A Simple Tricky Example

Suppose we have:

• two sets of facts, `{fact1, fact2}` and `{fact3, fact4}`, among others
• two tests `s` and `t`, with the following rules, plus possibly others which don't involve these facts or test results:
```	s-result1 IF f`act`1
s-result1 IF f`act`3
...
t-result1 IF f`act`1
t-result1 IF f`act`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

• If `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.
• Making either one false means `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.

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