Thanks Waclaw, (01)
I think in BFO, the classes in continuant has no temporal part.
However the instance of a continuant can't avoid the fact the it bears
a temporal stamp. (02)
In the paper :http://genomebiology.com/2005/6/5/R46
There are two concerns for "part_of" relations:
1. Part_of between instances. (c part_of c1 at t and c1 part_of c2
at t, then also c part_of c2 at t)
I infer that if ( c part_of c1 at t1 and c1 part_of c2 at t2)
there is no c part_of c2, because of the time difference.
Here I think it is C(c)@t
2. Part_of between classes.
- 2.1 Part_of between continuant (C part_of C1 if and only if
any instance of C at any time is an instance-level part of some
instance of C1 at that time)
It seems that if there is a C(c@t) is part_of C1(c1@t);
then C part_of C1 (and there is no temporal part)
There are further C temporary_part_of C1 (every C
exists at some time in its existence as part of some C1)
C initial_part_of C1 (every
C is such that it begins to exist as part of some instance of C1).
- 2.2 Part_of between process (P part_of P1 if and only if any
instance of P is an instance-level part of some instance of P1)
temporal parts are included in process, so it is easier
to get the meaning. (03)
Cct here if we use R(a,b) to reform:
It should be R(C,c) R=instance relationship
All c at a time t is a instance of C: (04)
c1 at time t1 is an instance of C;
c2 at time t2 is an instance of C;
.... (05)
We got R(C,c@t) (06)
Since C as continuant has not temporal part:
So 1. C(c@t) is true. It means: c at time t is instance of C.
And 3. C(c)@t is true. It means: at time t there is a c, which is instance of C. (07)
But 2. C@t(c) is true only when C is a process class. (08)
Regards,
Asiyah Yu Lin (09)
************************************************************
Part_of (010)
Parthood as a relation between instances. The primitive instance-level
relation p part_of p1 is illustrated in assertions such as: this
instance of rhodopsin mediated phototransduction part_of this instance
of visual perception. (011)
This relation satisfies at least the following standard axioms of
mereology: reflexivity (for all p, p part_of p); anti-symmetry (for
all p, p1, if p part_of p1 and p1 part_of p then p and p1 are
identical); and transitivity (for all p, p1, p2, if p part_of p1 and
p1 part_of p2, then p part_of p2). Analogous axioms hold also for
parthood as a relation between spatial regions. (012)
For parthood as a relation between continuants, these axioms need to
be modified to take account of the incorporation of a temporal
argument. Thus for example the axiom of transitivity for continuants
will assert that if c part_of c1 at t and c1 part_of c2 at t, then
also c part_of c2 at t. (013)
Parthood as a relation between classes. To define part_of as a
relation between classes we again need to distinguish the two cases of
continuants and processes, even though the explicit reference to
instants of time now falls away. For continuants, we have C part_of C1
if and only if any instance of C at any time is an instance-level part
of some instance of C1 at that time, as for example in: cell nucleus
part_ of cell. (014)
Formally: (015)
C part_of C1 = [definition] for all c, t, if Cct then there is some c1
such that C1c1t and c part_of c1 at t. (016)
Note the 'all-some' structure of this definition, a structure which
will recur in almost all the relations treated here. (017)
C part_of C1 defines a relational property of permanent parthood for
Cs. It tells us that Cs, whenever they exist, exist as parts of C1s.
We can also define in the obvious way C temporary_part_of C1 (every C
exists at some time in its existence as part of some C1) and also C
initial_part_of C1 (every C is such that it begins to exist as part of
some instance of C1). (018)
For processes, we have by analogy, P part_of P1 if and only if any
instance of P is an instance-level part of some instance of P1, as for
example in: M phase part_of cell cycle or neuroblast cell fate
determination part_of neurogenesis. Formally: (019)
P part_of P1 = [definition] for all p, if Pp then there is some p1
such that: P1p1 and p part_of p1. (020)
An assertion to the effect that P part_of P1 thus tells us that Ps in
general are in every case such as to exist as parts of P1s. P1s
themselves, however, may exist without having Ps as parts (consider:
menopause part_of aging). (021)
Note that part_of is in fact two relations, one linking classes of
continuants, the other linking classes of processes. While both of the
mentioned relations are transitive, this does not mean that part_of
relations could be inferred which would cross the continuant-process
divide.
********************************************************************************************** (022)
On Thu, Feb 3, 2011 at 12:51 PM, Waclaw Kusnierczyk <waku@xxxxxxxxxxx> wrote:
> On 02/03/2011 11:28 AM, Yu Lin wrote:
>>> Is Cct
>>>
>>> 1. C(c)@t ?
>>> 2. C@t(c) ?
>>> 3. C(c@t) ?
>> I think it is 1. C(c)@t
>
> On what grounds?
>
> I would actually think it is C@t(c) (which is 2. C(c,t) in the
> traditional AI/KR notation Pat mentioned), because of the definition
>
> c instance_of C at t - a primitive relation between a continuant
> instance and a class which it instantiates at a specific time [1]
>
> which talks about *instantiating at time* (hence it seems to be the
> relation that is time-qualified) rather than the sentence being true at
> a time (hence it seems not to be the sentence that is time-qualified, as
> you suggest). The cited paper does not use the R(...) notation,
> however, so it's not immediately obvious where those author would put
> the time variable.
>
> vQ
>
> [1] http://genomebiology.com/2005/6/5/R46
>
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