From 710c85b15c83577128bf9c0efa363e357fd5507f Mon Sep 17 00:00:00 2001
From: josd <josderoo@gmail.com>
Date: Mon, 15 Apr 2024 01:01:21 +0200
Subject: [PATCH 1/6] refreshing

---
 README.md | 1 -
 1 file changed, 1 deletion(-)

diff --git a/README.md b/README.md
index c53f227..4d42cae 100644
--- a/README.md
+++ b/README.md
@@ -9,4 +9,3 @@ See the living document [RDF Surfaces Primer](https://w3c-cg.github.io/rdfsurfac
 ### Latest Examples and Test Cases
 
 - https://github.com/eyereasoner/rdfsurfaces-tests
-- https://github.com/eyereasoner/eye/tree/master/reasoning/rdfsurfaces

From ef8bc403156f99e06b348dde939aa631f5559f4c Mon Sep 17 00:00:00 2001
From: josd <josderoo@gmail.com>
Date: Tue, 30 Apr 2024 10:32:28 +0200
Subject: [PATCH 2/6] translating rdfsurfaces predicates

---
 index.bs   | 62 +++++++++++++++++++++++++++---------------------------
 index.html |  6 +++---
 2 files changed, 34 insertions(+), 34 deletions(-)

diff --git a/index.bs b/index.bs
index 33dc25d..406abea 100644
--- a/index.bs
+++ b/index.bs
@@ -205,7 +205,7 @@ First-order logic using *positive* and *negative* surfaces.
 **First-order logic in Notation3**
 
 RDF Surfaces provides a way to express the notion of *positive* and *negative surfaces*
-in Notation3 with help of the built-in `log:nand`. The `log:nand` built-in is equivalent to the logical NAND function ("not and"). A `log:nand` is true when at least one of the nested triples in the object is false. A *positive* surface can be constructed from double nested `log:nand` built-in. A *negative* surface can be constructed from a single `log:nand` built-in.
+in Notation3 with help of the built-in `log:onNegativeSurface`. The `log:onNegativeSurface` built-in is equivalent to the logical NAND function ("not and"). A `log:onNegativeSurface` is true when at least one of the nested triples in the object is false. A *positive* surface can be constructed from double nested `log:onNegativeSurface` built-in. A *negative* surface can be constructed from a single `log:onNegativeSurface` built-in.
 
 The subject of both built-ins are the blank nodes that need to be put on the 
 surface (so that they become existential or universal quantified variables depending on the nesting level of the surface). 
@@ -217,8 +217,8 @@ surface (so that they become existential or universal quantified variables depen
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-() log:nand {
-  (_:X) log:nand {
+() log:onNegativeSurface {
+  (_:X) log:onNegativeSurface {
     _:X a :City .
   }
 } .
@@ -246,8 +246,8 @@ _:X a :City .
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-(_:X) log:nand {
-  () log:nand {
+(_:X) log:onNegativeSurface {
+  () log:onNegativeSurface {
     _:X a :City .
   }
 } .
@@ -262,7 +262,7 @@ _:X a :City .
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-(_:X) log:nand {
+(_:X) log:onNegativeSurface {
     _:X a :Problem .
 } .
 </pre>
@@ -277,14 +277,14 @@ mean alive, or dead, or both alive and dead.
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-(_:X) log:nand {
+(_:X) log:onNegativeSurface {
     _:X a :Cat .
 
-    () log:nand {
+    () log:onNegativeSurface {
         _:X :is :Alive .
     } .
 
-    () log:nand {
+    () log:onNegativeSurface {
         _:X :is :Dead .
     } .
 } .
@@ -299,10 +299,10 @@ mean alive, or dead, or both alive and dead.
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-(_:X) log:nand {
+(_:X) log:onNegativeSurface {
     _:X a :Cat ;
         :is :Alive .
-    () log:nand {
+    () log:onNegativeSurface {
         _:X :says :Meow .
     } .
 } .
@@ -310,7 +310,7 @@ mean alive, or dead, or both alive and dead.
 
 </div>
 
-A surface can be queried by providing a query surface with the `log:nans` ("not an answer") built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.
+A surface can be queried by providing a query surface with the `log:onNegativeAnswerSurface` ("not an answer") built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.
 
 <div class=example>
 
@@ -325,17 +325,17 @@ that is a `:City`, it implies that `_:S` needs be be also a `:HumanCommunity`.
 ex:Ghent a ex:City.
 
 # Every city is a human community
-(_:S) log:nand {
+(_:S) log:onNegativeSurface {
     _:S a ex:City.
-    () log:nand {
+    () log:onNegativeSurface {
         _:S a ex:HumanCommunity.
     }.
 }.
 
 # Query
-(_:S _:C) log:nand {
+(_:S _:C) log:onNegativeSurface {
     _:S a _:C.
-    () log:nans {
+    () log:onNegativeAnswerSurface {
       _:S a _:C.
     } .
 }.
@@ -400,7 +400,7 @@ special semantics:
  </thead>
  <tbody>
  <tr>
-  <td>`log:nand`
+  <td>`log:onNegativeSurface`
   <td>Negative surface claim that any RDF graph in the object position is false.
  </tbody>
 </table>
@@ -471,8 +471,8 @@ and
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-() log:nand {
-  () log:nand {
+() log:onNegativeSurface {
+  () log:onNegativeSurface {
     :Alice a :Person .
   } .
 }
@@ -509,8 +509,8 @@ As RDF Surface:
 :Alice a :Person .
 :Alice :knows :Bob .
 
-() log:nand {
-  () log:nand {
+() log:onNegativeSurface {
+  () log:onNegativeSurface {
     :Bob a :Person .
     :Bob :knows :Alice .
   } .
@@ -544,8 +544,8 @@ As RDF Surface:
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-() log:nand {
-  (_:X) log:nand {
+() log:onNegativeSurface {
+  (_:X) log:onNegativeSurface {
     _:X a :Person .
     _:X :knows :Alice .
   } .
@@ -594,8 +594,8 @@ As RDF Surface:
 @prefix : &lt;http://example.org/ns#&gt; .
 @prefix log: &lt;http://www.w3.org/2000/10/swap/log#&gt; .
 
-(_:X) log:nand {
-  () log:nand {
+(_:X) log:onNegativeSurface {
+  () log:onNegativeSurface {
     _:X a :Person .
     _:X :knows :Alice .
   } .
@@ -638,7 +638,7 @@ As RDF Surface:
 :Alice a :Person .
 :Alice :knows :Bob .
 
-() log:nand {
+() log:onNegativeSurface {
     :Bob a :Person .
     :Bob :knows :Alice .
 } .
@@ -687,7 +687,7 @@ As RDF Surface:
 :Alice a :Person .
 :Alice :knows :Bob .
 
-(_:X) log:nand {
+(_:X) log:onNegativeSurface {
     _:X a :Person .
     _:X :knows :Alice .
 } .
@@ -729,16 +729,16 @@ As RDF Surface:
 :Alice a :Person .
 :Alice :knows :Bob .
 
-() log:nand {
-    () log:nand {
+() log:onNegativeSurface {
+    () log:onNegativeSurface {
       :Alice a :Person .
     } .
 
-    () log:nand {
+    () log:onNegativeSurface {
       :Bob a :Person .
     } .
 
-    () log:nand {
+    () log:onNegativeSurface {
       :Charly a :Person .
     } .
 }.
diff --git a/index.html b/index.html
index 60b8080..f18990f 100644
--- a/index.html
+++ b/index.html
@@ -2222,7 +2222,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
     <p><img alt="blank surface" src="images/first_order_logic.svg" width="500"></p>
    </div>
    <p><strong>First-order logic in Notation3</strong></p>
-   <p>RDF Surfaces provides a way to express the notion of <em>positive</em> and <em>negative surfaces</em> in Notation3 with help of the built-in <code>log:nand</code>. The <code>log:nand</code> built-in is equivalent to the logical NAND function ("not and"). A <code>log:nand</code> is true when at least one of the nested triples in the object is false. A <em>positive</em> surface can be constructed from double nested <code>log:nand</code> built-in. A <em>negative</em> surface can be constructed from a single <code>log:nand</code> built-in.</p>
+   <p>RDF Surfaces provides a way to express the notion of <em>positive</em> and <em>negative surfaces</em> in Notation3 with help of the built-in <code>log:onNegativeSurface</code>. The <code>log:onNegativeSurface</code> built-in is equivalent to the logical NAND function ("not and"). A <code>log:onNegativeSurface</code> is true when at least one of the nested triples in the object is false. A <em>positive</em> surface can be constructed from double nested <code>log:onNegativeSurface</code> built-in. A <em>negative</em> surface can be constructed from a single <code>log:onNegativeSurface</code> built-in.</p>
    <p>The subject of both built-ins are the blank nodes that need to be put on the
 surface (so that they become existential or universal quantified variables depending on the nesting level of the surface).</p>
    <div class="example" id="example-f0d0e6c6">
@@ -2301,7 +2301,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
-   <p>A surface can be queried by providing a query surface with the <code>log:nans</code> ("not an answer") built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.</p>
+   <p>A surface can be queried by providing a query surface with the <code>log:onNegativeAnswerSurface</code> ("not an answer") 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-82c4ace5">
     <a class="self-link" href="#example-82c4ace5"></a> 
     <p><code>:Ghent a :City</code> is a triple on the implicit positive surface. The two nested
@@ -2373,7 +2373,7 @@ <h2 class="heading settled" data-level="3" id="Surface"><span class="secno">3. <
       <td>semantics 
     <tbody>
      <tr>
-      <td><code>log:nand</code> 
+      <td><code>log:onNegativeSurface</code> 
       <td>Negative surface claim that any RDF graph in the object position is false. 
    </table>
    <p>A surface can contain zero or more other surfaces. These surfaces are then nested.

From 9540f5c057ba50310dda5dd28a763f0a71ccaa5d Mon Sep 17 00:00:00 2001
From: josd <josderoo@gmail.com>
Date: Tue, 30 Apr 2024 15:13:05 +0200
Subject: [PATCH 3/6] translating rdfsurfaces predicates

---
 index.html | 171 +++++++++++++++++++++++++++--------------------------
 1 file changed, 86 insertions(+), 85 deletions(-)

diff --git a/index.html b/index.html
index f18990f..cc3f137 100644
--- a/index.html
+++ b/index.html
@@ -1488,8 +1488,8 @@
 		}
 	}
 </style>
-  <meta content="Bikeshed version d765c696b, updated Fri Mar 8 15:58:52 2024 -0800" name="generator">
-  <meta content="dark light" name="color-scheme">
+  <meta content="Bikeshed version 4416b18d5, updated Tue Jan 2 15:52:39 2024 -0800" name="generator">
+  <meta content="ef8bc403156f99e06b348dde939aa631f5559f4c" name="revision">
 <style>
 table {
   margin: 25px auto;
@@ -2044,10 +2044,11 @@
   <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="2024-04-05">5 April 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="2024-04-30">30 April 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>)
@@ -2057,7 +2058,7 @@ <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 5 April 2024,
+In addition, as of 30 April 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>
@@ -2225,14 +2226,14 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
    <p>RDF Surfaces provides a way to express the notion of <em>positive</em> and <em>negative surfaces</em> in Notation3 with help of the built-in <code>log:onNegativeSurface</code>. The <code>log:onNegativeSurface</code> built-in is equivalent to the logical NAND function ("not and"). A <code>log:onNegativeSurface</code> is true when at least one of the nested triples in the object is false. A <em>positive</em> surface can be constructed from double nested <code>log:onNegativeSurface</code> built-in. A <em>negative</em> surface can be constructed from a single <code>log:onNegativeSurface</code> built-in.</p>
    <p>The subject of both built-ins are the blank nodes that need to be put on the
 surface (so that they become existential or universal quantified variables depending on the nesting level of the surface).</p>
-   <div class="example" id="example-f0d0e6c6">
-    <a class="self-link" href="#example-f0d0e6c6"></a> <em>"Something is a city"</em> in Notation3. 
+   <div class="example" id="example-51ab59e2">
+    <a class="self-link" href="#example-51ab59e2"></a> <em>"Something is a city"</em> in Notation3. 
 <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- nn>log</c-><c- p>:</c-><c- f>nand</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>nand</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- 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- p>}</c-> <c- p>.</c->
 </pre>
@@ -2243,67 +2244,67 @@ <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- 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- f>X</c-> <c- b>a</c-> <c- p>:</c-><c- f>City</c-> <c- p>.</c->
 </pre>
    </div>
-   <div class="example" id="example-aa24e825">
-    <a class="self-link" href="#example-aa24e825"></a> <em>"Everything is a city"</em> in Notation3. Notice how we can make universal or existential quantified variables by placing blank nodes on a odd or even nested surface. 
+   <div class="example" id="example-81be5796">
+    <a class="self-link" href="#example-81be5796"></a> <em>"Everything is a city"</em> in Notation3. Notice how we can make universal or existential quantified variables by placing blank nodes on a odd or even nested surface. 
 <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</c-> <c- p>{</c->
-  <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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- p>}</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
-   <div class="example" id="example-c2f96003">
-    <a class="self-link" href="#example-c2f96003"></a> <em>"Nothing is a problem"</em> in Notation3 . 
+   <div class="example" id="example-2a1c53c6">
+    <a class="self-link" href="#example-2a1c53c6"></a> <em>"Nothing is a problem"</em> in Notation3 . 
 <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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-><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- p>.</c->
 </pre>
    </div>
-   <div class="example" id="example-5059dfe0">
-    <a class="self-link" href="#example-5059dfe0"></a> <em>"All cats are alive OR dead"</em> in Notation3. These are Schrödinger cats: logical OR can
+   <div class="example" id="example-3507dd11">
+    <a class="self-link" href="#example-3507dd11"></a> <em>"All cats are alive OR dead"</em> in Notation3. These are Schrödinger cats: logical OR can
 mean alive, or dead, or both alive and dead. 
 <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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>log</c-><c- p>:</c-><c- f>nand</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- 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- p>}</c-> <c- p>.</c->
 
-    <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
-   <div class="example" id="example-45929b62">
-    <a class="self-link" href="#example-45929b62"></a> <em>"If any cat X is alive, then X says meow"</em> in Notation3 . 
+   <div class="example" id="example-5508fab5">
+    <a class="self-link" href="#example-5508fab5"></a> <em>"If any cat X is alive, then X says meow"</em> in Notation3 . 
 <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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- 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>nand</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- 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- 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> ("not an answer") 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-82c4ace5">
-    <a class="self-link" href="#example-82c4ace5"></a> 
+   <div class="example" id="example-85a03cf8">
+    <a class="self-link" href="#example-85a03cf8"></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> needs be be also a <code>:HumanCommunity</code>.</p>
@@ -2313,18 +2314,18 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <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- nn>_</c-><c- p>:</c-><c- f>S</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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>nand</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- 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>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- p>}.</c->
 <c- p>}.</c->
 
 <c- c># Query</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>nand</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>nans</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- 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>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- p>}</c-> <c- p>.</c->
 <c- p>}.</c->
 </pre>
@@ -2393,17 +2394,17 @@ <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- 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- 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- 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- 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- 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- 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- 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- 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- 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- p>.</c->
     <c- p>}.</c->
 <c- p>}</c-> <c- p>.</c->
@@ -2413,8 +2414,8 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
    <p>A positive surface is an RDF graph which claims that an RDF Graph on it is true.
 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-406b8db0">
-    <a class="self-link" href="#example-406b8db0"></a> The two surfaces below are equal (because a double negation of a statement is the same as claiming the statement is true: positive): 
+   <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): 
 <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->
 
@@ -2424,8 +2425,8 @@ <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- nn>log</c-><c- p>:</c-><c- f>nand</c-> <c- p>{</c->
-  <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
     <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- p>.</c->
 <c- p>}</c->
@@ -2440,8 +2441,8 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
     <li data-md>
      <p>When two or more triples are placed on a positive surface, then the surface is valid when the logical conjunction of all triples is true.</p>
    </ul>
-   <div class="example" id="example-04837ca9">
-    <a class="self-link" href="#example-04837ca9"></a> The surface below should be interpreted as: "Alice is a person and knows Bob, and Bob is a 
+   <div class="example" id="example-c5f71126">
+    <a class="self-link" href="#example-c5f71126"></a> The surface below should be interpreted as: "Alice is a person and knows Bob, and Bob is a 
 person that knows Alice". 
     <p>As a logical statement:</p>
 <pre>:Alice a :Person AND 
@@ -2457,8 +2458,8 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><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- nn>log</c-><c- p>:</c-><c- f>nand</c-> <c- p>{</c->
-  <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
     <c- p>:</c-><c- f>Bob</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
     <c- p>:</c-><c- f>Bob</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
   <c- p>}</c-> <c- p>.</c->
@@ -2466,8 +2467,8 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
 </pre>
    </div>
    <p>When a blank node is marked on an even nested negative surface, then it is interpreted as an existential quantified variable in the scope of the nested surface.</p>
-   <div class="example" id="example-c301f0df">
-    <a class="self-link" href="#example-c301f0df"></a> The surface below should be interpreted as : "There is a person that knows Alice". 
+   <div class="example" id="example-b7a6456a">
+    <a class="self-link" href="#example-b7a6456a"></a> The surface below should be interpreted as : "There is a person that knows Alice". 
     <p>As a logical statement:</p>
 <pre>∃ _:X : _:X a :Person AND _:X :knows :Alice
 </pre>
@@ -2479,10 +2480,10 @@ <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- nn>log</c-><c- p>:</c-><c- f>nand</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>nand</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- 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- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2493,13 +2494,13 @@ <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- 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- 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->
 </pre>
    </div>
    <p>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.</p>
-   <div class="example" id="example-6a666d4d">
-    <a class="self-link" href="#example-6a666d4d"></a> The surface below should be interpreted as : "Every person knows Alice". 
+   <div class="example" id="example-90425235">
+    <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>
@@ -2511,10 +2512,10 @@ <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</c-> <c- p>{</c->
-  <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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- p>}</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
 </pre>
@@ -2531,8 +2532,8 @@ <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="s
     <li data-md>
      <p>When two or more triples are placed on a positive surface, then the surface is valid when the logical conjunction of all triples is false.</p>
    </ul>
-   <div class="example" id="example-a4a03935">
-    <a class="self-link" href="#example-a4a03935"></a> The surface below should be interpreted as: "Alice is a person and knows Bob and Bob is
+   <div class="example" id="example-562ee4eb">
+    <a class="self-link" href="#example-562ee4eb"></a> The surface below should be interpreted as: "Alice is a person and knows Bob and Bob is
 not a person that knows Alice". 
     <p>As a logical statement:</p>
 <pre>:Alice a :Person AND 
@@ -2548,7 +2549,7 @@ <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- nn>log</c-><c- p>:</c-><c- f>nand</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>Bob</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
     <c- p>:</c-><c- f>Bob</c-> <c- p>:</c-><c- f>knows</c-> <c- p>:</c-><c- f>Alice</c-> <c- p>.</c->
 <c- p>}</c-> <c- p>.</c->
@@ -2556,8 +2557,8 @@ <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="s
    </div>
    <p>When a blank node is marked on a negative surface, then it should be interpreted as an existential
 quantified variable in the scope of the negative surface.</p>
-   <div class="example" id="example-3f9a06f8">
-    <a class="self-link" href="#example-3f9a06f8"></a> The surface below should be interpreted as "Alice is a Person and knows Bob 
+   <div class="example" id="example-0b36aace">
+    <a class="self-link" href="#example-0b36aace"></a> The surface below should be interpreted as "Alice is a Person and knows Bob 
 and there isn’t a person that knows Alice". 
     <p>As a logical statement:</p>
 <pre>:Alice a :Person AND 
@@ -2585,16 +2586,16 @@ <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- nn>_</c-><c- p>:</c-><c- f>X</c-><c- p>)</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- 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- p>.</c->
 </pre>
    </div>
    <p>When two or more negative surfaces are nested in a parent negative surface, then it should
 be interpreted as a logical disjunction.</p>
-   <div class="example" id="example-9b498063">
-    <a class="self-link" href="#example-9b498063"></a> The surface below should be interpreted as "Alice is a Person OR Bob is a Person
+   <div class="example" id="example-240df7f2">
+    <a class="self-link" href="#example-240df7f2"></a> The surface below should be interpreted as "Alice is a Person OR Bob is a Person
 OR Charly is a person". 
     <p>As a logical statement:</p>
 <pre>:Alice a :Person OR
@@ -2615,16 +2616,16 @@ <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- nn>log</c-><c- p>:</c-><c- f>nand</c-> <c- p>{</c->
-    <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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- nn>log</c-><c- p>:</c-><c- f>onNegativeSurface</c-> <c- p>{</c->
       <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- p>.</c->
 
-    <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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>Bob</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 
-    <c- p>()</c-> <c- nn>log</c-><c- p>:</c-><c- f>nand</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>Charly</c-> <c- b>a</c-> <c- p>:</c-><c- f>Person</c-> <c- p>.</c->
     <c- p>}</c-> <c- p>.</c->
 <c- p>}.</c->

From 77fd0cd4654ad9195a3fa11f6371b574a1632622 Mon Sep 17 00:00:00 2001
From: josd <josderoo@gmail.com>
Date: Wed, 1 May 2024 02:12:04 +0200
Subject: [PATCH 4/6] translating rdfsurfaces predicates

---
 index.bs   | 2 +-
 index.html | 8 ++++----
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/index.bs b/index.bs
index 406abea..231a8b8 100644
--- a/index.bs
+++ b/index.bs
@@ -310,7 +310,7 @@ mean alive, or dead, or both alive and dead.
 
 </div>
 
-A surface can be queried by providing a query surface with the `log:onNegativeAnswerSurface` ("not an answer") built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.
+A surface can be queried by providing a query surface with the `log:onNegativeAnswerSurface` built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.
 
 <div class=example>
 
diff --git a/index.html b/index.html
index cc3f137..815bc02 100644
--- a/index.html
+++ b/index.html
@@ -1489,7 +1489,7 @@
 	}
 </style>
   <meta content="Bikeshed version 4416b18d5, updated Tue Jan 2 15:52:39 2024 -0800" name="generator">
-  <meta content="ef8bc403156f99e06b348dde939aa631f5559f4c" name="revision">
+  <meta content="9540f5c057ba50310dda5dd28a763f0a71ccaa5d" name="revision">
 <style>
 table {
   margin: 25px auto;
@@ -2044,7 +2044,7 @@
   <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="2024-04-30">30 April 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="2024-05-01">1 May 2024</time></span></h2>
    <div data-fill-with="spec-metadata">
     <dl>
      <dt>Issue Tracking:
@@ -2058,7 +2058,7 @@ <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 30 April 2024,
+In addition, as of 1 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>
@@ -2302,7 +2302,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
 <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> ("not an answer") built-in. The results of this query will be the final result of the reasoning engine interpreting the surfaces.</p>
+   <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> 
     <p><code>:Ghent a :City</code> is a triple on the implicit positive surface. The two nested

From 2ffb3feb2725fc1f1aba9e2f1b16bd7c28195595 Mon Sep 17 00:00:00 2001
From: Joachim Van Herwegen <joachimvh@gmail.com>
Date: Mon, 13 May 2024 11:49:45 +0200
Subject: [PATCH 5/6] Fix typos

---
 index.html | 32 ++++++++++++++++----------------
 1 file changed, 16 insertions(+), 16 deletions(-)

diff --git a/index.html b/index.html
index 815bc02..9e7f568 100644
--- a/index.html
+++ b/index.html
@@ -2099,7 +2099,7 @@ <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 a sheet of paper on which RDF graphs can be written.
+   <p>An RDF surface is a kind of 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 +2123,7 @@ <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 is a cat"</em>). 
+and another one with the triple <code>[] a :Cat</code> (which means <em>"There is something that 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 +2140,7 @@ <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 there is more than one RDF graph on the surface, then it is a logical conjunction (AND).
+   <p>When 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>
@@ -2159,8 +2159,8 @@ <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 contradicton. When there are one
-or more RDF graphs written on an <em>negative</em> surface they mean the negation of those RDF graphs.</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
 that:</p>
 <pre>NOT(∃ x : P(x)) ⇔ ∀ x : NOT(P(x))
@@ -2208,7 +2208,7 @@ <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 made from an 
+an existential quantified variable and using the rule that a universal quantified variable can be 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>
@@ -2307,7 +2307,7 @@ <h2 class="heading settled" data-level="1" id="Introduction"><span class="secno"
     <a class="self-link" href="#example-85a03cf8"></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> needs be be also a <code>:HumanCommunity</code>.</p>
+that is a <code>:City</code>, it implies that <code>_:S</code> also needs to be 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->
 
@@ -2363,9 +2363,9 @@ <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 a RDF graph or the <code>true</code> or <code>false</code> literal. The blank nodes in the 
+The <code>object</code> is an 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-in have 
+the kind of surface. Any kind of surface may be used but the following built-ins have 
 special semantics:</p>
    <table>
     <thead>
@@ -2378,7 +2378,7 @@ <h2 class="heading settled" data-level="3" id="Surface"><span class="secno">3. <
       <td>Negative surface claim that any RDF graph in the object position is false. 
    </table>
    <p>A surface can contain zero or more other surfaces. These surfaces are then nested.
-Nested surfaces can share the same <a data-link-type="biblio" href="#biblio-uri" title="Uniform Resource Identifier (URI): Generic Syntax">[URI]</a>-s and literals (by copying the data), 
+Nested surfaces can share the same <a data-link-type="biblio" href="#biblio-uri" title="Uniform Resource Identifier (URI): Generic Syntax">[URI]</a>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 <em>coreferences</em> to the
 blank node graffiti defined on a parent RDF Surface. If no such parent RDF Surface
@@ -2412,7 +2412,7 @@ <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 interperation of <a href="https://www.w3.org/TR/rdf11-mt/">RDF Semantics</a>.
+This is the current default interpretation 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): 
@@ -2488,7 +2488,7 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
 <c- p>}</c-> <c- p>.</c->
 </pre>
    </div>
-   <p>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:</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->
@@ -2498,9 +2498,9 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
 _<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 an universal quantified variable in the scope of the nested surface.</p>
+   <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>
    <div class="example" id="example-90425235">
-    <a class="self-link" href="#example-90425235"></a> The surface below should be interpreted as : "Every person knows Alice". 
+    <a class="self-link" href="#example-90425235"></a> The surface below should be interpreted as : "Everything is a person and knows Alice". 
     <p>As a logical statement:</p>
 <pre>∀ _:X : _:X a :Person AND _:X :knows :Alice
 </pre>
@@ -2522,7 +2522,7 @@ <h3 class="heading settled" data-level="3.1" id="PositiveSurface"><span class="s
    </div>
    <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="secno">3.2. </span><span class="content">Negative Surface</span><a class="self-link" href="#NegativeSurface"></a></h3>
    <p>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.</p>
+interpretation of the negative surface is the negation of RDF Graph on it.</p>
    <p>The semantics of a negative surface is interpreted as a logical falsehood:</p>
    <ul>
     <li data-md>
@@ -2631,7 +2631,7 @@ <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="s
 <c- p>}.</c->
 </pre>
    </div>
-   <p>With combinations of AND and NOT other logical truth function can be build. E.g.</p>
+   <p>With combinations of AND and NOT other logical truth function can be built. E.g.</p>
    <ul>
     <li data-md>
      <p>Disjunction: <code>P ∨ Q</code> : <code>NOT( NOT(P) AND NOT(Q))</code></p>

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 6/6] 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>