Suppose we have:
{fact1, fact2}
and
{fact3, fact4}
, among others
s
and t
, with the
following rules, plus possibly others which don't involve these
facts or test results:
s-result1 IF fact
1 s-result1 IF fact
3 ... t-result1 IF fact
1 t-result1 IF fact
4 ...
Now assume that the student gets s-result1
and
t-result1
, and the question is "Is fact2
consistent with those results?"
Since fact2
doesn't predict any results, it can't be
ruled out directly by any result that does or doesn't occur. And yet
fact2
is, in fact, provably inconsistent with the above
results. Why? Because
s-result1
and t-result1
are both
true, then fact1 OR fact3
and fact1 OR
fact4
are both true.
fact3
and fact4
can't both be true,
therefore one has to be false.
fact1
has to be
true.
fact1
and fact2
can't both be true,
so fact2
has to be false.
Hence, even if the rules were constrained to single causes, which they weren't, you would still need something equivalent to a propositional theorem prover.