From 4300b64c5b910b4142e07f9edd564d9a241a9c5c Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Mon, 27 Jan 2025 17:42:40 +0100 Subject: [PATCH 01/26] First version of liberal semantics - it lack the entailment pattern for rdfs:Proposition --- spec/index.html | 67 +++++++++++++++++++++++++++++++++++++++---------- 1 file changed, 54 insertions(+), 13 deletions(-) diff --git a/spec/index.html b/spec/index.html index beb5ea5..073bb98 100644 --- a/spec/index.html +++ b/spec/index.html @@ -261,7 +261,7 @@

Notation and Terminology

A ground RDF graph is one that contains no blank nodes.

Suppose that M is a functional mapping from a set of blank - nodes to some set of literals, blank nodes and IRIs. Any graph obtained + nodes to some set of RTD terms. Any graph obtained from a graph G by replacing some or all of the blank nodes N in G by M(N) is an instance of G. Any graph is an instance of itself, an instance of an instance of G is an instance of G, @@ -298,6 +298,11 @@

Notation and Terminology

is lean. Ground graphs are lean.

+ +

+ A RDF term appears in a graph G if it is in the set TM(G) defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
+ A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, object appears in G. +

Shared blank nodes, unions and merges

@@ -936,7 +941,7 @@

RDF Interpretations

- rdf:type rdf:subject rdf:predicate rdf:object + rdf:type rdf:reifies rdf:subject rdf:predicate rdf:object rdf:first rdf:rest rdf:value rdf:nil rdf:List rdf:langString rdf:Property rdf:_1 rdf:_2 ... @@ -1060,6 +1065,7 @@

Patterns of RDF entailment (Informative)

In addition, the first RDF semantic condition justifies the following entailment pattern:

+ + + + + + + + + + + + + + + + +
if the triple or triple term appears in Sthen S RDF entails, recognizing D
rdfD2xxx aaa yyy aaa rdf:type rdf:Property .

So that the above example also RDF entails

ex:p rdf:type rdf:Property .

recognizing {xsd:integer}.

@@ -1118,6 +1141,7 @@

RDFS Interpretations

rdfs:domain rdfs:range rdfs:Resource rdfs:Literal rdfs:Datatype rdfs:Class rdfs:subClassOf rdfs:subPropertyOf + rdfs:Proposition rdfs:member rdfs:Container rdfs:ContainerMembershipProperty rdfs:comment rdfs:seeAlso rdfs:isDefinedBy rdfs:label @@ -1206,6 +1230,10 @@

RDFS Interpretations

x is in ICEXT(I(rdfs:Datatype)) then < x, I(rdfs:Literal) > is in IEXT(I(rdfs:subClassOf))

+ +

If + exist x,y,z such that RE(x,z,y)=r, or exists x such that < x,r > is in IEXT([I+A](rdf:reifies)),
then < r,[I+A](rdfs:Proposition)> is in IEXT([I+A](rdf:type))

+ @@ -1253,6 +1281,9 @@

RDFS Interpretations

rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso .

+ rdf:reifies rdf:range rdfs:Proposition .
+
+ rdfs:Datatype rdfs:subClassOf rdfs:Class .

rdf:_1 rdf:type rdfs:ContainerMembershipProperty .
@@ -1261,7 +1292,8 @@

RDFS Interpretations

rdf:_2 rdf:type rdfs:ContainerMembershipProperty .
rdf:_2 rdfs:domain rdfs:Resource .
rdf:_2 rdfs:range rdfs:Resource .
- ...
+ ...
+
@@ -1391,16 +1423,6 @@

Patterns of RDFS entailment (Informative)

yyy aaa zzz . zzz rdf:type xxx . - - rdfs4a - xxx aaa yyy . - xxx rdf:type rdfs:Resource . - - - rdfs4b - xxx aaa yyy. - yyy rdf:type rdfs:Resource . - rdfs5 xxx rdfs:subPropertyOf yyy .
@@ -1452,6 +1474,25 @@

Patterns of RDFS entailment (Informative)

+ +

+ + + + + + + + + + + + + + +
If the triple or triple term appears in S:then S RDFS entails recognizing D:
rdfs4xxx aaa yyy xxx rdf:type rdfs:Resource .
+ yyy rdf:type rdfs:Resource .
+

RDFS provides for several new ways to be unsatisfiable recognizing D. For example, the following graph is RDFS unsatisfiable recognizing {xsd:integer, xsd:boolean}:

From 61aa733d6c29c3792ac474ed71223c281bab7461 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Mon, 27 Jan 2025 18:12:57 +0100 Subject: [PATCH 02/26] Missing fix to rdfs14 --- spec/index.html | 42 ++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 40 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index 073bb98..e4c362f 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1490,6 +1490,12 @@

Patterns of RDFS entailment (Informative)

xxx rdf:type rdfs:Resource .
yyy rdf:type rdfs:Resource . + + rdfs14 + xxx yyy <<(aaa bbb ccc)>> + xxx yyy _:nnn .
+ _:nnn rdf:type rdfs:Proposition . + @@ -1598,11 +1604,21 @@

Entailment rules (Informative)

ex:d ex:a ex:e . ex:d rdf:type ex:c . + + + + RDFS entails + + + + ex:a ex:b ex:c . + <<(ex:a ex:b ex:c)>> rdf:type rdfs:Proposition . + -

Both of these can be handled by allowing the rules to apply to a generalization of the RDF syntax - in which literals may occur in subject position and blank nodes may occur in predicate position.

+

These examples can be handled by allowing the rules to apply to a generalization of the RDF syntax + in which literals and triple terms may occur in subject position and blank nodes may occur in predicate position.

@@ -1680,6 +1696,28 @@

Entailment rules (Informative)

As noted earlier, detecting datatype entailment for larger sets of datatype IRIs requires attention to idiosyncratic properties of the particular datatypes.

+ +

+ The complete entailment pattern for generalized RDF considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following, which supersedes the entailment pattern rdfs14: + + + + + + + + + + + + + + +
RDFS-T entailment pattern.
if S containsthen S RDFS entails
Grdfs14xxx rdf:type rdfs:Resource .
+ yyy rdf:type rdf:Property .
+ zzz rdf:type rdfs:Resource .
+ 		<<(xxx yyy zzz)>> rdf:type rdfs:Proposition .
+

From 553dfc9986e46d2a428e44057990f70fe7a80b48 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Mon, 27 Jan 2025 19:08:56 +0100 Subject: [PATCH 03/26] liberal baseline RDF and RDFS semantics --- spec/index.html | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index e4c362f..607d517 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1493,7 +1493,8 @@

Patterns of RDFS entailment (Informative)

rdfs14 xxx yyy <<(aaa bbb ccc)>> - xxx yyy _:nnn .
+ the graph S with the appearance replaced with
+ xxx yyy _:nnn
_:nnn rdf:type rdfs:Proposition . From 4204f21f069f43c73a569539edf93a112d09af6f Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Tue, 28 Jan 2025 10:30:24 +0100 Subject: [PATCH 04/26] Fixed HTML + RTD -> RDF --- spec/index.html | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/spec/index.html b/spec/index.html index 607d517..47bc720 100644 --- a/spec/index.html +++ b/spec/index.html @@ -113,7 +113,7 @@

This document is part of RDF 1.2 document suite. This is a revision of the 2014 Semantics specification for RDF [[RDF11-MT]] and supersedes that document. - The technical content of the document is unchanged, only minor editorial changes have been made. + The technical content of the document is unchanged, only minor editorial changes have been made.

@@ -261,7 +261,7 @@

Notation and Terminology

A ground RDF graph is one that contains no blank nodes.

Suppose that M is a functional mapping from a set of blank - nodes to some set of RTD terms. Any graph obtained + nodes to some set of RDF terms. Any graph obtained from a graph G by replacing some or all of the blank nodes N in G by M(N) is an instance of G. Any graph is an instance of itself, an instance of an instance of G is an instance of G, @@ -1230,7 +1230,7 @@

RDFS Interpretations

x is in ICEXT(I(rdfs:Datatype)) then < x, I(rdfs:Literal) > is in IEXT(I(rdfs:subClassOf))

- +

If exist x,y,z such that RE(x,z,y)=r, or exists x such that < x,r > is in IEXT([I+A](rdf:reifies)),
then < r,[I+A](rdfs:Proposition)> is in IEXT([I+A](rdf:type))

@@ -1492,7 +1492,7 @@

Patterns of RDFS entailment (Informative)

rdfs14 - xxx yyy <<(aaa bbb ccc)>> + xxx yyy <<(aaa bbb ccc)>> the graph S with the appearance replaced with
xxx yyy _:nnn
_:nnn rdf:type rdfs:Proposition . @@ -1613,7 +1613,7 @@

Entailment rules (Informative)

ex:a ex:b ex:c . - <<(ex:a ex:b ex:c)>> rdf:type rdfs:Proposition . + <<(ex:a ex:b ex:c)>> rdf:type rdfs:Proposition . @@ -1714,7 +1714,7 @@

Entailment rules (Informative)

yyy rdf:type rdf:Property .
zzz rdf:type rdfs:Resource .
- <<(xxx yyy zzz)>> rdf:type rdfs:Proposition . + <<(xxx yyy zzz)>> rdf:type rdfs:Proposition . From ad4faa53b52583f188653d2fe417420d3c5205c8 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Tue, 28 Jan 2025 10:35:14 +0100 Subject: [PATCH 05/26] Fixed more HTML --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 47bc720..9e67d7c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1699,7 +1699,7 @@

Entailment rules (Informative)

requires attention to idiosyncratic properties of the particular datatypes.

- The complete entailment pattern for generalized RDF considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following, which supersedes the entailment pattern rdfs14: + The complete entailment pattern for generalized RDF considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following: From 3999bd8f3db806f4573d1eacf957fe2fe3e031f9 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Tue, 28 Jan 2025 10:38:26 +0100 Subject: [PATCH 06/26] Minor fix in text for better English Co-authored-by: Ted Thibodeau Jr --- spec/index.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index 9e67d7c..d93b395 100644 --- a/spec/index.html +++ b/spec/index.html @@ -300,8 +300,8 @@

Notation and Terminology

is lean. Ground graphs are lean.

- A RDF term appears in a graph G if it is in the set TM(G) defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
- A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, object appears in G. + An RDF term appears in a graph G if it is in the set TM(G), defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
+ A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, and object appears in G.

From 4e1cef6d08647168b84c6d0961c7feb53adaa25d Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:07:44 +0100 Subject: [PATCH 07/26] Better English: added comma --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index d93b395..90630c1 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1699,7 +1699,7 @@

Entailment rules (Informative)

requires attention to idiosyncratic properties of the particular datatypes.

- The complete entailment pattern for generalized RDF considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following: + The complete entailment pattern for generalized RDF, considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following:

RDFS-T entailment pattern.
From 8487a1388b2cb439e9a8f5fa98f21acf89acd019 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:10:10 +0100 Subject: [PATCH 08/26] Added axiomatic triple in RDF for rdf:reifies --- spec/index.html | 1 + 1 file changed, 1 insertion(+) diff --git a/spec/index.html b/spec/index.html index 90630c1..97728cc 100644 --- a/spec/index.html +++ b/spec/index.html @@ -974,6 +974,7 @@

RDF Interpretations

rdf:subject rdf:type rdf:Property .
rdf:predicate rdf:type rdf:Property .
rdf:object rdf:type rdf:Property .
+ rdf:reifies rdf:type rdf:Property .
rdf:first rdf:type rdf:Property .
rdf:rest rdf:type rdf:Property .
rdf:value rdf:type rdf:Property .
From c5914b40266887053ecbf4eb175709800a87b5f8 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:18:59 +0100 Subject: [PATCH 09/26] Moved the "appears in" definition before its first use. --- spec/index.html | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/spec/index.html b/spec/index.html index 97728cc..770a00f 100644 --- a/spec/index.html +++ b/spec/index.html @@ -260,9 +260,14 @@

Notation and Terminology

A ground RDF graph is one that contains no blank nodes.

+

+ An RDF term appears in a graph G if it is in the set TM(G), defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
+ A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, and object appears in G. +

+

Suppose that M is a functional mapping from a set of blank nodes to some set of RDF terms. Any graph obtained - from a graph G by replacing some or all of the blank nodes N in G by M(N) is + from a graph G by replacing some or all of the blank nodes N appearing in G by M(N) is an instance of G. Any graph is an instance of itself, an instance of an instance of G is an instance of G, and if H is an instance of G then every triple in H is an instance of at least one triple @@ -299,11 +304,6 @@

Notation and Terminology

is lean. Ground graphs are lean.

-

- An RDF term appears in a graph G if it is in the set TM(G), defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
- A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, and object appears in G. -

-

Shared blank nodes, unions and merges

From fd09c1f8a1a8d251ab85c47c16b234c358feafcc Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:23:00 +0100 Subject: [PATCH 10/26] "RDF term" definition is exported 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 770a00f..9cdc85c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -266,7 +266,7 @@

Notation and Terminology

Suppose that M is a functional mapping from a set of blank - nodes to some set of RDF terms. Any graph obtained + nodes to some set of [=RDF terms=]. Any graph obtained from a graph G by replacing some or all of the blank nodes N appearing in G by M(N) is an instance of G. Any graph is an instance of itself, an instance of an instance of G is an instance of G, From d734184aac5d3bc7c95e4a2dd03dda8abe8f8b62 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:33:13 +0100 Subject: [PATCH 11/26] Added the reference to RTDF symmetric triple --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 9cdc85c..8554ae3 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1700,7 +1700,7 @@

Entailment rules (Informative)

requires attention to idiosyncratic properties of the particular datatypes.

- The complete entailment pattern for generalized RDF, considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following: + The complete entailment pattern for generalized RDF with [=symmetric RDF triple=]s, considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following:

RDFS-T entailment pattern.
From b9c0e070a2d2bd518eb591b2a2e051d5b66be492 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Wed, 29 Jan 2025 16:38:51 +0100 Subject: [PATCH 12/26] Changed rdf:range to rdfs:range 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 8554ae3..449a31c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1282,7 +1282,7 @@

RDFS Interpretations

rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso .

- rdf:reifies rdf:range rdfs:Proposition .
+ rdf:reifies rdfs:range rdfs:Proposition .

rdfs:Datatype rdfs:subClassOf rdfs:Class .
From e35b24781fc813f5d0d6eae806ea3986274b142e Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 11:55:29 +0100 Subject: [PATCH 13/26] Replaced [I+A] with I for rdf/rdfs namespace IRIs --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 449a31c..9a6019a 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1233,7 +1233,7 @@

RDFS Interpretations

 + exist x,y,z such that RE(x,z,y)=r, or exists x such that < x,r > is in IEXT(I(rdf:reifies)),
then < r,I(rdfs:Proposition)> is in IEXT(I(rdf:type))

RDFS-T entailment pattern.

If - exist x,y,z such that RE(x,z,y)=r, or exists x such that < x,r > is in IEXT([I+A](rdf:reifies)),
then < r,[I+A](rdfs:Proposition)> is in IEXT([I+A](rdf:type))
From 5c36aea6543d9760777c0878c227747ea651dd61 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 11:58:51 +0100 Subject: [PATCH 14/26] Better spacing Co-authored-by: Ted Thibodeau Jr --- spec/index.html | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index 9a6019a..305a64a 100644 --- a/spec/index.html +++ b/spec/index.html @@ -261,8 +261,16 @@

Notation and Terminology

A ground RDF graph is one that contains no blank nodes.

- An RDF term appears in a graph G if it is in the set TM(G), defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); (2) for each triple term in TH(G), its subject, predicate, and object are in TM(G).
- A triple appears in a graph G if it is in G or if the triple term composed by its subject, predicate, and object appears in G. + An RDF term appears in a graph G if it is in the set TM(G), + defined inductively as follows: + (1) for each triple in the graph G, + its subject, predicate, and object are in TM(G); + (2) for each triple term in TH(G), + its subject, predicate, and object are in TM(G). +

+ A triple appears in a graph G + if it is in G or + if the triple term composed by its subject, predicate, and object appears in G.

Suppose that M is a functional mapping from a set of blank From c6e946f096c24cbd3df0c311d3eafe5d9510cbbb Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 12:03:24 +0100 Subject: [PATCH 15/26] Better formatting of rdfssemcond11 definition. --- spec/index.html | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 305a64a..7eb9b1c 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1241,7 +1241,12 @@

RDFS Interpretations

If - exist x,y,z such that RE(x,z,y)=r, or exists x such that < x,r > is in IEXT(I(rdf:reifies)),
then < r,I(rdfs:Proposition)> is in IEXT(I(rdf:type))

+ exist x,y,z such that RE(x,z,y)=r, or + exists x such that < x,r > + is in IEXT(I(rdf:reifies)), +
+ then < r,I(rdfs:Proposition)> + is in IEXT(I(rdf:type))

From 78f45a14df1db6ba4f48da9e3b3b9b4025605369 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 12:07:48 +0100 Subject: [PATCH 16/26] Fixed a plural reference Co-authored-by: Ted Thibodeau Jr --- spec/index.html | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index 7eb9b1c..67b6170 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1713,7 +1713,9 @@

Entailment rules (Informative)

requires attention to idiosyncratic properties of the particular datatypes.

- The complete entailment pattern for generalized RDF with [=symmetric RDF triple=]s, considering that, according to the semantics, the denotation of triple terms should be of type rdfs:Proposition, is the following: + The complete entailment pattern for generalized RDF with [=symmetric RDF triples=], + considering that, according to the semantics, the denotation of triple terms should + be of type rdfs:Proposition, is the following: From f8b16032b02bff8c9e73ef15b6cd29bbbcabf645 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 15:44:36 +0100 Subject: [PATCH 17/26] Fixed redundant condition "triple or triple term" --- spec/index.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index 67b6170..299af98 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1096,7 +1096,7 @@

Patterns of RDF entailment (Informative)

 - + @@ -1495,7 +1495,7 @@

Patterns of RDFS entailment (Informative)

- + From 42f0fc2188a9c8b4cc3b53bfa3dbe08339f1c206 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 18:08:01 +0100 Subject: [PATCH 18/26] Fixed wording of rdfs14, and references to issue about external references and completeness proof --- spec/index.html | 20 +++++++++++++------- 1 file changed, 13 insertions(+), 7 deletions(-) diff --git a/spec/index.html b/spec/index.html index 163a76c..e5073e9 100644 --- a/spec/index.html +++ b/spec/index.html @@ -274,12 +274,15 @@

Notation and Terminology

Suppose that M is a functional mapping from a set of blank - nodes to some set of [=RDF terms=]. Any graph obtained + nodes to some set of RDF terms. Any graph obtained from a graph G by replacing some or all of the blank nodes N appearing in G by M(N) is an instance of G. Any graph is an instance of itself, an instance of an instance of G is an instance of G, and if H is an instance of G then every triple in H is an instance of at least one triple in G.

+ +

the defined term "RDF term" is not accessible from outside this document, which is a problem (RDF semantics, and probably other specs, need to reference it). There are other definitions in this spec that need to be exported - see issue #152 in RDF-concepts.

+

An instance with respect to a vocabulary V is an instance in which all the @@ -1106,7 +1109,7 @@

Patterns of RDF entailment (Informative)

 - + @@ -1504,16 +1507,16 @@

Patterns of RDFS entailment (Informative)

- + - - + +
RDFS-T entailment pattern.
if the triple or triple term appears in Sif the triple appears in S then S RDF entails, recognizing D
If the triple or triple term appears in S:If the triple appears in S: then S RDFS entails recognizing D:
rdfD2xxx aaa yyy xxx aaa yyy . aaa rdf:type rdf:Property .
rdfs4xxx aaa yyy xxx aaa yyy . xxx rdf:type rdfs:Resource .
yyy rdf:type rdfs:Resource .
rdfs14xxx yyy <<(aaa bbb ccc)>> the graph S with the appearance replaced with
- xxx yyy _:nnn
- _:nnn rdf:type rdfs:Proposition .		xxx yyy <<(aaa bbb ccc)>> .
  • the graph S with the appearance replaced with
    + xxx yyy _:nnn
    • +
  • _:nnn rdf:type rdfs:Proposition .
@@ -1739,6 +1742,9 @@

Entailment rules (Informative)

+ +

We don't have a completeness proof for the RDFS entailment rules (yet).

+ From d853efbd951b8b901ec030f55ad119230c16484a Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 18:15:21 +0100 Subject: [PATCH 19/26] Better rdfs14 --- spec/index.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/spec/index.html b/spec/index.html index e5073e9..6a7a3a8 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1514,9 +1514,9 @@

Patterns of RDFS entailment (Informative)

rdfs14 xxx yyy <<(aaa bbb ccc)>> . -
  • the graph S with the appearance replaced with
    - xxx yyy _:nnn
    • -
  • _:nnn rdf:type rdfs:Proposition .
+ the graph S with the appearance replaced with
+ xxx yyy _:nnn

+ _:nnn rdf:type rdfs:Proposition . From e0716d1cfa8f6a5be818c8265ea016b0d790b73b Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Fri, 31 Jan 2025 19:01:23 +0100 Subject: [PATCH 20/26] Added example for rdfs14 --- spec/index.html | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/spec/index.html b/spec/index.html index 6a7a3a8..7b64cd9 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1521,6 +1521,16 @@

Patterns of RDFS entailment (Informative)

+

As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph:

+ +

ex:a ex:b <<( ex:c ex:d <<(ex:e ex:f ex:g)>> )>> .

+ +

RDFS entails:

+ +

ex:a ex:b <<( ex:c ex:d _:b1 )>> .
+ ex:a ex:b _:b2 .
+ _:b1 rdf:type rdfs:Proposition .
+ _:b2 rdf:type rdfs:Proposition .

RDFS provides for several new ways to be unsatisfiable recognizing D. For example, the following graph is RDFS unsatisfiable recognizing {xsd:integer, xsd:boolean}:

From 961a1aede43f74da03c180f9af650be422415f8d Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Sat, 1 Feb 2025 15:38:53 +0100 Subject: [PATCH 21/26] Change: emdashes are better than the colons Co-authored-by: Ted Thibodeau Jr --- spec/index.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index 7b64cd9..f578644 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1521,11 +1521,11 @@

Patterns of RDFS entailment (Informative)

-

As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph:

+

As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph &emdash;

ex:a ex:b <<( ex:c ex:d <<(ex:e ex:f ex:g)>> )>> .

-

RDFS entails:

+

&emdash; RDFS entails &emdash;

ex:a ex:b <<( ex:c ex:d _:b1 )>> .
ex:a ex:b _:b2 .
From 809ea61133cf5263c191886adda1cb8af8d9ee22 Mon Sep 17 00:00:00 2001 From: doerthe Date: Tue, 4 Feb 2025 14:08:20 +0100 Subject: [PATCH 22/26] Small typo in index.html --- spec/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/spec/index.html b/spec/index.html index f578644..a5baeb6 100644 --- a/spec/index.html +++ b/spec/index.html @@ -265,7 +265,7 @@

Notation and Terminology

defined inductively as follows: (1) for each triple in the graph G, its subject, predicate, and object are in TM(G); - (2) for each triple term in TH(G), + (2) for each triple term in TM(G), its subject, predicate, and object are in TM(G).

A triple appears in a graph G From 1670e37203f80ea2c6e9c33585d3b9d23edf5e71 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Tue, 4 Feb 2025 16:10:44 +0100 Subject: [PATCH 23/26] fixed: emdash written as mdash --- spec/index.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index a5baeb6..ef4002b 100644 --- a/spec/index.html +++ b/spec/index.html @@ -1521,11 +1521,11 @@

Patterns of RDFS entailment (Informative)

-

As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph &emdash;

+

As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph —

ex:a ex:b <<( ex:c ex:d <<(ex:e ex:f ex:g)>> )>> .

-

&emdash; RDFS entails &emdash;

+

— RDFS entails —

ex:a ex:b <<( ex:c ex:d _:b1 )>> .
ex:a ex:b _:b2 .
From d15e0c2f10fbba0d6d8d9ab2a6836be178673aa2 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 13 Feb 2025 15:57:04 +0100 Subject: [PATCH 24/26] Added semantic properties in 5.3 relating triple terms and asserted triples --- spec/index.html | 22 ++++++++++++++++++++-- 1 file changed, 20 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index ef4002b..b902ce9 100644 --- a/spec/index.html +++ b/spec/index.html @@ -422,7 +422,7 @@

Simple Interpretations

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 interpretation of triple terms.

+

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

@@ -650,7 +650,7 @@

Simple Entailment

-

Properties of simple entailment (Informative)

+

Properties of simple entailment and satisfiability (Informative)

The properties described here apply only to simple entailment, not to extended notions of entailment introduced in later sections. @@ -706,6 +706,24 @@

Properties of simple entailment (Informative)

If E contains an IRI which does not occur anywhere in S, then S does not simply entail E.

+ +

The following semantic properties relate triple terms and triples asserted in a graph, and they introduce a general definition of satisfiability.
+ We define the set of propositions as follows: + +

The set of propositions in an interpretation I is IPR(I) = { <x, y, z>｜x is in IR, y is in IP, z is in IR }; we observe that the propositions are exactly the domain of the RE mapping used to denote triple terms as resources.

+ +

We define the set of facts as follows:

+ +

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

+ +

We define the set of facts asserted by a graph G as follows:

+ +

The set of all facts asserted by a graph G with a blank node mapping A in an interpretation I is FEXT(G, I, A) = { < [I+A](s), I(p), [I+A](o) >｜`s p o.` is in G }; given an interpretation and a graph, the asserted facts of the graph may not necessarily be among the facts of the interpretation.

+ +

Given a mapping A, we introduce a general definition of satisfiability as follows:

+ +

Given an interpretation and a graph with a blank node mapping, the facts asserted by the graph are among the facts of the interpretation if and only if the interpretation (simply) satisfies the graph.

+
From ddda4d99bd1440ea3fdd932d5469f754763b265a Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 13 Feb 2025 17:39:43 +0100 Subject: [PATCH 25/26] Better formatting MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Niklas Lindström --- spec/index.html | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/spec/index.html b/spec/index.html index b902ce9..837a4fe 100644 --- a/spec/index.html +++ b/spec/index.html @@ -707,8 +707,8 @@

Properties of simple entailment and satisfiability (Informative)

If E contains an IRI which does not occur anywhere in S, then S does not simply entail E.

-

The following semantic properties relate triple terms and triples asserted in a graph, and they introduce a general definition of satisfiability.
- We define the set of propositions as follows: +

The following semantic properties relate triple terms and triples asserted in a graph, and they introduce a general definition of satisfiability.

+

We define the set of propositions as follows:

The set of propositions in an interpretation I is IPR(I) = { <x, y, z>｜x is in IR, y is in IP, z is in IR }; we observe that the propositions are exactly the domain of the RE mapping used to denote triple terms as resources.

From 9618b1a760d05eedfc7b6bd7f53a4efbb45bf180 Mon Sep 17 00:00:00 2001 From: Enrico Franconi Date: Thu, 13 Feb 2025 18:31:23 +0100 Subject: [PATCH 26/26] Rewording after suggestion of pfps --- spec/index.html | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/spec/index.html b/spec/index.html index 837a4fe..2328ea3 100644 --- a/spec/index.html +++ b/spec/index.html @@ -708,23 +708,23 @@

Properties of simple entailment and satisfiability (Informative)

then S does not simply entail E.

The following semantic properties relate triple terms and triples asserted in a graph, and they introduce a general definition of satisfiability.

-

We define the set of propositions as follows:

+ +

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

The set of propositions in an interpretation I is IPR(I) = { <x, y, z>｜x is in IR, y is in IP, z is in IR }; we observe that the propositions are exactly the domain of the RE mapping used to denote triple terms as resources.

-

We define the set of facts as follows:

+

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

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

-

We define the set of facts asserted by a graph G as follows:

+

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

-

The set of all facts asserted by a graph G with a blank node mapping A in an interpretation I is FEXT(G, I, A) = { < [I+A](s), I(p), [I+A](o) >｜`s p o.` is in G }; given an interpretation and a graph, the asserted facts of the graph 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) = { < [I+A](s), I(p), [I+A](o) >｜`s p o.` is in G }; 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.

-

Given a mapping A, we introduce a general definition of satisfiability as follows:

+

Given a blank node mapping, we introduce a general definition of satisfiability of a graph in an interpretation as follows:

-

Given an interpretation and a graph with a blank node mapping, the facts asserted by the graph are among the facts of the interpretation if and only if the interpretation (simply) satisfies the graph.

+

Given a blank node mapping, the facts asserted in an interpretation by a graph are among the facts of the interpretation if and only if the interpretation (simply) satisfies the graph.

-