field == true => { <field> : true }
field == false => { <field> : false }
field != true => { <field> : { $ne : true } }
field != false => { <field> : { $ne : false } }

predicate == true => { <predicate> }
predicate == false => { $not : { <predicate> } }
predicate != true => { $not : { <predicate> } }
predicate != false => { <predicate> }