I see Andrian beat me to it, but here's my response. (01)
CM > 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 (02)
Sorry Chris, I should have referenced the following threads better: (03)
AW >> The problem with the "syllogisms will never work" argument
>> is that, if you allow them to be recursive, they have Turing
>> machine power. That means that they can compute anything that
>> can be computed. (04)
JFS > Every major programming language (e.g., FORTRAN, COBOL, LISP,
> ALGOL, PL/I, C, C++, C#, Ada, Java, Python, Ruby, PHP, etc.)
> has the following two properties:
>
> 1. They have the power of a Turing machine.
>
> 2. It's undecidable whether an arbitrary program written in
> any of those languages will terminate. (05)
My response was to the argument that if we allow syllogisms to be
recursive, they will become useless. JFS's point, I believe, was that
this since programming language constructs are based on turing
machines, which are recursive, there's no issue here. My point was,
apologies for not stating it clearly, this would rid of completeness,
for example in FOL. There are ways to get around this, by not
allowing infinite lists in the conclusion, hence defining a stop
condition. This led me to the rest of my post regarding defining a
stop condition which may change, specifically the idea of contexts
changing a definition of an object, where the object's state may or
may not be a stop condition, depending on the context. (06)
CM> 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..... A "stop condition" (if
> I'm understanding you) is a programming construct that has nothing to
> do with functions per se. (07)
I meant it as a purely programming construct. Some of the original
arguments about syllogisms, I felt, were not always applicable to
implementation. I mentioned that ontologies are practical things for
us to use. The same goes for programming languages. So if we can get
around the unsatifiability of turing machines in programming
languages, why not ontologies. (08)
I recognize that the idea of objects changing in contexts is
problematic, mainly because it does not follow the classic definition
of identity, logical or philosophical, mainly the transitive,
reflexive, and symmetric properties. But I'm wondering if we can apply
uncertainty or transitions. Perhaps use temporal logic and define an
object as changing from time (t) to time (t+1). Or perhaps, as with my
"general ontology" and "ontology as a context" description earlier,
encompassing all of an objects possible states within some ontology,
which allows for internal transitions, but still defining the same
object. (09)
CM>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. (010)
You're correct. I wasn't referring to the a program that calculates
any recursive function, satisfiable or not. Here, a "proper recursive
function" is one that does terminates, and the calling program will
terminate, or not terminate for an "improper function" accordingly.
So the rest of my post was a description of how a stop condition can
be defined to make it terminate, in terms of an ontology prover, for
example. (011)
Hope that clarifies my points, and thank you for your analysis. Made
me go back and think about it some more.
--
Bart Gajderowicz
MSc Candidate, '10
Dept. of Computer Science
Ryerson University
http://www.scs.ryerson.ca/~bgajdero (012)
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