RHM: There is a simple solution: when you walk the hierarchy, keep a
visit count -- never traverse the same node twice. (01)
Thanks Richard. I don't think visit counts would be sufficient
though. I can have cyclic relationships, but not within the same
context. I could keep track of how many visits I have on a node,
within a particular context, but that's a false representation of
what's happening. What I would need is a distinction between
attributes (variable structures) and properties (atomic), and a way to
model the transition between contexts. This in turn would be an
attributes transition into a property, which would then cause a stop
MSc Candidate, '10
Dept. of Computer Science
2009/4/16 Richard H. McCullough <rhm@xxxxxxxxxxxxx>:
> Here's your two cents worth.
> Try the mKR language (http://mkrmke.org); you'll like it.
> There is a recursion problem with a lot of the ontologies,
> especially OpenCyc.
> There is a simple solution: when you walk the hierarchy,
> keep a visit count -- never traverse the same node twice.
> Dick McCullough
> ----- Original Message -----
> From: "Bart Gajderowicz" <bgajdero@xxxxxxxxxx>
> To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
> Sent: Thursday, April 16, 2009 4:32 PM
> Subject: Re: [ontolog-forum] web-syllogism-and-worldview
>> 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.
>> Ontologies, however are practical things for us to use. Nothing says
>> that we can't have an ontology which models some phenomenon defined by
>> our worldview, in a particular context. By context I mean situational
>> circumstances, which change the way an object can be viewed. I'm not
>> an expert on situation calculus, but I believe one could apply its
>> axioms to formally define this idea of a context.
>> If an ontology was the context, it would be represented by a set of
>> functions. The domain then would be the traditional domain of a
>> function, and encompass the entire object, all its attributes and
>> properties, and the functions would represent any situation (context)
>> that that object may find itself in. A general ontology would then be
>> a theory modeling all the stricter ontologies which are functions that
>> relate a domain to all the possible ranges (contexts).
>> If our syllogisms are recursive, and our domain has cyclic
>> definitions, a context could determine what a stop condition would be.
>> Specifically, depending on where you are in the hierarchy of
>> functions that define an object in a particular context, the set of
>> attributes and properties will change. For example, let's say that a
>> property is atomic. Attributes can be atomic but they can also be
>> structures themselves. Furthermore, depending on the context, an
>> attribute can become a property, which cannot be broken down any
>> further. This would be our stop condition. The moment you have a
>> cyclic definition where all properties are the same, you stop.
>> Attributes wouldn't qualify as a stop condition because they can be
>> structures which differ, and the only way to find that out is to
>> traverse the attribute's structure further down. This is how
>> fixpoints work in Description Logic.
>> My question would be, can contexts be determined automatically through
>> deductive means, or do we have to resort to inductive means, and delve
>> into data mining?
>> Situation Calculus and Description Logic both have their roots in
>> First Order Logic, so perhaps we could get away with deductive means
>> Temporal identifiers could be a representation of a context. The same
>> object my have different roles throughout its life span, and interact
>> differently with other objects. Processes have this property.
>> Transitions from one state to another can tell us how to move between
>> these contexts.
>> .... 2 cents
>> Bart Gajderowicz
>> MSc Candidate, '10
>> Dept. of Computer Science
>> Ryerson University
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