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

[Adrian Walker <adriandwalker@xxxxxxxxx>]

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

    www.reengineeringllc.com/demo_agents/TransitiveOver1.agent

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
Reengineering

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

_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx

_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (01)