EDIT: Casio support, in an email, confirms that the CDP-135 does not support a half-damper.
Thank you for contacting Casio
There is no half-damper support on the CDP-135
My read of the MIDI implementation manual is that the CDP-135 does not support a half-pedal.
The relevant passages are on page 9, section 8.7
and page 18, section 18.1.