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Adding pathway example
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phochste committed May 15, 2024
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102 changes: 100 additions & 2 deletions index.bs
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Expand Up @@ -771,9 +771,107 @@ Issue: TODO
Examples {#Examples}
================

Issue: TODO
As an illustration of RDF Surface we offer a graph traversal example. Example 26 provides information about French roads where some roads are blocked due road works. In the example we use the predicate `:oneway` to indicate that a connection is possible from one city to another. To deny this connection, we use a negative surface.

See:
<div class="example">
Possible connections between the French cities including a blocked connection between Chartes and Lemans.

```
@prefix : <urn:example:>.

:Paris :oneway :Orleans.
:Paris :oneway :Chartres.
:Paris :oneway :Amiens.
:Orleans :oneway :Blois.
:Orleans :oneway :Bourges.
:Blois :oneway :Tours.
:Lemans :oneway :Angers.
:Lemans :oneway :Tours.
:Angers :oneway :Nantes.

# blocking some roads
() log:onNegativeSurface {
:Chartres :oneway :Lemans.
}.
```
</div>

Next, we would like to provide the logic of a "path" through the French road system. We would like to share an RDF document that states: "When a the is a `:oneway` from one city to another city, then there is a `:path` between those cities". Or, expressed in a symbolic form:

```
∀ _:A,_:B : ( _:A :oneway _:B ) IMPLIES ( _:A :path _:B )
```

These paths are transitive. When there is a path from A to B and a path from B to C, then there is a path from A to C. Or, expressed in a symbolic form:

```
∀ _:A,_:B,_:C : ( ( _:A :path _:B ) AND (_:B :path _:C) ) IMPLIES ( _:A :path _:C )
```

Using the patterns for `IMPLIES` from the previous sections these logical formulas can be written as RDF Surfaces in Example 27.

<div class="example">
The RDF Surfaces of a path algorithm.

```
@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix : <urn:example:>.

# oneway subproperty of path
(_:A _:B) log:onNegativeSurface {
_:A :oneway _:B .
() log:onNegativeSurface {
_:A :path _:B .
} .
} .

# path transitive property
(_:A _:B _:C) log:onNegativeSurface {
_:A :path _:B .
_:B :path _:C .
() log:onNegativeSurface {
_:A :path _:C .
}.
} .
```
</div>

Based on the RDF documents in Example 26 and 27, we can construct a query to find out which paths are possible that end in Nantes. For this we use a specialized answer surface that expresses: "If there is some path from A to Nantes, then this is an answer. This is expressed as RDF Surfaces in Example 28.

<div class="example">
Query for a possible path from A to Nantes.

```
@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix : <urn:example:>.

(_:A) log:onNegativeSurface {
_:A :path :nantes .
() log:onNegativeAnswerSurface {
_:A :path :nantes .
:test :is :true .
}.
} .
```
</div>

Combining the RDF documents from Examples 26, 27 and 28, a RDF Surfaces reasoner should give as answer:

```
:angers :path :nantes .
:lemans :path :nantes .
```

If we would remove the negative surface around `:chartes :oneway :lemans`, a RDF Surfaces reasoner should provide more answers:

```
:angers :path :nantes .
:lemans :path :nantes .
:chartres :path :nantes .
:paris :path :nantes .
```

For more RDF Surfaces examples see:

- [https://github.com/eyereasoner/eye/tree/master/reasoning/rdfsurfaces](https://github.com/eyereasoner/eye/tree/master/reasoning/rdfsurfaces)
- [https://github.com/eyereasoner/rdfsurfaces-tests](https://github.com/eyereasoner/rdfsurfaces-tests)
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80 changes: 77 additions & 3 deletions index.html
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Expand Up @@ -2653,8 +2653,83 @@ <h3 class="heading settled" data-level="3.2" id="NegativeSurface"><span class="s
<h3 class="heading settled" data-level="3.3" id="answer-surface"><span class="secno">3.3. </span><span class="content">Answer Surface</span><a class="self-link" href="#answer-surface"></a></h3>
<p class="issue" id="issue-b7b1e314"><a class="self-link" href="#issue-b7b1e314"></a> TODO</p>
<h2 class="heading settled" data-level="4" id="Examples"><span class="secno">4. </span><span class="content">Examples</span><a class="self-link" href="#Examples"></a></h2>
<p class="issue" id="issue-b7b1e314①"><a class="self-link" href="#issue-b7b1e314①"></a> TODO</p>
<p>See:</p>
<p>As an illustration of RDF Surface we offer a graph traversal example. Example 26 provides information about French roads where some roads are blocked due road works. In the example we use the predicate <code>:oneway</code> to indicate that a connection is possible from one city to another. To deny this connection, we use a negative surface.</p>
<div class="example" id="example-584499c3">
<a class="self-link" href="#example-584499c3"></a> Possible connections between the French cities including a blocked connection between Chartes and Lemans.
<pre>@prefix : &lt;urn:example:>.

:Paris :oneway :Orleans.
:Paris :oneway :Chartres.
:Paris :oneway :Amiens.
:Orleans :oneway :Blois.
:Orleans :oneway :Bourges.
:Blois :oneway :Tours.
:Lemans :oneway :Angers.
:Lemans :oneway :Tours.
:Angers :oneway :Nantes.

# blocking some roads
() log:onNegativeSurface {
:Chartres :oneway :Lemans.
}.
</pre>
</div>
<p>Next, we would like to provide the logic of a "path" through the French road system. We would like to share an RDF document that states: "When a the is a <code>:oneway</code> from one city to another city, then there is a <code>:path</code> between those cities". Or, expressed in a symbolic form:</p>
<pre>∀ _:A,_:B : ( _:A :oneway _:B ) IMPLIES ( _:A :path _:B )
</pre>
<p>These paths are transitive. When there is a path from A to B and a path from B to C, then there is a path from A to C. Or, expressed in a symbolic form:</p>
<pre>∀ _:A,_:B,_:C : ( ( _:A :path _:B ) AND (_:B :path _:C) ) IMPLIES ( _:A :path _:C )
</pre>
<p>Using the patterns for <code>IMPLIES</code> from the previous sections these logical formulas can be written as RDF Surfaces in Example 27.</p>
<div class="example" id="example-a55cb7b7">
<a class="self-link" href="#example-a55cb7b7"></a> The RDF Surfaces of a path algorithm.
<pre>@prefix log: &lt;http://www.w3.org/2000/10/swap/log#>.
@prefix : &lt;urn:example:>.

# oneway subproperty of path
(_:A _:B) log:onNegativeSurface {
_:A :oneway _:B .
() log:onNegativeSurface {
_:A :path _:B .
} .
} .

# path transitive property
(_:A _:B _:C) log:onNegativeSurface {
_:A :path _:B .
_:B :path _:C .
() log:onNegativeSurface {
_:A :path _:C .
}.
} .
</pre>
</div>
<p>Based on the RDF documents in Example 26 and 27, we can construct a query to find out which paths are possible that end in Nantes. For this we use a specialized answer surface that expresses: "If there is some path from A to Nantes, then this is an answer. This is expressed as RDF Surfaces in Example 28.</p>
<div class="example" id="example-5e23bfb9">
<a class="self-link" href="#example-5e23bfb9"></a> Query for a possible path from A to Nantes.
<pre>@prefix log: &lt;http://www.w3.org/2000/10/swap/log#>.
@prefix : &lt;urn:example:>.

(_:A) log:onNegativeSurface {
_:A :path :nantes .
() log:onNegativeAnswerSurface {
_:A :path :nantes .
:test :is :true .
}.
} .
</pre>
</div>
<p>Combining the RDF documents from Examples 26, 27 and 28, a RDF Surfaces reasoner should give as answer:</p>
<pre>:angers :path :nantes .
:lemans :path :nantes .
</pre>
<p>If we would remove the negative surface around <code>:chartes :oneway :lemans</code>, a RDF Surfaces reasoner should provide more answers:</p>
<pre>:angers :path :nantes .
:lemans :path :nantes .
:chartres :path :nantes .
:paris :path :nantes .
</pre>
<p>For more RDF Surfaces examples see:</p>
<ul>
<li data-md>
<p><a href="https://github.com/eyereasoner/eye/tree/master/reasoning/rdfsurfaces">https://github.com/eyereasoner/eye/tree/master/reasoning/rdfsurfaces</a></p>
Expand Down Expand Up @@ -2822,5 +2897,4 @@ <h3 class="no-num no-ref heading settled" id="informative"><span class="content"
<h2 class="no-num no-ref heading settled" id="issues-index"><span class="content">Issues Index</span><a class="self-link" href="#issues-index"></a></h2>
<div style="counter-reset:issue">
<div class="issue"> TODO <a class="issue-return" href="#issue-b7b1e314" title="Jump to section">↵</a></div>
<div class="issue"> TODO <a class="issue-return" href="#issue-b7b1e314①" title="Jump to section">↵</a></div>
</div>

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