It seems that the <input> element's <change> event fires when that object is first rendered, however it's <initialValue> is not set until after this occurs. I found this can be overcame by pre-setting the checkbox token within the form or dashboard's <init> block. The following Simple XML then uses "eval" and "match" to catch the change conditions and sets the display tokens to either "true" or null (<unset>).
<dashboard>
<label>Checkbox with mutiple Values (3)</label>
<init>
<set token="C">c1,c2,c3</set>
</init>
<fieldset submitButton="false">
<input type="checkbox" token="C">
<label></label>
<choice value="c1">C1</choice>
<choice value="c2">C2</choice>
<choice value="c3">C3</choice>
<initialValue>c1,c2,c3</initialValue>
<change>
<condition>
<eval token="c1">if(match($C$,"c1"),"true",null</eval>
<eval token="c2">if(match($C$,"c2"),"true",null</eval>
<eval token="c3">if(match($C$,"c3"),"true",null</eval>
</condition>
</change>
</input>
<input type="text" token="t1" depends="$c1$">
<label>T1</label>
</input>
<input type="text" token="t2" depends="$c2$">
<label>T2</label>
</input>
<input type="text" token="t3" depends="$c3$">
<label>T3</label>
</input>
</fieldset>
<row>
<html>
<div>C: $C$</div>
<div>c1: $c1$</div>
<div>c2: $c2$</div>
<div>c3: $c3$</div>
</html>
</row>
</dashboard>
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