Matthew West wrote: (01)
> If you are objecting to a temporal part of a state, that would depend upon
> what meaning of "state" you are using.
>
> A state (State1) could be a set of properties, in which case a state is
> timeless, can not have a temporal part,
> and may be possessed by different entities at the same or different times. (02)
[EJB] I think of the set of properties as a classifier/predicate State1 and
everything Matthew says is then true of State1, but I agree that people do use
the term 'state' in this sense. (03)
>
> A state (State2) could be a situation of some individual being in (State1). (04)
[EJB] That is, a slice of space-time in which State1(X) holds for a given
individual X. (05)
> This could be an instantaneous state (State2a), an extended situation
> during which the individual is in that state (State2b), or the maximal
> temporal situation during which the individual is in that State1 (State2c).
>
> A State2a can not have a temporal part. A State2b can have a State2b
> as a temporal part for which they both share a State1. A State2c can
> not have a State2c as a temporal part if they both share the same State1.
>
> A State2c can have a State2c as a temporal part if the second State2c
> has a more detailed State1 (e.g., the first State1 is that the oil
> temperature is
> between 140C and 160C and the second State1 is that the oil temperature
> is between 150C and 155C). In this case the second State2c is a temporal
> part of the first State2c. (06)
[EJB] Ah! This is the problem. (07)
I understand 'S is a temporal part of X' to mean: there is some
characterization C such that C(X) holds over a time interval T, and S is
understood to be the triple holds(C, X,T). And S1 is a different temporal part
of X iff S1 = holds(C1, X, T1) for some C1 and T1, where Not (C1 = C) or Not
(T1 = T). There are clearly other possible relationships of interest, to wit
C1 implies C (class C1 is a subclass of C), T1 is a subinterval of T, and S1
is a part of S2, where X1 is a part of X2, and holds(C2, X2, T1) implies
holds(C1, X1, T1), i.e. a state of the whole (X2) implies a state of a part
(X1). [this is what I meant about the need for axioms that describe
isTemporalPartOf.] (08)
>From the example below, Matthew apparently uses 'S is a temporal part of X'
>to mean: S is a state/situation that involves X in some role, which is just a
>generalized view of "some C(X) holds". (09)
But what Matthew says here is that S2c is a temporal part of S (not X!) if S2c
= holds(C1, X, T1) and C1 implies C and T1 is-within T! I would expect that
temporalPartOf(S2c, S) would mean there is a C1 and a T1 such that holds(C1,
*S*, T1) ! In the generalized view, S2C (X having the narrower temperature
range) plays a role in S (X having the broader temperature range). I don't
understand the ontological commitment that permits S2c to be viewed as playing
a role in S. So, I don't know what temporalPartOf means! (010)
> ...
> > [MW] Consider the temporal part of pump with serial no. P1234
> > (materialized physical object) that is installed as tag 21P101 (functional
> > physical object). It is a temporal part of each of these, not just one.
> > The thing to note is that they are two different types of whole life
> > individual, but you need all the elements of the type. (011)
If S is a temporal part of the FPO named 21P101, then S =
holds(instantiatedByP1234, 21P101, T) for some T. And if S is a temporal part
of the Pump named P1234, then S = holds(placedAs21P101, P1234, T) for the same
T. What we really have here is that instantiatedBy(fpo, po) = placedAs(po,
fpo), or more accurately: forall (T) instantiatedBy(fpo, po, T) iff
placedAs(po, fpo, T). So the State S is an instance of both ternary relations.
And S can be described as a temporal part of both the pump and the place. And
to carry any semantics, S must be an instance of the class Placement, or
something like that. Further, the fact that S is a temporal part of Pump and
Place tells me how to formulate the relation, but only because the 'types' of
the arguments to placedAs are disjoint. (012)
Now, let us consider flowsInto(equipment1, equipment2). And suppose that at
time T, Pump P1234 is connected to HeatExchanger H5678, in such a way that the
process fluid flows from P1234 to H5678. Then we have a FlowsInto state that
is a temporal part of P1234 and a temporal part of H1234 for the same time
interval T. But which is the source and which is the destination? They are
both Equipment, so we can't tell. This is admittedly contrived. But the
problem is intrinsic. The state that is a temporal part of two things
represents a ternary relation that involves them in distinct roles over a
common time interval. In general, the types of the non-temporal arguments to
the ternary relation represented by the state may not be distinct. So the
relationship between the State and the participants is not just
isTemporalPartOf, but rather some refinement of it that represents each role in
the ternary relation. (013)
Using a language in which the only relationship to a State is
'isTemporalPartOf', the solution will be to create things that are instances of
a class representing a role in the state, and make the role things temporal
parts of the role players and also temporal parts of the state thing. So we
have a FlowSource that is a temporal part of the Pump and the FlowsInto state,
and FlowDestination that is a temporal part of the HeatExchanger and also a
temporal part of the FlowsInto state. Thus the state thing involves things of
two distinguished types, and the ternary relation can be properly
reconstructed. It is a work-around, and most modeling languages force such
contrivances from time to time. But coupled with the above confusion about
relationships between states, I can't be sure that anyone can reconstruct the
intent of 'isTemporalPartOf'. (014)
Famous last words: "It is not how I would have modeled it, but it works."
This is knowledge engineering in which the knowledge is contorted by the
engineering. (015)
-Ed (016)
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