Here's your two cents worth.
Try the mKR language (http://mkrmke.org); you'll like it. (01)
There is a recursion problem with a lot of the ontologies,
especially OpenCyc. (02)
There is a simple solution: when you walk the hierarchy,
keep a visit count -- never traverse the same node twice. (03)
Dick McCullough
http://mkrmke.org
----- 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 (04)
> 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
> here.
>
> 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
> http://www.scs.ryerson.ca/~bgajdero
>
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