Adrian and Pat, (01)
I agree with Pat's comments, but I'd like to add a few more points. (02)
AW> The CL and IKL approach [is] deprecated: infeasible for this
> group [W3C Rule Interchange], as major differences appeared
> irreconcilable (e.g. non-mon vs. mon) (03)
That statement is misleading to the point of creating a hopelessly
unsolvable confusion. As Pat comments below, there is nothing
remotely resembling one, unified nonmonotonic theory. There is
an overwhelming number of different nonmonotonic versions. (04)
But there is one unifying approach that does bring order to *every*
practical and theoretical study, proposal, or implementation of
any and every version of non-monotonic logic: the resolution of
the non-mon features by interpreting them in terms of a classical
monotonic semantics. (05)
For example, belief or theory revision systems interpret every
nonmonotonic feature as a shorthand notation for showing how
a particular theory can be revised to form a monotonic theory
that applies to given circumstances. Other versions of non-mon
logic can be interpreted in terms of belief revision. (06)
PH> If however you read on in the same slides, you will find that the
> language finally adopted as the initial Rule standard, though much
> weaker than CL, in fact is a classical logic with a classical
> negation, just like negation in every other logic with a clear
> semantics. (07)
AW>> CL and IKL have chosen a theoretical semantics for negation... (08)
PH> Its not especially 'theoretical'. It is simply what negation means
> in ordinary language. (09)
I would qualify the second sentence by saying that words like 'no'
and 'not' in natural languages have many different interpretations,
one of which is classical FOL. However, there are as many different
interpretations of negation as there are versions of nonmonotonic
systems: denial, absence, prohibition, rejection, etc. (010)
Whenever any of those other interpretations of negation are defined
precisely, they embed the nonmonotonic system inside a system with
a classical, monotonic semantics. (011)
PH> Can you prove that every finite abelian group can be expressed as
> the direct sum of cyclic subgroups of prime-power order? (012)
Examples like that are not likely to carry much weight among people
who have no clue what those words mean. It is better to use examples
of the kind that people who use computer systems actually worry about. (013)
AW> SQL and most logic based programming languages use a different
> meaning for negation... (014)
PH> It can be formalized, for sure. It can in fact be formalized in
> many different, incompatible, ways. All of them however make it
> vividly clear that this is not a generally correct inference rule. (015)
I agree with Pat that the various formalizations of nonmonotonic
logics are incompatible with one another. Furthermore, they are
incompatible with the way that SQL, Prolog, and other systems are
actually used by (a) knowledgeable practitioners, (b) clueless
newbies, and (c) theoreticians whose primary goal is to publish
papers in the Journal of Tenure and Promotion. (016)
The solution to this problem is not to add yet another notation to
the cacophony of RDF(S) + OWL + RuleML + SPARQL + ... (017)
My recommendation is the following: (018)
1. Adopt *one* very clean, very general, very flexible abstract
syntax that has a precise classical semantics. CL is my
recommended version, but there are others. (019)
2. Show how each of those other notations map to the syntax of #1. (020)
3. For each nonmonotonic interpretation of the syntax, show how
what interpretation means in terms of the classical semantics. (021)
4. Provide suitable tools, methodologies, and documentation about
how to apply the theories that support #1, #2, and #3 to the
very serious problems of IT. (022)
For some further thoughts about logic, I suggest the following paper
(which Jim Hendler, the editor of the IEEE Journal in which it was
published, actually likes -- despite the fact that we often disagree
about many issues related to logic): (023)
http://www.jfsowa.com/pubs/fflogic.pdf
Fads and Fallacies about Logic (024)
I should probably write a follow-on paper "Fads and Fallacies about
Nonmonotonic Logics". (025)
John (026)
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