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. (01)
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. (02)
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. (03)
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). (04)
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. (05)
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? (06)
Situation Calculus and Description Logic both have their roots in
First Order Logic, so perhaps we could get away with deductive means
here. (07)
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. (08)
.... 2 cents (09)
--
Bart Gajderowicz
MSc Candidate, '10
Dept. of Computer Science
Ryerson University
http://www.scs.ryerson.ca/~bgajdero (010)
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