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Question
I want to know how to query the resource index against the date. What is the predicate I can use in the ITQL for date comparison ?

Answer
To do this, you'll need to query against a datatyping model. The full documentation for this is here: http://docs.mulgara.org/itqloperations/datatypingmodels.html#o265

Fedora does maintain a <#xsd> datatyping model, so in your example below, you will need to use something like:

select $object
from <#ri>                                                     
where  $object <fedora-model:hasModel>  <info:fedora/MY-CModel>
and       $object <fedora-view:lastModifiedDate> $modified
and       $ modified <mulgara:after> '2010-02-22T12:54:59.265Z'^^<xml-schema:dateTime> in <#xsd>

Note: Mulgara does not parse time zones for dateTime.