Dear Matthew, Doug, and Pat, (01)
At the bottom of this note is a copy of my note from March 15,
which includes the following passage: (02)
JFS> Translations to CLIF using the above ontology:
>
> at t1, Kermit egg.
>
> (exists (p t1) (and (namedEntity p "Kermit") (egg p) (coord 4 t1)))
>
> at t2, Kermit tadpole
>
> (exists (p t2) (and (namedEntity p "Kermit") (tadpole p) (coord 4
t2))).
>
> at t3, Kermit frog.
>
> (exists (p t3) (and (namedEntity p "Kermit") (frog p) (coord 4 t3)))
>
> I claim that these observations can be used in either a 3D or a 4D
> theory. (03)
MW> Yes, but they are not terribly useful. What I am missing is whether
> these observations are about the same egg/frogspawn/frog or different
> ones that just happen to be named Kermit. (04)
That is indeed a good question. (05)
MW> What I would expect to see is some relation that affirmed this. (06)
One approach would be to add another relation with suitable axioms: (07)
(uniqueName "Kermit") (08)
DF> 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. (09)
I would be happy to add a relation (alias x y) and an axiom: (010)
(forall (p x y) (if (and (namedEntity p x) (namedEntity p y))
(alias x y) )) (011)
But I agree that adding another variable e to refer to the named
entity explicitly would also solve the problem: (012)
DF> Since ternary relations are allowed, making namedEntity()
> ternary and making egg() binary should solve this problem.
> Also, t1 is a free variable and should be removed from the
> existential variable list:
> (exists (p e)
> (and (namedEntity p e "Kermit")
> (egg e p)
> (coord p 4 t1))) (013)
Yes. That would be a good solution. (014)
I had tried to keep the ontology simple by not having variables
whose values could not be stated in ordinary language. In a
database, one could have internal identifiers that are distinct
from the external names. But I had tried to keep the observational
language free from such theoretical terms. (015)
However, I agree that such internal identifiers are useful in
a linear logic. (In a graph logic, they could be avoided by
just linking all the statements to a common node, which would
represent the entity e.) (016)
MW> [In 4D] You are far more likely to want to say something like:
>
> Three states of Kermit are his egg state s1, from t1 to t2, his
> tadpole state, s2, from t2 to t3 and his frog state, s3, from t3
> to t4. (017)
DF> Agreed. There is a difference between finding a vocabulary that
> is "natural" to use in both 3D and 4D and a vocabulary that can be
> given semantics in both 3D and 4D. (018)
MW> I suspect that there are limits to what it is useful to say in
> a neutral underspecified way, because you lose the character of the
> foundation. I would be quite happy to see just a subtype/supertype
> hierarchy that was underspecified as to whether its members were
> sets or types. That would already be a big bonus (019)
Yes. The general, underspecified theory might not be "natural" in
either a 3D or a 4D way of talking, but it could be extended to a
consistent and "natural" 3D theory or a consistent and "natural"
4D theory. (020)
John (021)
 Original Message 
Subject: Re: [ontologforum] Re Foundation ontology, CYC, and Mapping
Date: Mon, 15 Mar 2010 19:51:06 0400 (EDT)
From: sowa@xxxxxxxxxxx
To: [ontologforum] <ontologforum@xxxxxxxxxxxxxxxx> (022)
Pat, (023)
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. (024)
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. (025)
I 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. (026)
In this ontology there are only three types of entities: points with
coordinates p=(x,y,z,t), integers, and character strings. (027)
Monadic relations (or types): (028)
frog(p), tadpole(p), egg(p)  a frog/tadpole/egg is observed at p. (029)
Dyadic naming relation: (030)
namedEntity(p,s)  an entity with name s is observed at p. (031)
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. (032)
Coordinate selector: (033)
coord(p,n,x)  point p has x as coordinate n (for n from 1 to 4) (034)
Translations to CLIF using the above ontology: (035)
>> at t1, Kermit egg. (036)
(exists (p t1) (and (namedEntity p "Kermit") (egg p) (coord 4 t1))) (037)
>> at t2, Kermit tadpole (038)
(exists (p t2) (and (namedEntity p "Kermit") (tadpole p) (coord 4 t2))). (039)
>> at t3, Kermit frog. (040)
(exists (p t3) (and (namedEntity p "Kermit") (frog p) (coord 4 t3))) (041)
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. (042)
John (043)
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