Expression Nodes

Dependencies between expression nodes are listed in the following table.

The <expression> node is a root node that represents the expression. Use the <expression> tag to define any expression in Boolean language.

<expression>

<and>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_17inch" />

</eq>

</and>

</expression>

This example represents the Boolean expression for Color = Red AND WheelSize = 17 inch.

The <eq> node defines equivalence. Equivalence can be done between Variable and NamedConstant. <eq> has a strict content: it must include the node pair <variable> and <named-constant>.
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>

This example represents the Boolean expression for Color = Red.

The <variable> node defines a variable element. Use this element to define the first part of an equivalence. The first part of an equivalence should always be the variable. The “id” attribute is required; it defines the unique identifier for the instance
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
This example represents the Boolean expression for Color = Red where Color is the variable.

The <named-constant> node defines the namedConstant element. Use this element to define the second part of equivalence. The second part of equivalence should always be namedConstant. The “id” attribute is required; it defines the unique identifier for the instance.
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
This example represents the Boolean expression for Color = Red where Red is the named constant.

The <and> node that defines the Boolean operation “and”. It can contain an unlimited number of child tags.

<and>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
<eq>

<variable id="item_id_color” />
<named-constant id="item_id_green” />
</eq>
</and>

This example represents the Boolean expression for Color = Red AND Color = Green.

The <or> node defines the Boolean operation “or”. It can contain an unlimited number of child tags. <or>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_green” />
</eq>
</or>

This example represents the Boolean expression for Color = Red OR Color = Green.
The following is an example of an OR node using an inner AND node:

<or>
<eq>
<variable id="item_id_color" />
<named-constant id="item_id_red" />
</eq>
<and>
<eq>
<variable id="item_id_wheelsize" />
<named-constant id="item_id_17inch" />
</eq>
<eq>
<variable id="item_id_color" />
<named-constant id="item_id_green" />
</eq>
</and>
</or>

This example represents the Boolean expression for Color = Red OR (WheelSize = 17inch AND Color = Green).

The <not> node defines the Boolean operation “not”. It can contain an unlimited number of child tags.
<not>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
</not>

This example represents the Boolean expression for NOT(Color = Red).

<not>

<or>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_17inch" />

</eq>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_green" />

</eq>

</or>

</not>

This example represents the Boolean expression for NOT(WheelSize = 17 inch OR Color = Green). This is the same as NOT(WheelSize = 17 inch) AND NOT(Color = Green).

The following example has multiple child nodes contained within the <not> node:

<not>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_16inch" />

</eq>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

</not>

The above example is equivalent to the case when child nodes are wrapped by <and> node as below: <not>
<and>
<eq>
<variable id="item_id_wheelsize” />
<named-constant id="item_id_16inch” />
</eq>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
</and>
</not>

This example represents the Boolean expression for NOT(WheelSize = 16 inch AND Color = Red). This is the same as NOT(WheelSize = 16 inch) OR NOT(Color = Red).

The <implication> node defines a Boolean operation “implication” for example “if Color = Red then WheelSize = 17inch”. This node should always contain the <condition> and <consequence> child nodes. The order of the child nodes is important: the <condition>node must always precede the <consequence> node. These nodes should not be left empty.

<implication>

<condition>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

</condition>

<consequence>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_17inch" />

</eq>

</consequence>

</implication>

This example represents the Boolean expression for IF Color = Red THEN WheelSize = 17inch.

The following example shows multiple child nodes contained within the <condition> and <consequence> nodes:

<implication>

<condition>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

<eq>

<variable id="item_id_type" />

<named-constant id="item_id_mountain" />

</eq>

</condition>

<consequence>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_16inch" />

</eq>

<eq>

<variable id="item_id_framesize" />

<named-constant id="item_id_large" />

</eq>

</consequence>

</implication>

The above example is equivalent to the case when they are wrapped by <and> node as shown below:

<implication>

<condition>

<and>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

<eq>

<variable id="item_id_type" />

<named-constant id="item_id_mountain" />

</eq>

</and>

</condition>

<consequence>

<and>

<eq>

<variable id="item_id_wheelsize" />

<named-constant id="item_id_16inch" />

</eq>

<eq>

<variable id="item_id_framesize" />

<named-constant id="item_id_large" />

</eq>

</and>

</consequence>

</implication>

This example represents the Boolean expression for IF (Color = Red AND Type = Mountain) THEN WheelSize = 16inch AND FrameSize = Large.

The <exactly-one> node defines an operation. The operator describes a condition that means “one and only one of the listed equivalencies can be true”. <exactly-one> should contain a set of <eq> child nodes.

<exactly-one>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_red" />

</eq>

<eq>

<variable id="item_id_color" />

<named-constant id="item_id_green" />

</eq>

</exactly-one>

This example represents the Boolean expression for EXACTLY-ONE(Color = Red | Color = Green).

The <at-most-one> node defines an operation. The operator describes a condition that means “either none or just one of the listed equivalencies can be true”. <at-most-one> should contain a set of <eq> child nodes. <at-most-one>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_green” />
</eq>
</at-most-one>

This example represents the Boolean expression for AT-MOST-ONE(Color = Red | Color = Green).

The <at-least-one> node defines an operation. The operator describes a condition that means “at least one of the listed equivalencies should be true”. <at-least-one> should contain a set of <eq> child nodes:

<at-least-one>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_red” />
</eq>
<eq>
<variable id="item_id_color” />
<named-constant id="item_id_green” />
</eq>
</at-least-one>

This example represents the Boolean expression for AT-LEAST-ONE(Color = Red | Color = Green).