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<div class="document" id="forward-chaining">
<h1 class="title">Forward Chaining</h1>
<p>Forward chaining <a class="reference external" href="index.html">rules</a> are processed automatically as each <a class="reference external" href="../../knowledge_bases/rule_bases.html">rule base</a> is
<a class="reference external" href="../../using_pyke/index.html#getting-started">activated</a>.</p>
<p>When a rule base is <a class="reference external" href="../../using_pyke/index.html#getting-started">activated</a>, all of its forward-chaining <a class="reference external" href="index.html">rules</a> are run
in the order that they appear in the <a class="reference external" href="../../pyke_syntax/krb_syntax/index.html">.krb file</a> for that rule base.</p>
<div class="section" id="overview-of-forward-chaining">
<h2>Overview of Forward-Chaining</h2>
<p>To do forward-chaining, Pyke finds rules whose <em>if</em> clause matches Pyke's list
of already known facts (the <em>if</em> clause may match, or <em>succeed</em>, multiple time;
see <a class="reference external" href="index.html#backtracking">backtracking</a>). Each time a rule succeeds, it <em>fires</em> this rule, which
adds the facts in the <em>then</em> clause of that rule to the list of already known
facts.</p>
<p>These new facts may fire other forward-chaining rules by matching their
<em>if</em> clause. This can go on to any depth. So Pyke ends up linking (or
<em>chaining</em>) the <em>then</em> clause of the first rule to the <em>if</em> clause of the next
rule.</p>
<div class="note">
<p class="first admonition-title">Note</p>
<p class="last">Forward-chaining continues until no more <a class="reference external" href="index.html">rules</a> can be fired.</p>
</div>
<div class="section" id="reviewing">
<h3>Reviewing</h3>
<ol class="arabic simple">
<li>Pyke starts with the <em>if</em> clause of the first rule and checks to see if it
matches the known facts.</li>
<li>If so, it proceeds to the <em>then</em> clause of that rule (<em>firing</em> the rule).</li>
<li>Which may link (or <em>chain</em>) to the <em>if</em> clause of another rule.</li>
</ol>
<p>Since Pyke processes these rules from <em>if</em> to <em>then</em> to <em>if</em> to <em>then</em> in the
manner that we normally think of using rules, it's called <em>forward</em> chaining.</p>
</div>
</div>
<div class="section" id="foreach-assert-rather-than-if-then">
<h2>"Foreach", "Assert" Rather than "If", "Then"</h2>
<p>Finally, since the statements within the <em>if</em> clause of the rule contain
<a class="reference external" href="../pattern_matching/index.html">patterns</a>; they may each match several facts. In this case, the rule will
succeed and be fired multiple times.</p>
<p>The statements in the <em>then</em> clause of the rule also contain patterns.
Each time the rule is fired, the pattern variables within the <em>then</em>
statements are bound to different values so that different facts are asserted.</p>
<p>To avoid confusion, Pyke uses the words <strong>foreach</strong> and <strong>assert</strong> rather
than <strong>if</strong> and <strong>then</strong> for forward-chaining rules. This is to suggest that
"for each" combination of facts matching the first list of statements,
the rule is fired to "assert" the facts in the second list of statements.</p>
<div class="note">
<p class="first admonition-title">Note</p>
<p class="last">The use of <strong>foreach</strong> and <strong>assert</strong> identifies the rule as a
forward-chaining rule.</p>
</div>
</div>
<div class="section" id="example">
<h2>Example</h2>
<p>This example will figure out the paternal ancestry of individuals given a list
of starting statements about who the sons of each father are. (Daughters and
mothers are omitted to keep the example brief). These facts are stored in a
<a class="reference external" href="../../knowledge_bases/fact_bases.html">fact base</a> called <tt class="docutils literal">family1</tt> as <tt class="docutils literal">son_of(son, father)</tt>:</p>
<pre class="literal-block">
1 son_of(david, bruce)
2 son_of(bruce, thomas)
3 son_of(thomas, frederik)
4 son_of(frederik, hiram)
</pre>
<p>We want to derive <tt class="docutils literal">father_son</tt> relationships of the following form:</p>
<pre class="literal-block">
father_son($father, $son, $prefix)
</pre>
<p>where</p>
<blockquote>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">$son:</th><td class="field-body">is the name of the son (e.g., david)</td>
</tr>
<tr class="field"><th class="field-name">$father:</th><td class="field-body">is the name of the father (e.g., bruce)</td>
</tr>
<tr class="field"><th class="field-name">$prefix:</th><td class="field-body">is a tuple of prefixes before the 'father' and 'son' titles to
indicate the number of generations (e.g., <tt class="docutils literal">()</tt> for direct
father_son relationships, <tt class="docutils literal">(grand)</tt>, <tt class="docutils literal">(great, grand)</tt>, etc).</td>
</tr>
</tbody>
</table>
</blockquote>
<p>This is done using three forward-chaining rules. Each rule is presented as a
separate step:</p>
<ul class="simple">
<li><a class="reference internal" href="#step-1-direct-father-son">Step 1: Direct_father_son</a><ul>
<li>Step 1 demonstrates the use of <a class="reference external" href="../pattern_matching/index.html">pattern matching</a> to transfer values
from one statement within the rule to another statement.</li>
</ul>
</li>
<li><a class="reference internal" href="#step-2-grand-father-son">Step 2: Grand_father_son</a><ul>
<li>Step 2 demonstrates <a class="reference external" href="index.html#backtracking">backtracking</a> within the <a class="reference external" href="index.html#premises-and-conclusions">premises</a> of a
forward-chaining rule. Understanding this will help you to understand
<a class="reference external" href="backward_chaining.html">backward-chaining rules</a>.</li>
</ul>
</li>
<li><a class="reference internal" href="#step-3-great-grand-father-son">Step 3: Great_grand_father_son</a><ul>
<li>Step 3 demonstrates a recursive forward-chaining rule.</li>
</ul>
</li>
</ul>
<p>Finally, you will be shown how to <a class="reference internal" href="#running-the-example">Run the Example</a> yourself.</p>
</div>
<div class="section" id="step-1-direct-father-son">
<h2>Step 1: Direct_father_son</h2>
<p>First we need to establish the direct father_son relationships (those whose
<tt class="docutils literal">$prefix</tt> is <tt class="docutils literal">()</tt>):</p>
<pre class="literal-block">
1 direct_father_son
2 foreach
3 family1.son_of($son, $father)
4 assert
5 family1.father_son($father, $son, ())
</pre>
<div class="section" id="the-use-of-pattern-variables">
<h3>The Use of Pattern Variables</h3>
<p>This demonstrates how <a class="reference external" href="../pattern_matching/pattern_variables.html">pattern variables</a> are used to transfer values from
one statement within a rule into another statement within the rule.</p>
<p>This rule has a single statement in its <tt class="docutils literal">foreach</tt> clause (on line 3). This
statement matches all four <tt class="docutils literal">son_of</tt> facts, so the rule succeeds four times;
but with different bindings for the <tt class="docutils literal">$son</tt> and <tt class="docutils literal">$father</tt> pattern variables.
This causes different facts to be asserted when the same <tt class="docutils literal">assert</tt> clause (on
line 5) is run four times; because each time line 5 is run, the values for
<tt class="docutils literal">$son</tt> and <tt class="docutils literal">$father</tt> are transferred from the statement on line 3 to the
statement on line 5.</p>
<p>When the rule fires matching line 3 to:</p>
<pre class="literal-block">
1 son_of(david, bruce)
</pre>
<p>It runs line 5 to assert:</p>
<pre class="literal-block">
5 father_son(bruce, david, ())
</pre>
<p>And when the rule fires a second time matching line 3 to:</p>
<pre class="literal-block">
2 son_of(bruce, thomas)
</pre>
<p>It runs line 5 a second time to assert:</p>
<pre class="literal-block">
6 father_son(thomas, bruce, ())
</pre>
<p>The rule fires twice more for the remaining <tt class="docutils literal">son_of</tt> facts, asserting
two more <tt class="docutils literal">father_son</tt> relationships. So this rule adds a total of four
new facts:</p>
<pre class="literal-block">
5 father_son(bruce, david, ())
6 father_son(thomas, bruce, ())
7 father_son(frederik, thomas, ())
8 father_son(hiram, frederik, ())
</pre>
</div>
</div>
<div class="section" id="step-2-grand-father-son">
<h2>Step 2: Grand_father_son</h2>
<p>Now we want to add grand son-father relationships. We have a new rule for
this:</p>
<pre class="literal-block">
6 grand_father_son
7 foreach
8 family1.father_son($father, $grand_son, ())
9 family1.father_son($grand_father, $father, ())
10 assert
11 family1.father_son($grand_father, $grand_son, (grand))
</pre>
<div class="section" id="the-use-of-backtracking">
<h3>The Use of Backtracking</h3>
<p>The <tt class="docutils literal">grand_father_son</tt> <a class="reference external" href="index.html">rule</a> is run for all combinations of <tt class="docutils literal">father_son</tt>
<a class="reference external" href="../../knowledge_bases/fact_bases.html#facts">facts</a> that satisfy the two <tt class="docutils literal">foreach</tt> <a class="reference external" href="../statements.html">statements</a> (on lines 8 and 9) and
<a class="reference external" href="../../using_pyke/adding_facts.html">asserts</a> a <tt class="docutils literal">(grand)</tt> <tt class="docutils literal">father_son</tt> statement (on line 11) for each
combination.</p>
<p>This rule is a good example for <a class="reference external" href="index.html#backtracking">backtracking</a> and will help later in your
understanding of backtracking with <a class="reference external" href="backward_chaining.html">backward-chaining</a>. So let's follow the
backtracking in the execution of this rule.</p>
<p>The <tt class="docutils literal">foreach</tt> clause has two statements (on lines 8 and 9) in it that are
both looking for <tt class="docutils literal">father_son</tt> facts with a prefix of <tt class="docutils literal">()</tt>:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ())
9 family1.father_son($grand_father, $father, ())
</pre>
<p>These will be matched to the following <tt class="docutils literal">family1</tt> facts (facts 5 through 8):</p>
<pre class="literal-block">
5 father_son(bruce, david, ())
6 father_son(thomas, bruce, ())
7 father_son(frederik, thomas, ())
8 father_son(hiram, frederik, ())
</pre>
<p>Pyke starts at the top of the list of premises and looks for a match for the
first premise (on line 8). This matches fact 5, so the first premise
succeeds, binding <tt class="docutils literal">$father</tt> to <tt class="docutils literal">bruce</tt>:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 5, SUCCESS
9 family1.father_son($grand_father, $father, ())
</pre>
<p><em>Success</em> means go <em>down</em>, so Pyke goes to the next premise on line 9. This
succeeds with fact 6 (because <tt class="docutils literal">$father</tt> is bound to <tt class="docutils literal">bruce</tt>):</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 5
9 family1.father_son($grand_father, $father, ()) => fact 6, SUCCESS
</pre>
<p><em>Success</em> means go <em>down</em>, but Pyke is at the end of the list of premises,
so the <em>rule</em> succeeds and Pyke fires the rule to assert:</p>
<pre class="literal-block">
9 father_son(thomas, david, (grand))
</pre>
<p>Since this is a forward-chaining rule, Pyke wants to get <em>all</em> of the answers
from it that it can, so it continues as if it had a failure (i.e., as if it's
not happy with this answer).</p>
<div class="note">
<p class="first admonition-title">Note</p>
<p class="last">You'll see later that Pyke doesn't do this automatically with
<a class="reference external" href="backward_chaining.html">backward-chaining</a> rules.</p>
</div>
<p>So Pyke <em>fails</em> back <em>up</em> to the second premise and looks for another
<tt class="docutils literal">father_son</tt> after fact 6 with <tt class="docutils literal">bruce</tt> as the first argument. This
fails:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 5
9 family1.father_son($grand_father, $father, ()) => FAILS
</pre>
<p><em>Fail</em> means go <em>up</em>, so Pyke goes up to the first premise and looks for
another <tt class="docutils literal">father_son</tt> after fact 5, which succeeds for fact 6, binding
<tt class="docutils literal">$father</tt> to <tt class="docutils literal">thomas</tt>:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 6, SUCCESS
9 family1.father_son($grand_father, $father, ())
</pre>
<p><em>Success</em> means go <em>down</em>, so Pyke goes down to the second premise which
succeeds for fact 7:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 6
9 family1.father_son($grand_father, $father, ()) => fact 7, SUCCESS
</pre>
<p><em>Success</em> means go <em>down</em>, but Pyke is at the end of the list of premises,
so the <em>rule</em> succeeds and Pyke fires the rule to assert:</p>
<pre class="literal-block">
10 father_son(frederik, bruce, (grand))
</pre>
<p>Then Pyke <em>fails</em> back <em>up</em> to the second premise, and continues looking for
another match after fact 7. This fails:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 6
9 family1.father_son($grand_father, $father, ()) => FAILS
</pre>
<p><em>Fail</em> means go <em>up</em>, so Pyke goes back to the first premise and continues
looking for another match after fact 6. (Since fact 7 is just like the last
case, we'll skip matching fact 7 and go straight to the last fact, fact 8).
The match to fact 8 succeeds, binding <tt class="docutils literal">$father</tt> to <tt class="docutils literal">hiram</tt>:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 8, SUCCESS
9 family1.father_son($grand_father, $father, ())
</pre>
<p><em>Success</em> means go <em>down</em>, so Pyke goes to the second premise and looks for a
<tt class="docutils literal">father_son</tt> for <tt class="docutils literal">hiram</tt>. This fails:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => fact 8
9 family1.father_son($grand_father, $father, ()) => FAILS
</pre>
<p><em>Fail</em> means go <em>up</em>, so Pyke goes back up to the first premise and looks for
another match after fact 8. There are no more facts, so this fails:</p>
<pre class="literal-block">
8 family1.father_son($father, $grand_son, ()) => FAILS
9 family1.father_son($grand_father, $father, ())
</pre>
<p><em>Fail</em> means go <em>up</em>, but Pyke is at the top of the list of premises,
so the <em>rule</em> fails and Pyke is done processing it.</p>
<div class="important">
<p class="first admonition-title">Important</p>
<p>Note that the <em>last</em> statement in the <tt class="docutils literal">foreach</tt> clause may <em>succeed</em>
multiple times (which fires the <tt class="docutils literal">assert</tt> clause multiple times).</p>
<p class="last">But the <em>first</em> statement in the <tt class="docutils literal">foreach</tt> clause may only <em>fail</em> once.
When that happens, the whole rule fails and the show's over for this rule!</p>
</div>
<p>So running the <tt class="docutils literal">grand_father_son</tt> rule results in addition of these three
facts:</p>
<pre class="literal-block">
9 father_son(thomas, david, (grand))
10 father_son(frederik, bruce, (grand))
11 father_son(hiram, thomas, (grand)) (this is the one we skipped)
</pre>
</div>
</div>
<div class="section" id="step-3-great-grand-father-son">
<h2>Step 3: Great_grand_father_son</h2>
<p>Finally, we want to add great(...) grand son-father relationships. We have
a final rule for this:</p>
<pre class="literal-block">
12 great_grand_father_son
13 foreach
14 family1.father_son($father, $gg_son, ())
15 family1.father_son($gg_father, $father, ($prefix1, *$rest_prefixes))
16 assert
17 family1.father_son($gg_father, $gg_son,
(great, $prefix1, *$rest_prefixes))
</pre>
<div class="note">
<p class="first admonition-title">Note</p>
<p class="last">Note how the $prefixes for the statement on line 15 are specified as
<tt class="docutils literal">($prefix1, *$rest_prefixes)</tt>, rather than just <tt class="docutils literal">$prefix</tt>.
This is done so that it does <em>not</em> match <tt class="docutils literal">()</tt>. (But it will still match
<tt class="docutils literal">(grand)</tt> by binding <tt class="docutils literal">$rest_prefixes</tt> to <tt class="docutils literal">()</tt>).</p>
</div>
<p>This is the only rule that can be recursive. As this rule <a class="reference external" href="../../using_pyke/adding_facts.html">asserts</a> new <a class="reference external" href="../../knowledge_bases/fact_bases.html#facts">facts</a>,
those facts may be used by the same rule (by matching the statement on line
15) to produce even more great, great, ... <tt class="docutils literal">father_son</tt> relationships.</p>
<div class="section" id="recursive-rules">
<h3>Recursive Rules</h3>
<p>Running this rule normally will assert the following two facts:</p>
<pre class="literal-block">
12 father_son(frederik, david, (great, grand))
13 father_son(hiram, bruce, (great, grand))
</pre>
<p>But, since these facts may also be used by the same rule (on line 15), Pyke
checks each one by trying to run the rule again just for that new fact.</p>
<p>Trying this for the first new fact: <tt class="docutils literal">father_son(frederik, david,
(great, grand))</tt> fails to find anything because <tt class="docutils literal">david</tt> is not a father.</p>
<p>Trying this for the second new fact: <tt class="docutils literal">father_son(hiram, bruce, (great,
grand))</tt> results in one more new fact:</p>
<pre class="literal-block">
14 father_son(hiram, david, (great, great, grand))
</pre>
<p>Now this last new fact is tried again with this rule, which fails again
because <tt class="docutils literal">david</tt> is not a father.</p>
<p>So at this point Pyke is finished with this rule. The rule ended up firing
three times, asserting:</p>
<pre class="literal-block">
12 father_son(frederik, david, (great, grand))
13 father_son(hiram, bruce, (great, grand))
14 father_son(hiram, david, (great, great, grand))
</pre>
</div>
</div>
<div class="section" id="running-the-example">
<h2>Running the Example</h2>
<!-- This code is hidden. It will add '' to sys.path, change to the doc.examples
directory and store the directory path in __file__ for the code section
following:
>>> import sys
>>> if '' not in sys.path: sys.path.insert(0, '')
>>> import os
>>> os.chdir("../../../examples")
>>> __file__ = os.getcwd() -->
<p>These rules could be run as follows:</p>
<blockquote>
<pre class="doctest-block">
>>> from pyke import knowledge_engine
>>> engine = knowledge_engine.engine(__file__)
>>> engine.activate('fc_related') # This is where the rules are run!
>>> engine.get_kb('family1').dump_specific_facts()
father_son('bruce', 'david', ())
father_son('thomas', 'bruce', ())
father_son('frederik', 'thomas', ())
father_son('hiram', 'frederik', ())
father_son('thomas', 'david', ('grand',))
father_son('frederik', 'bruce', ('grand',))
father_son('hiram', 'thomas', ('grand',))
father_son('frederik', 'david', ('great', 'grand'))
father_son('hiram', 'bruce', ('great', 'grand'))
father_son('hiram', 'david', ('great', 'great', 'grand'))
</pre>
</blockquote>
<!-- ADD_LINKS MARKER -->
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<h3>More:</h3>
<div class="right-item"><a href="forward_chaining.html">Forward Chaining</a><p>Explanation of <em>forward-chaining rules</em> and how <em>forward-chaining</em>
works.</p>
</div>
<div class="right-item"><a href="backward_chaining.html">Backward Chaining</a><p>Explanation of <em>backward-chaining</em> rules, including how
<em>backward-chaining</em> and <em>backtracking</em> works.</p>
</div>
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Copyright © 2007-2009 Bruce Frederiksen
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Mon, Mar 08 2010.
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