Some improved language, punctuation, and markup in rdf-semantics (#126)

* Some improved language, punctuation, and markup in rdf-semantics

* delete extra space

* Editing text to enable removal of mdash punctuation

* re-fixing "standardize apart" dfn

* remove `graph described by the`

Co-authored-by: Peter F. Patel-Schneider <[email protected]>

* `represented by` -> `for`

Co-authored-by: Peter F. Patel-Schneider <[email protected]>

* `This new document describes a graph containing` -> `The graph for this new document contains`

* `more properly described by a surface form such as the following` -> `instead that shown below`

* `standardized</a> apart` -> `standardized apart</a>`

Co-authored-by: Peter F. Patel-Schneider <[email protected]>

* remove ineffectual "also"

* relocates ground graph is lean sentence

---------

Co-authored-by: Peter F. Patel-Schneider <[email protected]>

Author: TallTed

spec/index.html

@@ -293,26 +293,25 @@ <h2>Notation and Terminology</h2>
     <p>Two graphs are <a data-cite="RDF12-CONCEPTS#dfn-graph-isomorphism">isomorphic</a> when each maps into the other by a 1:1 mapping on blank nodes. Isomorphic graphs are mutual instances with an invertible instance
       mapping. As blank nodes have no particular identity beyond their location in a graph, we will often treat isomorphic graphs as identical.</p>
 
-    <p >An RDF graph is <dfn>lean</dfn> if it has no instance which is
-      a <a>proper subgraph</a> of itself. Non-lean graphs have internal redundancy
-      and express the same content as their lean <a>subgraphs</a>. For example, the graph</p>
+    <p>An RDF graph is <dfn>lean</dfn> if it has no instance which is
+      a <a>proper subgraph</a> of itself. A <a>ground RDF graph</a> is lean. Non-lean graphs have internal redundancy
+      and express the same content as their lean <a>subgraphs</a>. For example, the graph in Example 1 is not lean:</p>
 
     <pre class="example" title="Non-lean graph">
       ex:a ex:p _:x .
       _:y ex:p _:x .
     </pre>
 
-    <p >is not lean, but</p>
+    <p>In contrast, the graph in Example 2 <em>is</em> lean:</p>
 
     <pre class="example" title="Lean graph">
       ex:a ex:p _:x .
       _:x ex:p _:x .
     </pre>
 
-    <p>is lean. A <a>ground RDF graph</a> is lean. </p>
 
   <section id="unions_merges">
-    <h3>Shared blank nodes, unions and merges</h3>
+    <h3>Shared blank nodes, unions, and merges</h3>
 
     <p>Graphs share <a>blank nodes</a> only if they are derived from graphs
       described by documents or other structures (such as an RDF dataset)
@@ -321,7 +320,8 @@ <h3>Shared blank nodes, unions and merges</h3>
       graph are the same as the blank nodes coming from other downloads of
       the same document or from the same <a>RDF source</a>.</p>
 
-    <p> RDF applications which manipulate concrete syntaxes for RDF which use <a data-cite="RDF12-CONCEPTS#dfn-blank-node-identifier">blank node identifiers</a>
+    <p> RDF applications which manipulate concrete syntaxes for RDF which use
+      <a data-cite="RDF12-CONCEPTS#dfn-blank-node-identifier">blank node identifiers</a>
       should take care to keep track of the identity of the blank nodes they identify.
       Blank node identifiers often have a local scope,
       so when RDF from different sources is combined,
@@ -332,39 +332,46 @@ <h3>Shared blank nodes, unions and merges</h3>
       to identify a blank node, but unless these documents are in a shared identifier scope
       or are derived from a common source,
       the occurrences of "<code>_:x</code>" in one document
-      will identify a different blank node than the one in the graph described by the other document.
+      will identify a different blank node than the occurrences of "<code>_:x</code>"
+      in the other document.
       When graphs are formed by combining RDF from multiple sources,
       it may be necessary to <dfn class="no-export lint-ignore">standardize</dfn> apart the blank node identifiers
-      by replacing them by others which do not occur in the other document(s).
-      For example, the two graphs represented  by the following texts:</p>
+      by replacing them with other identifiers which do not occur in the other document(s).
+      For example, the two graphs for the two texts below contain two nodes each, 
+      for a total of four nodes:</p>
 
     <p><code>ex:a ex:p _:x . </code><br/><br/>
       <img src="RDF12SemanticsDiagrams/example1.svg" alt="Graph 1" /></p>
 
     <p><code>ex:b ex:q _:x . </code><br/><br/>
       <img src="RDF12SemanticsDiagrams/example2.svg" alt="Graph 2" ></p>
 
-    <p>contain four nodes. Their union would therefore also contain four nodes:</p>
+    <p>Their union would also contain four nodes:</p>
 
     <p><img src="RDF12SemanticsDiagrams/example4.svg" alt="Union Graph"></p>
 
-    <p>However, the document formed by simply concatenating these textual surface representations:</p>
+    <p>However, if we simply concatenate these textual surface representations 
+      to form a new document, as shown below:</p>
 
     <p><code>ex:a ex:p _:x .<br/>
     ex:b ex:q _:x .</code><br/></p>
 
-    <p>describes a graph containing three nodes:</p>
+    <p>The graph for this new document contains three nodes, because
+      the two occurrences of the blank node identifier "<code>_:x</code>
+      now occur in a common identifier scope, and thus identify the same blank node,
+      as shown below:</p>
 
     <p><img src="RDF12SemanticsDiagrams/example3.svg" alt="Incorrect Union Graph"></p>
 
-    <p> since the two occurrences of the blank node identifier "<code>_:x</code>" occurring in a common identifier scope identify the same blank node. The four-node union of these two graphs is more properly described by a surface form such as:</p>
+    <p>The four-node union
+      of these two graphs is instead that shown below:</p>
 
     <p><code>ex:a ex:p _:x1 .<br/>
       ex:b ex:q _:x2 .</code></p>
 
-    <p>in which the blank node identifiers have been <a data-lt="standardize">standardized</a>
-      apart to avoid conflating the distinct blank nodes.
-      (The particular blank node identifiers used have no significance, only that they are distinct.)</p>
+    <p>Here the blank node identifiers have been <a data-lt="standardize">standardized apart</a>
+      to avoid conflating the distinct blank nodes.
+      (The particular blank node identifiers used have no significance; it matters only that they are distinct.)</p>
 
     <p>It is possible for two or more graphs to share a blank node,
       for example if they are <a>subgraphs</a> of a single larger graph or derived from a common source.
@@ -377,15 +384,16 @@ <h3>Shared blank nodes, unions and merges</h3>
       which occur in more than one graph, to be distinct in each graph.
       The resulting graph is called the <dfn data-lt="RDF graph merge">merge</dfn>.
       The merge of <a>subgraphs</a> of a graph may be larger than the original graph.
-      For example, the result of merging the two singleton subgraphs of the three-node graph</p>
+      For example, the result of merging the two singleton subgraphs of the three-node 
+      graph shown below, is the four-node graph shown beneath:</p>
 
     <p><img src="RDF12SemanticsDiagrams/example3.svg" alt="Three-node Graph"></p>
 
-    <p>is the four-node graph</p>
-
     <p><img src="RDF12SemanticsDiagrams/example4.svg" alt="Four-node Graph"></p>
 
-    <p>The union is always an instance of the merge. If graphs have no blank nodes in common, then their merge and union are identical. </p>
+    <p>The union is always an instance of the merge. If graphs have no blank nodes in common,
+      then their merge and union are identical. </p>
+
   </section>
 </section>
 
@@ -1555,18 +1563,17 @@ <h4>Patterns of RDFS entailment</h4>
           </tr>
         </tbody>
       </table>
-      <p>As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14, the following graph &mdash;</p>
+      <p>As an example of a RDFS entailment involving triple terms using the entailment pattern rdfs14,
+        the graph below RDFS entails the triples that follow:</p>
 
       <p><code>ex:a ex:b &lt;&lt;( ex:c ex:d &lt;&lt;(ex:e ex:f ex:g)>> )>> .</code></p>
 
-      <p>&mdash; RDFS entails &mdash;</p>
-
       <p><code>ex:a ex:b &lt;&lt;( ex:c ex:d _:b1 )>> .<br/>
                ex:a ex:b _:b2 .<br/>
                _:b1 rdf:type rdfs:Proposition .<br/>
                _:b2 rdf:type rdfs:Proposition .</code></p>
 
-      <p>RDFS provides for several new ways to be <a>unsatisfiable</a> recognizing D.
+      <p>RDFS provides several new ways to be <a>unsatisfiable</a> recognizing D.
         For example, the following graph is RDFS unsatisfiable recognizing {<code>xsd:integer</code>, <code>xsd:boolean</code>}:</p>
 
       <p><code>ex:p rdfs:domain xsd:boolean .<br/>