Rule-based completeness

Hi,

I hope this group is the correct one to ask about this. I'm asking
about how to prove that a rule-based system is complete, i.e. that for
any input, there is always at least one rule that is fired. I've been
browsing some academic articles and it seems that the only general
solution is to generate an exhaustive number of cases. I don't know if
that is true, or if that is a consequence of Godel theorem or not. Or,
if there exist an NP algorithm to test completeness or not. Maybe
somebody can clarify these concepts for me. Moreover, I'm more
interested in a specific and limited case of a rule-based system:

In this system, there are n variables, say, a1, a2, ..., an.
Each variable is a real number and has a range of real values, for
example, a1 value is in [0..k1], a2 is in [0.., k2] and so on.
All the rules have ranges of their conditional part. For example:
rule 1: if (a1 > 30.88) then do-this
rule 2: if (a4 in [20..30] and a7 in [40..90] and a11 < 15.27) do-that
etc

does anybody has an idea how can I check completeness? Any help or
pointing to literature is welcome.

Thanks,

H.


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