This ontology does not state that only one thing can exist at 4D point p.
Thus the translations from English into the ontology are incomplete. (01)
See below. (02)
John Sowa wrote:
> I claim that I can state the following sentences in FOL in a
> way that is independent of any claims about the nature of individuals
> such as Kermit or about persistence, continuants, occurrents, or any
> similar kinds of theoretical notions.
> I will only assume a geometry
> that is independent of any notion of individuals that may be entangled in
> that geometry. I will also assume that it is possible for some observers
> to make observations at points in that 4D or 3+1 D geometry.
> won't make any assumptions about how the following relations are actually
> verified. I'll just assume that some observers agree about whether those
> relations are true or false at the designated points.
> In this
> ontology there are only three types of entities: points with coordinates
> p=(x,y,z,t), integers, and character strings.
> Monadic relations (or
> frog(p), tadpole(p), egg(p) -- a frog/tadpole/egg is
> observed at p..
> Dyadic naming relation:
> namedEntity(p,s) --
> an entity with name s is observed at p.
> Note to observers: The
> above relations should be considered true iff p is one of possibly many
> points for which the relation might be true.
> coord(p,n,x) -- point p has x as coordinate n (for n
> from 1 to 4)
> Translations to CLIF using the above
>>> at t1, Kermit egg.
> (exists (p t1)
> (and (namedEntity p "Kermit") (egg p) (coord 4 t1))) (03)
Presumably you mean "(coord p 4 t1)" (04)
This states that at some point p and some time t1, there is an entity named
Kermit and that there is an egg at that point. It does not state
that the egg is named Kermit. The named entity could be the nucleus of
the egg, the egg mass of which the entity is a part, or even the flood
which is carrying the egg (if an event can be a named entity). (05)
Since ternary relations are allowed, making namedEntity() ternary and
making egg() binary should solve this problem. Also, t1 is a free
varible and should be removed from the existential variable list:
(exists (p e)
(and (namedEntity p e "Kermit")
(egg e p)
(coord p 4 t1))) (06)
>>> at t2, Kermit tadpole
> (exists (p t2)
> (and (namedEntity p "Kermit") (tadpole p) (coord 4 t2))). (07)
Similarly, this does not require that tadpole to be the named entity.
(exists (p t)
(and (namedEntity p t "Kermit")
(tadpole t p)
(coord p 4 t2))) (08)
>>> at t3, Kermit frog.
> (exists (p t3)
> (and (namedEntity p "Kermit") (frog p) (coord 4 t3))) (09)
(exists (p f)
(and (namedEntity p f "Kermit")
(frog f p)
(coord p 4 t3))) (010)
> I claim
> that these observations can be used in either a 3D or a 4D theory.
> Furthermore, I claim that any predictions made by either of those theories
> that can be expressed in terms of the above ontology will not conflict
> with any predictions made by the other theory that are similarly
> restricted. (011)
I think these claims apply to the modifications which i made, as well. (012)
-- doug (013)
> John (014)
doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (015)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
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