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Re: [ontolog-forum] web-syllogism-and-worldview

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Adrian Walker <adriandwalker@xxxxxxxxx>
Date: Fri, 17 Apr 2009 14:25:12 -0400
Message-id: <1e89d6a40904171125g799b490bvb66aa3740e70887f@xxxxxxxxxxxxxx>
Hi Chris --

In reply to Bart, you wrote...

Could you say what you mean by a recursive syllogism and perhaps give an example?

Actually, I'm the guilty one (:-) who introduced this expanded notion of a syllogism -- that is, allowing it to be recursive.

Here is such a syllogism:

some-organization has a department called some-dept
that-dept has a department called some-sub-dept
that-organization has a department called that-sub-dept

It's executable as a part of the example


At one time, OWL was unable to do the "transitive over" computation defined at the above link.  But perhaps OWL has been extended to cover this?

                                   Cheers,   -- Adrian
Internet Business Logic
A Wiki and SOA Endpoint for Executable Open Vocabulary English over SQL and RDF
Online at www.reengineeringllc.com    Shared use is free

Adrian Walker

On Fri, Apr 17, 2009 at 1:50 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
On Apr 16, 2009, at 6:32 PM, Bart Gajderowicz wrote:
> Here's the way I see the argument whether syllogisms, recursive or
> not, are valid, and why we can continue using programming languages
> based on the principles of turing machines.
> As with any proper recursive function, we need a stop condition. We
> of course can't use a turing machine to figure this out, as it will
> not stop if the program does not terminate.  That's a theoretical
> issue.

I am not understanding some of your terminology here.  As standardly
(and pretty much universally) defined in logic, syllogisms are
arguments with two premises and a conclusion satisfying a certain
general form in which the notion of recursion plays no role whatever
(understandably, since the notion of a syllogism is largely unchanged
since it was first introduced by Aristotle).  Could you say what you
mean by a recursive syllogism and perhaps give an example?

Second, what do you mean by a "proper recursive function"?  A
recursive function is simply a mathematical function from (n-tuples
of) natural numbers to natural numbers.  (Through the magic of
encoding, of course, we can extend the notion to functions on, e.g.,
real numbers, strings, database records, etc.)  A "stop condition" (if
I'm understanding you) is a programming construct that has nothing to
do with functions per se.  Of course, it is possible to *characterize*
the class of recursive functions in terms of programming languages --
a recursive function is any function (from N^m into N) calculated by a
program in a language meeting certain conditions.  But even then I am
confused by your comment that "any proper recursive function" --
understood to mean any proper *program* that calculates a recursive
function -- needs a "stop condition".  For this appears to mean that,
for any recursive function, a program that calculates that function
has to terminate when executed.  And that, of course, is false.

Perhaps you could clarify.

Chris Menzel

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