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Re: [ontolog-forum] Types of Formal (logical) Definitions inontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Barkmeyer, Edward J" <edward.barkmeyer@xxxxxxxx>
Date: Wed, 9 Jul 2014 16:33:40 +0000
Message-id: <40413fafe3484d9cb645db9729b17cfe@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
John wrote:
> A major problem with OWL is the deliberate limitation to models that can be
> represented as trees.  That restriction is key to their proof of decidability.
> But cycles are required in every branch of science and engineering.    (01)

Not quite 'trees' -- classification lattices, with 'property links' that 
produce more or less general semantic networks, including cycles.  The problem 
is that the expressiveness (intentionally) limits path navigation, and thus 
limits the nature and scope of axiomatic constraints on paths through the 
network.    (02)

It is always possible to see a semantic network as a viewpoint lattice.  Pick 
one class to be a focal point -- the root -- and the part of the network that 
is connected at all is a lattice emanating from that point, as long as you can 
ignore any 'direction' on the arcs in the base network.  (This is why 
relational algebras are powerful.)  The problem with languages like OWL is that 
the stated network includes directed arcs, and thus the viewpoint lattice has 
arcs that cannot be traversed 'downward' from the end of a navigable path from 
the root.      (03)

-Ed    (04)

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