Truth here is twice ! Internal, Intrinsic, as pointed Matthew and Fabian,
Check can be made that "no inintended consequences" of the Inferences,
Implies Contradictory Statements.
External, Extrinsic,
Check can be made that "no inintended consequences" of the Inferences,
involving what behavior was expected against any "Real" other Entity.
In a Theory named "X", the Axioms are "True" because setted as So !
In, within, a classical, monoton, Logic, if no contradiction occurs, Deductions are
"True" too.
But, there are moderns Logics, as Lewis's for example, as soon as there are,
even finite, several "Logic Values", so "True", "False", "Zero", "Both", "Starting in Truth (0+),
Starting in False (0-) and so on,
Transitivity (The Friend of my Friend is a Friend of mine), will often cease to
work for example !
Matthew points that "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. "
A good Scientific Theory, even in Medecine, is one also "Good in Practice" !
Well, I hope that Peter Yim received well the "Attached Document" in my last "Mail" to
him, and will find a way to insert it in the discussion !
Happy to read You All Again !
Beaussart Eric.
> Message du 25/01/13 09:53
> De : "'Matthew West'"
> A : "'Ontology Summit 2013 discussion'"
> Copie à :
> Objet : [ontology-summit] Delivery Status Notification (Failure)
>
> 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" wrote:
>
> > 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.
> >
>
>
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