Re: [ontolog-forum] Incompatibilities in 3D to 4D

[Christopher Menzel <cmenzel@xxxxxxxx>]

On Mar 10, 2009, at 12:02 PM, Ali Hashemi wrote:

eep! Aside from the typos, i think the cl snippet i posted was actually a second order statement. Regardless however, any CL axioms would be along those lines.

It was "syntactically" second-order, in the sense that it involved a predicate quantifier, but whether a framework is truly first- or second-order is determined by its semantics and CL's (without sequence markers) is entirely first-order.

-chris

...

Finally, as many have pointed it, we haven't really come across any ontology which has formalized these notions of perdurance and endurance. I would imagine if one wanted to actually enforce a 4D view in an ontology, they'd need a second order axiom, otherwise, they could use CL's ability to quantify over explicit relations via an axiom similar too

whenever you have a relation (i.e. Rel1)  you want to be restricted to the 4d view, you would state:

(forall (Rel1)  (4DRel Rel1))

then you would have to have something akin to:

(forall (R ...)

    (if   (4Drel R)

          (exists (t)

             (and (R ... t) (time t) (argument ...) )

)))

with appropriate axioms to define what an argument is.

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