epf_prac_151/practice.tech.abrd.base/guidances/guidelines/boolean_logic.xmi - epf/org.eclipse.epf.libraries - Git at Google

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   <mainDescription>&lt;p>
     Criteria in rule is true or false. So when combining criteria together to build the condition part of a rule we need to
     clearly understand the Boolean logic, and its operations.
 &lt;/p>
 &lt;h5>
     AND / Conjunction
 &lt;/h5>
 &lt;p>
     We will use the following notation the dot as operator for AND so A.B is equivalent to A&amp;nbsp;AND B. The conjunction of
     two propositions is true when both propositions are true. The truth table is
 &lt;/p>&lt;br />
 &lt;br />
 &lt;table title=&quot;&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; width=&quot;85%&quot; border=&quot;1&quot;>
     &lt;tbody>
         &lt;tr>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>AND&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;/strong>
                 &lt;/p>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>B&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>True&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>False&lt;/strong>
                 &lt;/p>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>True&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;em>True&lt;/em>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;em>False&lt;/em>
                 &lt;/p>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>False&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;em>False&lt;/em>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;em>False&lt;/em>
                 &lt;/p>
             &lt;/td>
         &lt;/tr>
     &lt;/tbody>
 &lt;/table>&amp;nbsp;&lt;br />
 &lt;br />
 &lt;h5>
     OR&amp;nbsp; / Disjunction
 &lt;/h5>
 &lt;p>
     We use the + operator for A OR B like A + B. Disjunction of two propositions is false when both propositions are false.
 &lt;/p>
 &lt;p>
     &lt;br />
 &lt;/p>
 &lt;table title=&quot;&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; width=&quot;85%&quot; border=&quot;1&quot;>
     &lt;tbody>
         &lt;tr>
             &lt;td>
                 &lt;p>
                     &lt;strong>OR&amp;nbsp;&amp;nbsp; A&lt;/strong>
                 &lt;/p>
                 &lt;p>
                     &lt;strong>B&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>True&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>False&lt;/strong>
                 &lt;/p>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>True&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;p dir=&quot;ltr&quot; style=&quot;MARGIN-RIGHT: 0px&quot;>
                     &lt;strong>False&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>False&lt;/em>
             &lt;/td>
         &lt;/tr>
     &lt;/tbody>
 &lt;/table>&lt;br />
 &lt;br />
 &lt;h5>
     NOT / Negation
 &lt;/h5>
 &lt;table title=&quot;&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; width=&quot;85%&quot; border=&quot;1&quot;>
     &lt;tbody>
         &lt;tr>
             &lt;td>
                 &lt;strong>A&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;strong>NOT A&lt;/strong>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>True&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>False&lt;/em>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>False&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
         &lt;/tr>
     &lt;/tbody>
 &lt;/table>&lt;br />
 &lt;br />
 &lt;h5>
     Implication
 &lt;/h5>
 &lt;p>
     A-&amp;gt; B, implication is a binary operation which is false when A is true and&amp;nbsp;B is false. A -&amp;gt; B can be
     expressed as NOT A OR B.
 &lt;/p>
 &lt;p>
     &lt;br />
 &lt;/p>
 &lt;table title=&quot;&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; width=&quot;85%&quot; border=&quot;1&quot;>
     &lt;tbody>
         &lt;tr>
             &lt;td>
                 &lt;p>
                     &lt;strong>A -&amp;gt;
                     B&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
                     A&lt;/strong>
                 &lt;/p>
                 &lt;p>
                     &lt;strong>B&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;strong>True&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;strong>False&lt;/strong>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>True&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>False&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>False&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
         &lt;/tr>
     &lt;/tbody>
 &lt;/table>&lt;br />
 &lt;br />
 &lt;h5>
     XOR or exclusive OR
 &lt;/h5>
 &lt;p>
     Exclusive-or of two propositions is true just when exactly one of the propositions is true&lt;br />
     &lt;br />
 &lt;/p>
 &lt;table title=&quot;&quot; cellspacing=&quot;0&quot; cellpadding=&quot;2&quot; width=&quot;85%&quot; border=&quot;1&quot;>
     &lt;tbody>
         &lt;tr>
             &lt;td>
                 &lt;p>
                     &lt;strong>XOR&amp;nbsp;&amp;nbsp;&amp;nbsp; A&lt;/strong>
                 &lt;/p>
                 &lt;p>
                     &lt;strong>B&lt;/strong>
                 &lt;/p>
             &lt;/td>
             &lt;td>
                 &lt;strong>True&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;strong>False&lt;/strong>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>True&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>False&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
         &lt;/tr>
         &lt;tr>
             &lt;td>
                 &lt;strong>False&lt;/strong>
             &lt;/td>
             &lt;td>
                 &lt;em>True&lt;/em>
             &lt;/td>
             &lt;td>
                 &lt;em>False&lt;/em>
             &lt;/td>
         &lt;/tr>
     &lt;/tbody>
 &lt;/table>
 &lt;h5>
     De Morgan's Law
 &lt;/h5>
 &lt;p>
     De Morgan's law are rules in formal logic relating pairs of dual logical operators in a systematic manner expressed in
     terms of negation:
 &lt;/p>
 &lt;p>
     &amp;nbsp; NOT (A AND B) = NOT A OR NOT B
 &lt;/p>
 &lt;p>
     &amp;nbsp;&amp;nbsp;NOT (A OR B) = NOT A AND NOT B&lt;br />
     &lt;br />
     It is important to leverage the De Morgan's law to improve rule writing during&amp;nbsp;the rule transformation.&lt;br />
     &lt;br />
     &amp;nbsp;
 &lt;/p>
 &lt;p>
     &lt;br />
     &amp;nbsp;
 &lt;/p></mainDescription>
 </org.eclipse.epf.uma:ContentDescription>
	<?xml version="1.0" encoding="UTF-8"?>
	<org.eclipse.epf.uma:ContentDescription xmi:version="2.0" xmlns:xmi="http://www.omg.org/XMI" xmlns:org.eclipse.epf.uma="http://www.eclipse.org/epf/uma/1.0.6/uma.ecore" xmlns:epf="http://www.eclipse.org/epf" epf:version="1.5.1" xmlns:rmc="http://www.ibm.com/rmc" rmc:version="7.5.1" xmi:id="-fZn4nTBQjy1YPY8BQSTvJg" name="new_guideline,_x_5XgH9iEd26h9j0X6pKmw" guid="-fZn4nTBQjy1YPY8BQSTvJg" changeDate="2008-09-10T11:05:45.000-0700" version="7.5.1">
	<mainDescription><p>
	Criteria in rule is true or false. So when combining criteria together to build the condition part of a rule we need to
	clearly understand the Boolean logic, and its operations.
	</p>
	<h5>
	AND / Conjunction
	</h5>
	<p>
	We will use the following notation the dot as operator for AND so A.B is equivalent to A&nbsp;AND B. The conjunction of
	two propositions is true when both propositions are true. The truth table is
	</p><br />
	<br />
	<table title="" cellspacing="0" cellpadding="2" width="85%" border="1">
	<tbody>
	<tr>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>AND&nbsp;&nbsp;&nbsp; A</strong>
	</p>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>B</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>True</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>False</strong>
	</p>
	</td>
	</tr>
	<tr>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>True</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<em>True</em>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<em>False</em>
	</p>
	</td>
	</tr>
	<tr>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>False</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<em>False</em>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<em>False</em>
	</p>
	</td>
	</tr>
	</tbody>
	</table>&nbsp;<br />
	<br />
	<h5>
	OR&nbsp; / Disjunction
	</h5>
	<p>
	We use the + operator for A OR B like A + B. Disjunction of two propositions is false when both propositions are false.
	</p>
	<p>
	<br />
	</p>
	<table title="" cellspacing="0" cellpadding="2" width="85%" border="1">
	<tbody>
	<tr>
	<td>
	<p>
	<strong>OR&nbsp;&nbsp; A</strong>
	</p>
	<p>
	<strong>B</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>True</strong>
	</p>
	</td>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>False</strong>
	</p>
	</td>
	</tr>
	<tr>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>True</strong>
	</p>
	</td>
	<td>
	<em>True</em>
	</td>
	<td>
	<em>True</em>
	</td>
	</tr>
	<tr>
	<td>
	<p dir="ltr" style="MARGIN-RIGHT: 0px">
	<strong>False</strong>
	</p>
	</td>
	<td>
	<em>True</em>
	</td>
	<td>
	<em>False</em>
	</td>
	</tr>
	</tbody>
	</table><br />
	<br />
	<h5>
	NOT / Negation
	</h5>
	<table title="" cellspacing="0" cellpadding="2" width="85%" border="1">
	<tbody>
	<tr>
	<td>
	<strong>A</strong>
	</td>
	<td>
	<strong>NOT A</strong>
	</td>
	</tr>
	<tr>
	<td>
	<strong>True</strong>
	</td>
	<td>
	<em>False</em>
	</td>
	</tr>
	<tr>
	<td>
	<strong>False</strong>
	</td>
	<td>
	<em>True</em>
	</td>
	</tr>
	</tbody>
	</table><br />
	<br />
	<h5>
	Implication
	</h5>
	<p>
	A-&gt; B, implication is a binary operation which is false when A is true and&nbsp;B is false. A -&gt; B can be
	expressed as NOT A OR B.
	</p>
	<p>
	<br />
	</p>
	<table title="" cellspacing="0" cellpadding="2" width="85%" border="1">
	<tbody>
	<tr>
	<td>
	<p>
	<strong>A -&gt;
	B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
	A</strong>
	</p>
	<p>
	<strong>B</strong>
	</p>
	</td>
	<td>
	<strong>True</strong>
	</td>
	<td>
	<strong>False</strong>
	</td>
	</tr>
	<tr>
	<td>
	<strong>True</strong>
	</td>
	<td>
	<em>True</em>
	</td>
	<td>
	<em>True</em>
	</td>
	</tr>
	<tr>
	<td>
	<strong>False</strong>
	</td>
	<td>
	<em>False</em>
	</td>
	<td>
	<em>True</em>
	</td>
	</tr>
	</tbody>
	</table><br />
	<br />
	<h5>
	XOR or exclusive OR
	</h5>
	<p>
	Exclusive-or of two propositions is true just when exactly one of the propositions is true<br />
	<br />
	</p>
	<table title="" cellspacing="0" cellpadding="2" width="85%" border="1">
	<tbody>
	<tr>
	<td>
	<p>
	<strong>XOR&nbsp;&nbsp;&nbsp; A</strong>
	</p>
	<p>
	<strong>B</strong>
	</p>
	</td>
	<td>
	<strong>True</strong>
	</td>
	<td>
	<strong>False</strong>
	</td>
	</tr>
	<tr>
	<td>
	<strong>True</strong>
	</td>
	<td>
	<em>False</em>
	</td>
	<td>
	<em>True</em>
	</td>
	</tr>
	<tr>
	<td>
	<strong>False</strong>
	</td>
	<td>
	<em>True</em>
	</td>
	<td>
	<em>False</em>
	</td>
	</tr>
	</tbody>
	</table>
	<h5>
	De Morgan's Law
	</h5>
	<p>
	De Morgan's law are rules in formal logic relating pairs of dual logical operators in a systematic manner expressed in
	terms of negation:
	</p>
	<p>
	&nbsp; NOT (A AND B) = NOT A OR NOT B
	</p>
	<p>
	&nbsp;&nbsp;NOT (A OR B) = NOT A AND NOT B<br />
	<br />
	It is important to leverage the De Morgan's law to improve rule writing during&nbsp;the rule transformation.<br />
	<br />
	&nbsp;
	</p>
	<p>
	<br />
	&nbsp;
	</p></mainDescription>
	</org.eclipse.epf.uma:ContentDescription>