From 921f6d1c707786e0abd75709c3be4b16d4bb1c0f Mon Sep 17 00:00:00 2001
From: Patrick Hochstenbach <patrick.hochstenbach@ugent.be>
Date: Mon, 13 May 2024 18:40:50 +0200
Subject: [PATCH] Fixing with @TallTed fixes

---
 index.bs   |  18 ++++-----
 index.html | 115 ++++++++++++++++++++++++++---------------------------
 2 files changed, 66 insertions(+), 67 deletions(-)

diff --git a/index.bs b/index.bs
index 231a8b8..1aa4ef6 100644
--- a/index.bs
+++ b/index.bs
@@ -134,9 +134,9 @@ asserts a logical negation. The examples below will use a sheet of paper with a
 as a negative surface.
 
 An empty *negative surface* on the default positive surface expresses a logical contradicton. When there are one
-or more RDF graphs written on an *negative* surface they mean the negation of those RDF graphs.
+or more RDF graphs written on a *negative* surface, they mean the negation of those RDF graphs.
 
-A blank node on a negative surface is interpreted as a universal quantified variable. The reason is 
+A blank node on a negative surface is interpreted as an universal quantified variable. The reason is 
 that:
 
 ```
@@ -316,7 +316,7 @@ A surface can be queried by providing a query surface with the `log:onNegativeAn
 
 `:Ghent a :City` is a triple on the implicit positive surface. The two nested
 negative surfaces express that for any subject `_:S` on the positive service
-that is a `:City`, it implies that `_:S` needs be be also a `:HumanCommunity`.
+that is a `:City`, it is implied that `_:S` if also a `:HumanCommunity`.
 
 <pre highlight="turtle">
 @prefix ex: &lt;http://example.org/ns#&gt;.
@@ -388,7 +388,7 @@ Surface {#Surface}
 Surfaces are written as triples where the `subject` is a list of zero or more blank nodes. 
 The `object` is a RDF graph or the `true` or `false` literal. The blank nodes in the 
 subject list are treated as marks on the object RDF graph. The `predicate` specifies 
-the kind of surface. Any kind of surface may be used but the following built-in have 
+the kind of surface. Any kind of surface may be used, but the following built-ins have 
 special semantics:
 
 <table>
@@ -406,7 +406,7 @@ special semantics:
 </table>
 
 A surface can contain zero or more other surfaces. These surfaces are then nested.
-Nested surfaces can share the same [[URI]]-s and literals (by copying the data), 
+Nested surfaces can share the same [[URI]]s and literals (by copying the data), 
 but can't share blank nodes. Any blank nodes that are written inside a surface 
 (not as subject of an RDF Surface) are to be interpreted as *coreferences* to the
 blank node graffiti defined on a parent RDF Surface. If no such parent RDF Surface
@@ -554,7 +554,7 @@ As RDF Surface:
 
 </div>
 
-In RDF Surfaces an default positive surface is implicitly assumed for each RDF document. On this default positive surface all existential variables are implicitly quantified. Example 20 can be rewritten as:
+In RDF Surfaces, a default positive surface is implicitly assumed for each RDF document. On this default positive surface, all existential variables are implicitly quantified. Example 20 can be rewritten as:
 
 <div class="example">
 A default positive surface with an implicit `_:X` existential variable.
@@ -569,7 +569,7 @@ _:X :knows :Alice .
 
 </div>
 
-When a blank node is marked on an odd nested negative surface, then it is interpreted as an universal quantified variable in the scope of the nested surface.
+When a blank node is marked on an odd nested negative surface, it is interpreted as an universal quantified variable in the scope of the nested surface.
 
 <div class="example">
 The surface below should be interpreted as : "Every person knows Alice".
@@ -607,7 +607,7 @@ As RDF Surface:
 ## Negative Surface ## {#NegativeSurface}
 
 A negative surface is an RDF graph which claims that an RDF Graph on it is false. The
-intepretation of the negative surface is the negation of RDF Graph on it. 
+interpretation of the negative surface is the negation of RDF Graph on it. 
 
 The semantics of a negative surface is interpreted as a logical falsehood:
 
@@ -746,7 +746,7 @@ As RDF Surface:
 
 </div>
 
-With combinations of AND and NOT other logical truth function can be build. E.g.
+With combinations of AND and NOT other logical truth function can be built. E.g.
 
 - Disjunction: `P ∨ Q` : `NOT( NOT(P) AND NOT(Q))`
 - Material implication `P → Q` : `NOT( P AND NOT Q )` .
diff --git a/index.html b/index.html
index 9e7f568..fa74dea 100644
--- a/index.html
+++ b/index.html
@@ -1488,8 +1488,8 @@
 		}
 	}
 </style>
-  <meta content="Bikeshed version 4416b18d5, updated Tue Jan 2 15:52:39 2024 -0800" name="generator">
-  <meta content="9540f5c057ba50310dda5dd28a763f0a71ccaa5d" name="revision">
+  <meta content="Bikeshed version d765c696b, updated Fri Mar 8 15:58:52 2024 -0800" name="generator">
+  <meta content="dark light" name="color-scheme">
 <style>
 table {
   margin: 25px auto;
@@ -2044,11 +2044,10 @@
   <div class="head">
    <p data-fill-with="logo"></p>
    <h1 class="p-name no-ref" id="title">RDF Surfaces Primer</h1>
-   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Living Document, <time class="dt-updated" datetime="2024-05-01">1 May 2024</time></span></h2>
+   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Living Document, <time class="dt-updated" datetime="2024-05-13">13 May 2024</time></span></h2>
    <div data-fill-with="spec-metadata">
     <dl>
      <dt>Issue Tracking:
-     <dd><a href="https://github.com/w3c-cg/rdfsurfaces/issues/">GitHub</a>
      <dd><a href="#issues-index">Inline In Spec</a>
      <dt class="editor">Editors:
      <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:patrick.hochstenbach@ugent.be">Patrick Hochstenbach</a> (<span class="p-org org"><a href="https://knows.idlab.ugent.be/team/">KNoWS</a></span>)
@@ -2058,7 +2057,7 @@ <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span cla
    <div data-fill-with="warning"></div>
    <p class="copyright" data-fill-with="copyright"><a href="http://creativecommons.org/publicdomain/zero/1.0/" rel="license"><img alt="CC0" height="15" src="https://licensebuttons.net/p/zero/1.0/80x15.png" width="80"></a> To the extent possible under law, the editors have waived all copyright
 and related or neighboring rights to this work.
-In addition, as of 1 May 2024,
+In addition, as of 13 May 2024,
 the editors have made this specification available under the <a href="http://www.openwebfoundation.org/legal/the-owf-1-0-agreements/owfa-1-0" rel="license">Open Web Foundation Agreement Version 1.0</a>,
 which is available at http://www.openwebfoundation.org/legal/the-owf-1-0-agreements/owfa-1-0.
 Parts of this work may be from another specification document.  If so, those parts are instead covered by the license of that specification document. </p>
@@ -2099,7 +2098,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 to express a revised RDF logic as envisoned by <a href="https://www.ihmc.us/groups/phayes/">Pat Hayes</a> in his 2009 ISWC Invited 
 Talk: <a href="https://www.slideshare.net/PatHayes/blogic-iswc-2009-invited-talk">BLOGIC</a>. RDF
 Surfaces logic can be thought as an implementation of <a href="https://en.wikipedia.org/wiki/Charles_Sanders_Peirce">Charles Sanders Peirce</a>'s <a href="http://www.jfsowa.com/peirce/ms514.htm">Existential Graphs</a> in RDF.</p>
-   <p>An RDF surface is a kind of sheet of paper on which RDF graphs can be written.
+   <p>An RDF surface is a kind of a sheet of paper on which RDF graphs can be written.
 All triples that are part of an RDF graph are then on this sheet of paper, including all <a data-link-type="biblio" href="#biblio-uri" title="Uniform Resource Identifier (URI): Generic Syntax">[URI]</a>s, literals and <a href="https://www.w3.org/TR/rdf11-mt/#blank-nodes">Blank nodes</a>. 
 A sheet of paper can contain more than one RDF graph. An RDF graph can’t be split
 over multiple sheets of paper. But, one can copy an RDF graph from one sheet of 
@@ -2123,7 +2122,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
    </div>
    <div class="example" id="example-0a1c769e">
     <a class="self-link" href="#example-0a1c769e"></a> Two <em>positive surfaces</em>, one with the triple <code>[] a :City</code> (which means <em>"There is something that is a city"</em>),
-and another one with the triple <code>[] a :Cat</code> (which means <em>"There is something that is a cat"</em>). 
+and another one with the triple <code>[] a :Cat</code> (which means <em>"There is something is a cat"</em>). 
     <p><img alt="blank surface" src="images/two_sheets.svg" width="600"></p>
     <p>One can copy these two RDFs graphs to a new surface. This will contain two graphs with
 two blank nodes:</p>
@@ -2140,7 +2139,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 For instance, the sheet of paper in Example 1 is an example of a <strong>positive surface</strong> (we use in this document a paper with a black border as a positive surface). Any
 RDF graph written on this surface is interpreted as logical assertion (true). An empty 
 sheet of positive paper is an empty claim and is treated as a logical tautology (true).</p>
-   <p>When there is more than one RDF graph on the surface, then it is a logical conjunction (AND).
+   <p>When there is there is more than one RDF graph on the surface, then it is a logical conjunction (AND).
 If we interpret the sheets of paper with the black border in the examples above as
 positive surfaces, then  they express:</p>
    <ul>
@@ -2159,9 +2158,9 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
    <p><strong>Negative surface</strong></p>
    <p>In the same way as a <em>positive surface</em> asserts a logical truth, a <strong>negative surface</strong> asserts a logical negation. The examples below will use a sheet of paper with a red border
 as a negative surface.</p>
-   <p>An empty <em>negative surface</em> on the default positive surface expresses a logical contradiction. When there are one
-or more RDF graphs written on a <em>negative</em> surface they mean the negation of those RDF graphs.</p>
-   <p>A blank node on a negative surface is interpreted as a universal quantified variable. The reason is
+   <p>An empty <em>negative surface</em> on the default positive surface expresses a logical contradicton. When there are one
+or more RDF graphs written on a <em>negative</em> surface, they mean the negation of those RDF graphs.</p>
+   <p>A blank node on a negative surface is interpreted as an universal quantified variable. The reason is
 that:</p>
 <pre>NOT(∃ x : P(x)) ⇔ ∀ x : NOT(P(x))
 </pre>
@@ -2208,7 +2207,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
    </div>
    <p><strong>First-order logic</strong></p>
    <p>First-order logic can be added to the RDF surfaces by interpreting the blank node as
-an existential quantified variable and using the rule that a universal quantified variable can be made from an
+an existential quantified variable and using the rule that a universal quantified variable can made from an 
 existential quantified variable by placing it in an enclosing negative surface:</p>
 <pre>∀ x : P(x) ⇔ NOT(∃ x : NOT P(x)):
 </pre>
@@ -2232,8 +2231,8 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
 <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-  <c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
+  <c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
   <c- p>}</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2244,7 +2243,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-_<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
+<c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
 </pre>
    </div>
    <div class="example" id="example-81be5796">
@@ -2252,9 +2251,9 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
   <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
   <c- p>}</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2264,8 +2263,8 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Problem</c-> <c- p>.</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Problem</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
@@ -2275,15 +2274,15 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Cat</c-> <c- p>.</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Cat</c-> <c- p>.</c->
 
     <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-        _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>is</c-> <c- p>:</c-><c- f>Alive</c-> <c- p>.</c->
+        <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>is</c-> <c- p>:</c-><c- f>Alive</c-> <c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 
     <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-        _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>is</c-> <c- p>:</c-><c- f>Dead</c-> <c- p>.</c->
+        <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>is</c-> <c- p>:</c-><c- f>Dead</c-> <c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2293,39 +2292,39 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Cat</c-> <c- p>;</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Cat</c-> <c- p>;</c->
         <c- p>:</c-><c- f>is</c-> <c- p>:</c-><c- f>Alive</c-> <c- p>.</c->
     <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-        _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>says</c-> <c- p>:</c-><c- f>Meow</c-> <c- p>.</c->
+        <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>says</c-> <c- p>:</c-><c- f>Meow</c-> <c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
    <p>A surface can be queried by providing a query surface with the <code>log:onNegativeAnswerSurface</code> built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.</p>
-   <div class="example" id="example-85a03cf8">
-    <a class="self-link" href="#example-85a03cf8"></a> 
+   <div class="example" id="example-0937bb03">
+    <a class="self-link" href="#example-0937bb03"></a> 
     <p><code>:Ghent a :City</code> is a triple on the implicit positive surface. The two nested
 negative surfaces express that for any subject <code>_:S</code> on the positive service
-that is a <code>:City</code>, it implies that <code>_:S</code> also needs to be a <code>:HumanCommunity</code>.</p>
+that is a <code>:City</code>, it is implied that <code>_:S</code> if also a <code>:HumanCommunity</code>.</p>
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>ex:</c-> <c- g>&lt;http://example.org/ns#></c-><c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-><c- p>.</c->
 
 <c- nn>ex</c-><c- p>:</c-><c- f>Ghent</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>City</c-><c- p>.</c->
 
 <c- c># Every city is a human community</c->
-<c- p>(</c->_<c- p>:</c-><c- f>S</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>City</c-><c- p>.</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>S</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>City</c-><c- p>.</c->
     <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-        _<c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>HumanCommunity</c-><c- p>.</c->
+        <c- nn>_</c-><c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>HumanCommunity</c-><c- p>.</c->
     <c- p>}.</c->
 <c- p>}.</c->
 
 <c- c># Query</c->
-<c- p>(</c->_<c- p>:</c-><c- f>S</c-> _<c- p>:</c-><c- f>C</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>S</c-> <c- b>a</c-> _<c- p>:</c-><c- f>C</c-><c- p>.</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>S</c-> <c- nn>_</c-><c- p>:</c-><c- f>C</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>_</c-><c- p>:</c-><c- f>C</c-><c- p>.</c->
     <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeAnswerSurface</c-> <c- p>{</c->
-      _<c- p>:</c-><c- f>S</c-> <c- b>a</c-> _<c- p>:</c-><c- f>C</c-><c- p>.</c->
+      <c- nn>_</c-><c- p>:</c-><c- f>S</c-> <c- b>a</c-> <c- nn>_</c-><c- p>:</c-><c- f>C</c-><c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 <c- p>}.</c->
 </pre>
@@ -2363,9 +2362,9 @@ <h2 class="heading settled" data-level="2" id="document-conventions"><span class
    </table>
    <h2 class="heading settled" data-level="3" id="Surface"><span class="secno">3. </span><span class="content">Surface</span><a class="self-link" href="#Surface"></a></h2>
    <p>Surfaces are written as triples where the <code>subject</code> is a list of zero or more blank nodes.
-The <code>object</code> is an RDF graph or the <code>true</code> or <code>false</code> literal. The blank nodes in the 
+The <code>object</code> is a RDF graph or the <code>true</code> or <code>false</code> literal. The blank nodes in the 
 subject list are treated as marks on the object RDF graph. The <code>predicate</code> specifies 
-the kind of surface. Any kind of surface may be used but the following built-ins have 
+the kind of surface. Any kind of surface may be used, but the following built-ins have 
 special semantics:</p>
    <table>
     <thead>
@@ -2394,17 +2393,17 @@ <h2 class="heading settled" data-level="3" id="Surface"><span class="secno">3. <
     <p>In the nested surface <code>ex:myThirdSurface</code>, the blank node in <code>_:X ex:is false</code> is a co-reference to the <code>_:X</code> blank node graffiti on <code>ex:myThirdSurface</code>. The new graffiti shields the <code>_:X</code> that was defined on <code>ex:myFirstSurface</code>: the scope of <code>_:X</code> co-references is now limited to <code>ex:myThirdSurface</code>.</p>
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>ex:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>ex</c-><c- p>:</c-><c- f>myFirstSurface</c-> <c- p>{</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>ex</c-><c- p>:</c-><c- f>myFirstSurface</c-> <c- p>{</c->
 
     <c- nn>ex</c-><c- p>:</c-><c- f>Statement1</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>NiceStatement</c-> <c- p>.</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>OtherStatement</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>OtherStatement</c-> <c- p>.</c->
      
     <c- p>()</c-> <c- nn>ex</c-><c- p>:</c-><c- f>mySecondSurface</c-> <c- p>{</c->
-        _<c- p>:</c-><c- f>X</c-> <c- nn>ex</c-><c- p>:</c-><c- f>is</c-> <c- l>true</c-> <c- p>.</c-> 
-        _<c- p>:</c-><c- f>Y</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>AnotherStatement</c-> <c- p>.</c->
+        <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- nn>ex</c-><c- p>:</c-><c- f>is</c-> <c- l>true</c-> <c- p>.</c-> 
+        <c- nn>_</c-><c- p>:</c-><c- f>Y</c-> <c- b>a</c-> <c- nn>ex</c-><c- p>:</c-><c- f>AnotherStatement</c-> <c- p>.</c->
 
-        <c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>ex</c-><c- p>:</c-><c- f>myThirdSurface</c-> <c- p>{</c->
-            _<c- p>:</c-><c- f>X</c-> <c- nn>ex</c-><c- p>:</c-><c- f>is</c-> <c- l>false</c-> <c- p>.</c->
+        <c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>ex</c-><c- p>:</c-><c- f>myThirdSurface</c-> <c- p>{</c->
+            <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- nn>ex</c-><c- p>:</c-><c- f>is</c-> <c- l>false</c-> <c- p>.</c->
         <c- p>}</c-> <c- p>.</c->
     <c- p>}.</c->
 <c- p>}</c-> <c- p>.</c->
@@ -2412,7 +2411,7 @@ <h2 class="heading settled" data-level="3" id="Surface"><span class="secno">3. <
    </div>
    <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="secno">3.1. </span><span class="content">Positive Surface</span><a class="self-link" href="#PositiveSurface"></a></h3>
    <p>A positive surface is an RDF graph which claims that an RDF Graph on it is true.
-This is the current default interpretation of <a href="https://www.w3.org/TR/rdf11-mt/">RDF Semantics</a>.
+This is the current default interperation of <a href="https://www.w3.org/TR/rdf11-mt/">RDF Semantics</a>.
 When no surfaces are provided, an implicit positive surface is assumed in the RDF document.</p>
    <div class="example" id="example-27b1f9f4">
     <a class="self-link" href="#example-27b1f9f4"></a> The two surfaces below are equal (because a double negation of a statement is the same as claiming the statement is true: positive): 
@@ -2481,26 +2480,26 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
 <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-  <c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
-    _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
+  <c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
   <c- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
-   <p>In RDF Surfaces a default positive surface is implicitly assumed for each RDF document. On this default positive surface all existential variables are implicitly quantified. Example 20 can be rewritten as:</p>
+   <p>In RDF Surfaces, a default positive surface is implicitly assumed for each RDF document. On this default positive surface, all existential variables are implicitly quantified. Example 20 can be rewritten as:</p>
    <div class="example" id="example-891ff7ba">
     <a class="self-link" href="#example-891ff7ba"></a> A default positive surface with an implicit <code>_:X</code> existential variable. 
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-_<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
-_<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
+<c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
+<c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
 </pre>
    </div>
-   <p>When a blank node is marked on an odd nested negative surface, then it is interpreted as a universal quantified variable in the scope of the nested surface.</p>
+   <p>When a blank node is marked on an odd nested negative surface, it is interpreted as an universal quantified variable in the scope of the nested surface.</p>
    <div class="example" id="example-90425235">
-    <a class="self-link" href="#example-90425235"></a> The surface below should be interpreted as : "Everything is a person and knows Alice". 
+    <a class="self-link" href="#example-90425235"></a> The surface below should be interpreted as : "Every person knows Alice". 
     <p>As a logical statement:</p>
 <pre>∀ _:X : _:X a :Person AND _:X :knows :Alice
 </pre>
@@ -2512,10 +2511,10 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
 <pre class="highlight"><c- k>@prefix</c-> <c- nn>:</c-> <c- g>&lt;http://example.org/ns#></c-> <c- p>.</c->
 <c- k>@prefix</c-> <c- nn>log:</c-> <c- g>&lt;http://www.w3.org/2000/10/swap/log#></c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
   <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
-    _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
   <c- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2586,9 +2585,9 @@ <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="s
 <c- p>:</c-><c- f>Alice</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
 <c- p>:</c-><c- f>Alice</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Bob</c-> <c- p>.</c->
 
-<c- p>(</c->_<c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
-    _<c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
-    _<c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
+<c- p>(</c-><c- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
+    <c- nn>_</c-><c- p>:</c-><c- f>X</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>