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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: KR-language <KR-language@xxxxxxxxxxxxxxx>
From: "Richard H. McCullough" <rhm@xxxxxxxxxxxxx>
Date: Tue, 17 Mar 2009 11:14:10 -0700
Message-id: <314F7C67F05E46309326184ABCFCB4FA@rhm8200>
----- Original Message ----- 
From: "Pat Hayes" <phayes@xxxxxxx>
Sent: Tuesday, March 17, 2009 9:47 AM
Subject: Re: [ontolog-forum] Incompatibilities in 3D to 4D
.....    (01)

> Sure we can.
> OBO and its cognates, including DOLCE, follow the continuant/occurrent  
> division quite rigorously, so can stand for the "3-D" case. Though  
> this 3/4-D terminology is misleading, as the 4-D of course includes 3- 
> D entities. The key dividing line is between those who insist that  
> continuants are distinct from occurrents, and the rest of us.
> I am working with Barry and others right now to rigorously axiomatize  
> a mereology of continuants, and hopefully this will result in a  
> rigorous mapping between (axiomatizations of) the two frameworks. But  
> the basic picture of how to map between them is pretty clear, in  
> outline. The endurantists refuse to write terms of the form (at C t)  
> when C is a continuant. Rather than write (P (at C t)), they want to  
> write (P C t). OK, the perdurantist can take (P C t) to be simply a  
> shorthand for (P (at C t)):
> (forall ((Continuant C)(time t) P) (iff (P C t)(P (at C t)) ))
> Note, this axiom (or translation rule if you prefer) is obvious to a  
> perdurantist but anathema to an endurantist. Looked at the other way,  
> the endurantist takes this to mean that the perdurantist is really  
> talking about the lifetime of C, not C itself:
> (forall ((Continuant C)(time t) )(= (at C t) (at (lifetime C) t) ))
> and again, this is a translation axiom for the endurantist, who can  
> treat the apparently meaningless term as a shorthand for the longer  
> term; and for the perdurantist, this is harmless because for them,  
> (lifetime C) = C in any case: the occurrent/continuant split that this  
> function bridges is meaningless to the perdurantist. So if both sides  
> are willing to not gag when they see something apparently meaningless,  
> treating it as ugly sugar for something meaningful, then both can get  
> along.
> The hard part is social, getting each side to not gag when they see  
> apparent nonsense in their ontology.
> Pat
> PS. Obviously this needs to be extended to handle relations between  
> continuants and temporal assertions about non-continuant entities, so  
> the details can get a bit messy, but the outline is clear.
>     (02)

The above is related to mKR as follows.
space, time, view are quantized.  Therefore, the basic proposition of
mKR is applicable at a particular "point" in space, time, view.    (03)

    at space=s, time=t, view=v { sentence; };    (04)

By choosing different units of measuring space, time, view
the same form can be applied to any "region" in space, time, view.    (05)

Thus for an action, at time could be considered the begin time,
the duration time, or the end time.  Since from/to are for initial/final
conditions, I generally favor    (06)

    at time = begin time {
        entity do action from time = begin time to time = end time done;
    };    (07)

This form is appropriate for actions and interactions such as "walk",
"live" (from birth to death), "marry" (from wedding to divorce).
However, there are some actions and interactions which favor
at time = end time, including "stop walk", "die", "divorce".    (08)

Finally, let me remind you that sentence can be one of
    statement, question, command, assignment, conditional, ...
or a list of propositions.    (09)

Dick McCullough
http://mkrmke.org    (010)

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