This page describes one way in which the model interpreter used earlier in the chaper to generate support trees can be extended to highlight inconsistencies in model behaviour. Our first step is to add a different definition for satisfaction of conditions from that given by the predicate satisfy in the earlier interpreter. For this we define the new predicate satisfy1 which succeeds if a condition can be both confirmed and denied (in which case the support tree records the support for and against the condition) or if the condition can be confirmed but not denied (in which case the support tree its support).
Whenever we are attempting to find some input for an operator (expression 3) we check to see if we know of another input which might conflict with it and, if so, attempt to confirm the conflicting input using our existing definition of satisfy. If the conflicting input is confirmed then the support tree contains the pair of inputs which are conflicting and the support for the conflicting one. Since inputs often appear in conjunctions of conditions we need to stipulate what constitutes a denial of the whole conjunction. For this, it is sufficient to deny any part of the conjunction which is allowed by expressions 4 and 5. These ``unpack'' conjunctions, searching for input expressions which we might deny, so for denial of any conjunction, in our sense, it is both necessary and sufficient to find within it one deniable input expression.
All that is left is to define which outputs can conflict. Since this
relationship is symmetrical (if output A conflicts with output B
then B also conflicts with A) we first define the symmetrical
property of 
:
We then say, for our example, which outputs could conflict. In our example, only the information on the loan risk of the applicant can be conflicting.
Using our new support tree generator (satisfy1) instead of the old one (satisfy) in our output generation mechanism we can produce support trees in which potential conflicts are identified. A graphical representation of one of these for loan disagreement for p1 is shown in Figure 2.8.
