Dear Fabian,
Yes, but how do we know all the axioms are true? One check you can make is
that there are no unintended consequences in the inferences.
Regards
Matthew
On Jan 23, 2013 8:08 PM, "Fabian Neuhaus" <fneuhaus@xxxxxxxx> wrote: (01)
>
>
>
> On 28 Dec 2012, at 17:50, Fabian Neuhaus wrote:
>
> Second, I don't see the need to explicitly talk about all inferences from
> the axioms as long as we are concerned with ontology languages that are
> based on truth-preserving deductive inference systems like Common Logic
or
> OWL. If all the axioms in X are true it follows that all inferences from
> the axioms in X are true.
>
>
>
> The statement as given is theoretically true but seriously misleading in
> practice. Belief in it has led to serious harm - e.g. potentially
> life-threatening errors in medical ontologies. If human beings could
> recognise all the inferences that follow from a set of axioms, we wouldn't
> need reasoners. Axioms can be superficially plausible but have unexpected
> consequences, especially when combined with other superficially plausible
> axioms. Subtle errors in axioms that are difficult to spot can have
> disproportionate effects.
>
>
>
> We can only know that a set of axioms is accurate by examining the
> inferences that follow from them to see if any are false. (Of course we
> can't examine all inferences except in trivial cases, but systematic
> searches for unanticipated inferences is central to the QA of any ontology
> in which inference plays a significant role.)
>
> I have watched top logicians spend hours trying to understand the
> reasoning that led to an obviously false inference from what seemed an
> obviously correct set of axioms, even with the help of automatic theorem
> provers, justification finders, etc.
>
> Add to this the difficulties of axioms derived from work by domain
> experts, no matter how clever the tools, and there is more than ample
> opportunity for incorrect inferences from apparently correct axioms.
> (02)
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