Boolean questions are represented as a multi-select <xforms:select> with only a single option to select. Default values are directly written into the XForms instance data.
QUESTION "Boolean question"
DFT FALSE
ANSWER bool_variable
<xsd:schema targetNamespace="http://example.info/types">
<xsd:simpleType name="question1">
<xsd:restriction base="string" />
</xsd:simpleType>
</xsd:schema>
<xforms:instance>
<response xmlns="">
<question0 />
</response>
</xforms:instance>
<xforms:bind nodeset="question1" id="question1" type="type:question1" />
<itp:question>
<xforms:select ref="question0" appearance="full">
<xforms:label>Boolean question</xforms:label>
<xforms:item>
<xforms:value>TRUE</xforms:value>
</xforms:item>
</xforms:select>
</itp:question>