- 1 file changed, 28 insertions(+), 9 deletions(-) diff --git a/spec/index.html b/spec/index.html index 9f37cd1..d088af1 100644 --- a/spec/index.html +++ b/spec/index.html @@ -504,7 +504,8 @@

Simple Interpretations

the referent of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.

-

We observe that no IRI, not even those in the rdf: namespace, has any special semantic condition associated with it in a simple interpretation.

+

We observe that no IRI, not even those in the rdf: namespace, + has any special semantic condition associated with it in a simple interpretation.

Semantic extensions may impose further constraints upon interpretation mappings by requiring some IRIs to denote in particular ways. @@ -723,9 +724,14 @@

Properties of simple entailment and satisfiability

We define the set of propositions in an interpretation as follows:

-

The set of propositions in an interpretation I is IPR(I) = { IT(x, y, z)｜x is in IR, y is in IP, z is in IR }.

+

The set of propositions in an interpretation I is + IPR(I) = { IT(x, y, z) ｜ x is in IR, + y is in IP, z is in IR }.

-

The denotation of a triple is a proposition, regardless of whether it is used as a triple term or an asserted triple. Given the semantics of RDFS Interpretations, a proposition is in the extension of the class rdfs:Proposition.

+

The denotation of a triple is a proposition, whether it is used as a triple + term or an asserted triple. Under RDFS + Interpretations (see below), a proposition is in the extension of the + class rdfs:Proposition.

We define the set of facts in an interpretation as follows:

@@ -735,13 +741,19 @@

Properties of simple entailment and satisfiability

Given a blank node mapping, we define the set of facts asserted by a graph in an interpretation as follows:

-

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) = { IT( [I+A](s), I(p), [I+A](o) )｜`s p o.` is in G }.

+

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) = { IT( [I+A](s), I(p), [I+A](o) )｜ + `s p o.` is in G }.

Given a blank node mapping and an interpretation, an asserted fact in a graph is the proposition corresponding to the denotation of a triple in the graph. These asserted facts may not necessarily be among the facts in the interpretation. Intuitively, this would only be the case if the interpretation satisfies the graph.

-

An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.

+

An interpretation I (simply) satisfies a graph G + if and only if there exists a blank node mapping A such that the facts + asserted by the graph in the interpretation FEXT(G,I,A) are a subset of + the facts of the interpretation F(I).

@@ -1251,10 +1263,17 @@

RDFS Interpretations

empty class extension. Two different classes can have the same class extension. The class extension of rdfs:Class contains the class rdfs:Class.

-

RDFS also introduces the class rdfs:Proposition, which denotes a resource whose extension is exactly the set of propositions as defined in [[[#simple_entailment_properties]]]. The denotation of rdfs:Proposition also includes the range of the rdf:reifies property. A triple where the predicate is rdf:reifies and the object is therefore a proposition, is a reifying triple, and its subject is called a reifier. - -

An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I - which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.

+

RDFS also introduces the class rdfs:Proposition, + whose extension is exactly the set of propositions as defined + in [[[#simple_entailment_properties]]]. + This class is also declared as `rdfs:range` of the `rdf:reifies` property. + In other words, the object of a reifying triple + always denotes a proposition. + +

An RDFS interpretation (recognizing D) is an + RDF interpretation (recognizing D) I which satisfies the + semantic conditions in the following table, and all the triples in the + subsequent table of RDFS axiomatic triples.

From 9f28109e98669b061811832eec5b5d9e8af20b08 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 11 Sep 2025 18:27:53 +0200 Subject: [PATCH 13/13] Applied @tallTed suggestion Co-authored-by: Ted Thibodeau Jr --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index d088af1..11ff70c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -737,7 +737,7 @@

Properties of simple entailment and satisfiability

The set F of facts in an interpretation I is F(I) = { IT(x, y, z)｜<x, z> is in IEXT(y) }.

-

A fact in an interpretation is a proposition which is true in the interpretation. In other words, a fact in an interpretation is the proposition corresponding to the denotation of an asserted triple in the interpretation.

+

A fact in an interpretation is a proposition that holds in it, corresponding to a triple which is true in that interpretation.

Given a blank node mapping, we define the set of facts asserted by a graph in an interpretation as follows:

RDFS semantic conditions.