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unify terminology for triples #158

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unify terminology for triples #158

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address w3c/rdf-star-wg#145
pchampin Feb 13, 2025
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replace 'recursively' with 'inductively' in definitions
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reorder text, re-introducing a 'Triple terms' section
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Expand Up @@ -67,8 +67,8 @@
are comprised of a default graph and zero or more named graphs.</li>
</ul>

<p>RDF 1.2 introduces <a>triple terms</a> as another kind of <a>RDF term</a>
which can be used as the <a>object</a> of another <a>triple</a>.
<p>RDF 1.2 introduces the ability to use an <a>RDF triple</a>
as a <a>triple term</a>, in the <a>object</a> position of another <a>triple</a>.
RDF 1.2 also introduces <a>directional language-tagged strings</a>,
which contain a <a>base direction</a> element that allows the
initial text direction to be specified for presentation by a user agent.</p>
Expand Down Expand Up @@ -288,9 +288,8 @@ <h3>RDF Vocabularies and Namespace IRIs</h3>
<section id="section-triple-terms-reification">
<h3>Triple Terms and Reification</h3>

<p>A <a>triple term</a> is an <a>RDF term</a> with the components of
an <a>RDF triple</a>, which can be used as the <a>object</a>
of another triple.</p>
<p>A <a>triple term</a> is an [=RDF triple=] used as an [=RDF term=]
in the [=object=] position of another triple.</p>

<p>A <a>triple term</a> is not necessarily asserted, allowing
statements to be made about other statements that may not be
Expand Down Expand Up @@ -417,12 +416,14 @@ <h3>Working with Multiple RDF Graphs</h3>
<section id="entailment">
<h3>Equivalence, Entailment and Inconsistency</h3>

<p>An <a>RDF triple</a> encodes a <a>statement</a>—a
simple <dfn class="export">logical expression</dfn>, or claim about the world.
<p>An <a>RDF triple</a> encodes a <dfn class="export">proposition</dfn> — a
simple logical expression, describing a relationship between two entities.
An [=asserted triple=] is a claim that the corresponding proposition is true.
An <a>RDF graph</a> is the conjunction (logical <em>AND</em>) of
its triples. The precise details of this meaning of RDF triples and graphs are
all the claims made by its [=asserted triples=].
The precise details of this meaning of [=RDF triples=] and [=RDF graphs=] are
the subject of [[[RDF12-SEMANTICS]]] [[RDF12-SEMANTICS]], which yields the
following relationships between <a>RDF graph</a>s:</p>
following relationships between <a>RDF graphs</a>:</p>

<dl>
<dt><dfn>Entailment</dfn></dt>
Expand Down Expand Up @@ -547,21 +548,45 @@ <h2>RDF Graphs</h2>

<p>An <dfn>RDF graph</dfn> is a set of <a>RDF triples</a>.</p>

<p>An RDF triple is said to be <dfn id="dfn-asserted-triple" data-lt="asserted|asserted triple">asserted</dfn> in an RDF graph if it is an element of the RDF graph.</p>
<p>An [=RDF triple=] is said to be <dfn id="dfn-asserted-triple" class=export data-lt="asserted triple|asserted triples" data-lt-no-plural=""
>asserted</dfn> in an [=RDF graph=] if it is an element of the [=RDF graph=].
</p>

<section id="section-triples">
<h3>Triples</h3>

<p>An <dfn data-local-lt="triple">RDF triple</dfn> (usually called "triple")
is a 3-tuple (|s|, |p|, |o|) with the following characteristics:</p>
<p>An <dfn data-local-lt="triple" class="export">RDF triple</dfn>
(often simply called "triple")
is a 3-tuple that is defined inductively as follows:</p>

<ul>
<li>|s| is an <a>IRI</a> or a <a>blank node</a>.</li>
<li>|p| is an <a>IRI</a>.</li>
<li>|o| is an <a>IRI</a>, a <a>blank node</a>, a <a>literal</a>,
or a <a>triple term</a>.</li>
<li>
If |s| is an [=IRI=] or a [=blank node=],
|p| is an [=IRI=], and
|o| is an [=IRI=], a [=blank node=], or a [=literal=],
then (|s|, |p|, |o|) is an [=RDF triple=].
</li>

<li>
If |s| is an [=IRI=] or a [=blank node=],
|p| is an [=IRI=], and
|o| is an [=RDF triple=],
then (|s|, |p|, |o|) is an [=RDF triple=].
</li>
</ul>

<p>The three components (|s|, |p|, |o|) of an [=RDF triple=] are respectively called the <dfn class=export >subject</dfn>, <dfn class=export >predicate</dfn> and <dfn class=export >object</dfn> of the triple.</p>


<p class="note">The definition of <a>triple</a> is recursive.
That is, a <a>triple</a> can itself have an
<a>object</a> component which is another <a>triple</a>.
However, by this definition, cycles of <a>triples</a> cannot be created.</p>
</section>

<section id="section-terms">
<h3>RDF Terms</h3>

<p><a>IRIs</a>, <a>literals</a>,
<a>blank nodes</a>, and <a>triple terms</a> are collectively known as
<span id="dfn-rdf-terms"><!-- obsolete term--></span><dfn data-lt="rdf term">RDF terms</dfn>.</p>
Expand All @@ -575,8 +600,8 @@ <h3>Triples</h3>
<code>http://example.org/</code>.</p>

<p>The set of <span id="dfn-nodes"><!-- obsolete term--></span><dfn data-lt="node">nodes</dfn> of an <a>RDF graph</a>
is the set of <a>subjects</a> and <a>objects</a> of the <a>triples</a> in the graph.
It is possible for a predicate IRI to also occur as a node in
is the set of <a>subjects</a> and <a>objects</a> of the <a>asserted triples</a> of the graph.
It is possible for a [=predicate=] [=IRI=] to also occur as a [=node=] in
the same graph.</p>
</section>

Expand Down Expand Up @@ -851,49 +876,26 @@ <h3>Blank Nodes</h3>
<section id="section-triple-terms">
<h3>Triple Terms</h3>

<p>A <dfn>triple term</dfn> is a 3-tuple that is defined recursively as follows:</p>
<p>An [=RDF triple=] used as the [=object=] of another [=triple=] is called a <dfn class=export >triple term</dfn>.
In a given [=RDF graph=], a [=triple=] can appear as a [=triple term=], an [=asserted triple=], or both.
</p>

<ul>
<li>
If |s| is an <a>IRI</a> or a <a>blank node</a>,
|p| is an <a>IRI</a>, and
|o| is an <a>IRI</a>, a <a>blank node</a>, or a <a>literal</a>,
then (|s|, |p|, |o|) is a triple term.
</li>
<p>The set of [=RDF terms=] <dfn class=export data-lt="appear">appearing</dfn> in an [=RDF triple=] |t| is defined inductively as follows:</p>

<li>
If |s| is an <a>IRI</a> or a <a>blank node</a>,
|p| is an <a>IRI</a>, and
|o| is a <a>triple term</a>,
then (|s|, |p|, |o|) is a triple term.
</li>
<ul>
<li>The [=subject=], [=predicate=] and [=object=] of |t| [=appear=] in |t|.
<li>If a [=triple term=] |t2| appears in |t|, then any [=RDF term=] [=appearing=] in |t2| also [=appears=] in |t|.
</ul>

<p>Given a <a>triple</a> (|s|, |p|, |o|),
|s| is called the <dfn>subject</dfn> of the triple,
|p| is called the <dfn>predicate</dfn> of the triple, and
|o| is called the <dfn>object</dfn> of the triple.
Similarly, given a <a>triple term</a> (|s|, |p|, |o|),
|s| is called the <em>subject</em> of the triple term,
|p| is called the <em>predicate</em> of the triple term, and
|o| is called the <em>object</em> of the triple term.</p>

<p class="note">While, syntactically, the notion of an <a>RDF triple</a>
and the notion of a <a>triple term</a> are the same, they represent
different concepts. RDF triples are the members of <a>RDF graphs</a>,
whereas triple terms can be used as components of RDF triples.</p>

<p class="note">The definition of <a>triple term</a> is recursive.
That is, a <a>triple term</a> can itself have an
<a>object</a> component which is another <a>triple term</a>.
However, by this definition, cycles of <a>triple terms</a> cannot be created.</p>

<p class="note">Every <a>triple</a> with a <a>triple term</a> as its object SHOULD
<p>By extension, an [=RDF term=] is said to [=appear=] in an [=RDF graph=] if it appears in an [=asserted triple=] of that graph. An [=RDF triple=] is said to [=appear=] in an [=RDF graph=] if it is either an [=asserted triple=] of that graph or a [=triple term=] [=appearing=] in that graph.</p>

<p class="note">Every <a>triple</a> with a <a>triple term</a> as its [=object=] SHOULD
use <code>http://www.w3.org/1999/02/22-rdf-syntax-ns#reifies</code> (<code>rdf:reifies</code>)
as its <a>predicate</a>.
Every <a>triple</a> whose <a>object</a> is not a <a>triple term</a> SHOULD NOT
use <code>http://www.w3.org/1999/02/22-rdf-syntax-ns#reifies</code> (<code>rdf:reifies</code>)
as its <a>predicate</a>.</p>

</section>

<section id="graph-isomorphism">
Expand Down
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