Dear all,
I, and so I've heard some other people, are not quite happy with the limitations that one can't really represent temporal stuff, yet some of the RO relations do allude to temporal things. The temporal-DL research is moving forward, but not rapidly in the sense that there will be implementation support for it anytime soon. There are several aspects of the temporality, however, that one can represent in an a-temporal setting. I gave that track a try taking RO's transformation_of relation as an example [1]. The additional constraints one can represent are fully backward compatible with RO's definition; i.e., they do not change the meaning, but instead seek to represent the intention of the relation in a more refined way.
Comments are welcome (if you are a BFO-groupie, then one is advised to read the 2-sentence caution at [2] before commenting).
[1] C. Maria Keet. Constraints for representing transforming entities in bio-ontologies. KRDB Research Centre Technical Report KRDB09-2, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy. April 22, 2009. http://www.inf.unibz.it/krdb/pub/TR/KRDB09-2.pdf
[2] http://keet.wordpress.com/2009/04/23/refining-constraints-on-ro%e2%80%99s-transformation_of-relation/
Best regards,
Marijke
C. Maria Keet
KRDB Research Centre
Faculty of Computer Science
Free University of Bozen-Bolzano
Via della Mostra 4
39100 Bolzano
Italy
tel: +39 04710 161287
fax: +39 04710 16009
email: ke...@inf.unibz.it
web: http://www.inf.unibz.it/krdb/
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Michel Dumontier writes:
> Just as you and I continue to maintain our identify while bend
> or stretch, molecules may also change their conformation (but
> not their configuration!) that yields new functionality. Thus,
> the use of ro:transformation_of seems most appropriate to describe
> the temporal relation from one conformation to another.
I concur, certainly for the protein complex case described by Alan.
> Unfortunately, the preRNA -> mRNA example provided in the
> ro:transformation_of description [1] is not consistent wrt
> to molecular identity championed above.
Hmm. Wearing both my chemist and Sequence Ontology hats, I would say that given that there is nothing inherent in the chemical structure of mRNAs that differentiates them from other kinds of RNA, I don't think molecular identity is appropriate here.
Or rather, the mRNA sequence may be a ro:transformation_of the preRNA sequence, but the mRNA molecule derives_from the preRNA molecule. As far as the OBO ontologies are set up, we have a rich description of transcript sequences but a very poor description of molecules.
But RNAs are a tricky edge case between molecular identity and biological identity anyway.
best wishes,
Colin.
--
Dr Colin Batchelor MChem MRSC, Team Leader, Informatics R&D
Informatics Department,
Royal Society of Chemistry, Thomas Graham House, Cambridge UK CB4 0WF
batch...@rsc.org t: +44 1223 432280
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What is your definition of molecule -- in particular does it include
On Apr 23, 2009, at 12:14 PM, Michel Dumontier wrote:
> Hi all,
>
> As a starting point, I've always advocated molecular identity on the
> basis of molecular structure. Thus non-covalent complexes are formed
> from molecules that maintain their identity throughout the lifetime
> of the complex. Just as you and I continue to maintain our identify
> while bend or stretch, molecules may also change their conformation
> (but not their configuration!) that yields new functionality. Thus,
> the use of ro:transformation_of seems most appropriate to describe
> the temporal relation from one conformation to another.
large macromolecules? It seems counterintuitive for a single base pair
mutation to cause an entire DNA molecule to cease to exist and be
replaced by a new one.
I agree this was a poor choice of example
> Unfortunately, the preRNA -> mRNA example provided in the
> ro:transformation_of description [1] is not consistent wrt to
> molecular identity championed above. I would argue that the
> configurational changes that occur between a preRNA to an mRNA is
> best described by ro:derives_from.
Not sure exactly what you mean
> Furthermore, I believe that ro:transformation_of should be limited
> to where the changes results in a change in a sub-class membership,
I think the opposite - I think in many cases, transformation_of will
> and never between disjoint classes.
hold between disjoint classes. I'm assuming a definition of
disjointness for continuants as follows
C1 disjoint_from C2 iff not exists i, t such that i instance_of C1 at
t and i instance_of C2 at t
The definition of transformation is in fact very precise:
A transformation_of B = every instance of A was once [identical to]
an instance of B
The problem pertains to the 'identical to'. This is so basic that it
cannot be defined -- there are some areas where we can apply it
perfectly well, for example as regards particular human beings
undergoing normal metabolism; and then there are difficult,
borderline cases. Philosophers have learned that there is no way to
precisify the meanings of basic terms such as 'identity' in such a
way as to remove all such cases; fortunately, again in many areas,
the existence of such cases does not prevent us from using a term
like 'identity' perfectly successfully for the many, many cases which
are not borderline.
The issue, I think, is whether it is appropriate to use
'transformation' as defined above with regard to molecules. Perhaps
it is not appropriate at all. If so, this is not a problem with
transformation, or with its definition, I think.
BS
The issue, I think, is whether it is appropriate to use
'transformation' as defined above with regard to molecules. Perhaps
it is not appropriate at all. If so, this is not a problem with
transformation, or with its definition, I think.
BS
for the S, at first impression, CT14' and CT15' would then apply for the
tautomerism. That is, there are, in your email below, 3 structural
isomers, i.e., same molecular formula but different structural formulas
and because of the different structural formula they can have different
functions, melting points, and whatnot. Let's call these classes Cring,
Cketo, and Cenol; and any of the instances /a/ \in Cring can change to
an /a/ \in Cketo or an /a/ \in Cenol and, at a later point in time,
transform back to /a/ \in Cring (or vice versa).
The characteristic that does not change and, in this case at least,
contributes to identity of a subsuming class C (or a Cringketoenol class
as the union of the three), is the molecular formula, so that diachronic
identity can be guaranteed. If we'd put Cring, Cketo, and Cenol willy
nilly in different branches in the taxonomy, then identity of the
molecules across the transformations cannot be guaranteed (if, on the
other hand, you'd have a taxonomy of, say, functions or roles they play
then they could be at different places).
does this make sense w.r.t. the unmentioned example for the tautomerism?
Best,
Marijke
Colin Batchelor ha scritto:
> (Marijke added to the list as I haven't got round to joining bfo-discuss, sorry.)
>
> Michel Dumontier writes:
>
>
>> let's start with glycolysis - please refer to the image at
>>
>
>
>> http://www.accessexcellence.org/RC/VL/GG/ecb/ecb_images/13_01Glycolysis-Steps_1-5.jpg
>>
>
> I like this example, for reasons I will list below.
>
>
>> [...]
>> My solution was that any difference in structure was an identity change.
>>
>
> What I would observe here is that glucose interchanging between ring and chain forms happens all the time in biological systems, not just in that particular reaction. In your connection table-based system, and let us remember that connection tables, which are based on a ball and stick model of molecules, are an administrative convenience for pharma companies rather than a realistic model of a wide range of molecules, we would have ring-glucose and chain-glucose popping into and out of existence all the time, to say nothing of the transition states between the two.
>
> There are more equilibria to consider: acid--base equilibria for example. Amino acid residues will exist in biological systems in a variety of protonation states. I genuinely wouldn't want to argue that simply gaining or losing a hydrogen atom changes the entire protein. One of the strengths of ChEBI is that it represents these equilibria in a number of biologically-relevant cases.
>
> I need to think a bit about how Marijke's S meta-property applies to the ring--keto-chain--enol-chain tautomerism case.
>
>
>> Then nobody has to debate any given pair of structural transformations.
>> The alternative is to make a social convention that any change over some
>> arbitrary fraction, like 1/4, uses derives_from, otherwise it's
>> transformation_of (if it can be applied as an instance level relation).
>>
>
> I don't think either of these alternatives are helpful. I don't believe this kind of thing can be modelled without thinking. I have some sympathy with the molecular identity criterion, but I would argue that it's naïve for the reasons listed above. Further, we are (non-multiplicatively, obviously) implicitly discussing many of these entities qua their participation in a biological process. Take a messenger RNA molecule M in your body and consider an atom-by-atom-identical molecule M' in a comet. The cometary one isn't, I claim, a messenger RNA. It wouldn't be in a universe where eukaryotes have never existed, so why would it be one in this?
>
> Best wishes,
> Colin.
> for the S, at first impression, CT14' and CT15' would then apply for the
> tautomerism. That is, there are, in your email below, 3 structural
> isomers, i.e., same molecular formula but different structural formulas
> and because of the different structural formula they can have different
> functions, melting points, and whatnot. Let's call these classes Cring,
> Cketo, and Cenol; and any of the instances /a/ \in Cring can change to
> an /a/ \in Cketo or an /a/ \in Cenol and, at a later point in time,
> transform back to /a/ \in Cring (or vice versa).
> The characteristic that does not change and, in this case at least,
> contributes to identity of a subsuming class C (or a Cringketoenol class
> as the union of the three), is the molecular formula, so that diachronic
> identity can be guaranteed.
There is something a bit stronger than just the molecular formula---nearly all of the molecule is the same in both forms---but yes.
(Incidentally, I've misremembered there being a Cenol! Cchain and Cring will do.)
> If we'd put Cring, Cketo, and Cenol willy
> nilly in different branches in the taxonomy, then identity of the
> molecules across the transformations cannot be guaranteed (if, on the
> other hand, you'd have a taxonomy of, say, functions or roles they play
> then they could be at different places).
>
> does this make sense w.r.t. the unmentioned example for the tautomerism?
Yes. This makes a lot of sense.
(Marijke added to the list as I haven't got round to joining bfo-discuss, sorry.)
Michel Dumontier writes:
> let's start with glycolysis - please refer to the image at
> http://www.accessexcellence.org/RC/VL/GG/ecb/ecb_images/13_01Glycolysis-Steps_1-5.jpg
I like this example, for reasons I will list below.
> [...]
> My solution was that any difference in structure was an identity change.
What I would observe here is that glucose interchanging between ring and chain forms happens all the time in biological systems, not just in that particular reaction. In your connection table-based system, and let us remember that connection tables, which are based on a ball and stick model of molecules, are an administrative convenience for pharma companies rather than a realistic model of a wide range of molecules, we would have ring-glucose and chain-glucose popping into and out of existence all the time, to say nothing of the transition states between the two.
There are more equilibria to consider: acid--base equilibria for example. Amino acid residues will exist in biological systems in a variety of protonation states. I genuinely wouldn't want to argue that simply gaining or losing a hydrogen atom changes the entire protein. One of the strengths of ChEBI is that it represents these equilibria in a number of biologically-relevant cases.
I need to think a bit about how Marijke's S meta-property applies to the ring--keto-chain--enol-chain tautomerism case.
> Then nobody has to debate any given pair of structural transformations.
> The alternative is to make a social convention that any change over some
> arbitrary fraction, like 1/4, uses derives_from, otherwise it's
> transformation_of (if it can be applied as an instance level relation).
I don't think either of these alternatives are helpful. I don't believe this kind of thing can be modelled without thinking. I have some sympathy with the molecular identity criterion, but I would argue that it's naïve for the reasons listed above. Further, we are (non-multiplicatively, obviously) implicitly discussing many of these entities qua their participation in a biological process. Take a messenger RNA molecule M in your body and consider an atom-by-atom-identical molecule M' in a comet. The cometary one isn't, I claim, a messenger RNA.
It wouldn't be in a universe where eukaryotes have never existed, so why would it be one in this?
Best wishes,
Colin.
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> At the same time I have been
> convinced that all the other seeming examples of 1-to-1 derivation do
> not work. Hence -- with general agreement, I think -- in the new
> version of RO we plan to insist that derivation is always either
> n-to-1 or 1-to-n, for n > 1 -- i.e. that all derivation is either
> fission or budding, or fusion or capture.
I've been looking recently at mechanisms of chemical reactions. This all goes back to Ingold's work in the 20s and 30s, but it seems to hold good today.
Most of the reactions are 2-to-1 or 1-to-2 as you say, but there are some concerted processes which I would like to model as 2-to-2. One of them is the SN2 reaction:
http://en.wikipedia.org/wiki/Sn2
If we consider the potential energy surface (not shown), the reactants are in one basin, the products are in another basin, and the transition state is the col or pass through which the system moves. In general I would be wary of admitting transition states to a molecular ontology, but I would be happy to admit intermediates (basins in between cols).
I have no objection to 2-to-2, too.
We can just say: transformation is always 1-1; everything else is derivation.
BS
>If we consider the potential energy surface (not shown), the
>reactants are in one basin, the products are in another basin, and
>the transition state is the col or pass through which the system
>moves. In general I would be wary of admitting transition states to
>a molecular ontology, but I would be happy to admit intermediates
>(basins in between cols).
>
>Best wishes,
>Colin.
>
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"everything else"
In the puzzle I posed the other day (http://tinyurl.com/dasyrw), one
of the things buzzing around the back of my head was that it feels
like neither derivation nor transformation is appropriate at the
molecular level.
The problem with derivation is that it posits that after some point in
time the previous entities cease to exist. However, in (perhaps only
some) chemical reactions, at molecular granularity, it seems to me
that entities retain identity even as they come together because they
can later come apart and be what they were before.
I assume that existence is such that there can't be temporal gaps.
To argue against that they are the same entity as before would seem to
me to be a losing argument. (at least I can't figure out a way to win
it)
One might argue that the same (that constituents come together and
apart retaining identity) is true for macroscopic arguments. This
certainly seems to be true in some cases. If I build a car and later
take one of the wheels off, it is the same wheel I put on when I was
building the car.
However for many other entities this will not happen. The orange I eat
will not sometimes appear back as a whole orange. Statistically
speaking, it is possible, but very unlikely. Therefore I conclude that
questions of when identity is lost have something to do with entropy
and thermodynamics.
So back to Barry's "everything else"...
There are certainly changes that involve neither transformation nor
derivation. Even aside from the above examples, if we think that there
are thinks that retain identity and class over time (like person),
that nonetheless change in physical constitution, then we have cases
of materials merging and dissociating (n->1, 1->n) without the ceasing
of existence posited by derives_from, nor change in classification
posited by transformation_of.
In the case of my earlier post - proteins, protein complexes, ligands,
and implicitly chemical reactions (molecular granularity), and in the
case of car parts (some macroscopic granularity), are there not other
relations that are more appropriate than the two we have in hand
currently?
-Alan
> I suppose you have to ask yourself whether you think two
> molecular entities that differ even from by a single bond
> are in fact *different*.
What about hydrogen bonds? Some weak covalent bonds are weaker than some strong hydrogen bonds, and in any case hydrogen bonds may well have some covalent character. Your definition of ChemicalBond, "The attractive interaction between atoms.", includes van der Waals forces and other interactions which are not significant at body temperature.
My feeling is that biologists would consider the breaking of all of the hydrogen bonds between two strands of DNA to be a more significant change than the gain or loss of a proton. Energetically it's massively more significant.
Anyway, even taking the bonds that the MDL mol file knows about, consider ozone. Consider isotopically-substituted ozone, 17O16O2. The resonance structures for this are (in SMILES notation):
[17O-][O+]=O and [17O]=[O+]O.
Their bonding is different. Yet they are the same molecule. It's a case of mesomerism. Munchnones (http://goldbook.iupac.org/M04068.html) are the same. Nitro groups are the same. There has to be something to point to that is more subtle than an OWLification of the mol file.
> computationally, it is not feasible to look them up in ChEBI using some natural language description.
If ChEBI had natural language descriptions of (more of) its terms it would be much more useful!
But yes, obviously we want a computable version of ChEBI and I think your contributions have been tremendously helpful.
> However for many other entities this will not happen. The orange I eat
> will not sometimes appear back as a whole orange. Statistically
> speaking, it is possible, but very unlikely. Therefore I conclude that
> questions of when identity is lost have something to do with entropy
> and thermodynamics.
I wonder whether the important quantity here isn't kT. What counts as a chemical entity at 3 K certainly doesn't count as a chemical entity at body temperature, and very little inside me would count as a chemical entity inside a star.
The only difference between changes that break bonds and changes that rearrange atoms in space but preserve bonding is one of energy, and what we think of as a bond is conditioned by the temperature we do our experiments at.
This is a bit like granularity. Could it even be a different sort granularity?
there is a good case to be made to the effect
that the existence of artifacts can have temporal gaps:
Poland in the era 1795–1918
your watch when it is lying in bits in different places in the repair shop
BS
I can't reason well about countries. The case of the watch is
interesting, though I note that your language still identifies the
watch with the bits. "your watch when".
What happens to the parts when they are part of the watch. Do they
cease to exist? If not, continuing my question, what is the relation
between the bits and the watch that is part of the family of relations
that include derives_from and transformation_of?
In the case of molecules we aren't dealing with "artifacts". Did you
mean to suggest that the compelling argument doesn't apply in that
case?
-Alan
>On Tue, May 5, 2009 at 1:33 PM, Barry Smith
><<mailto:phis...@buffalo.edu>phis...@buffalo.edu> wrote:
>
>At 12:06 PM 5/5/2009, Alan Ruttenberg wrote:
> >On Tue, May 5, 2009 at 11:23 AM, Barry Smith
> <<mailto:phis...@buffalo.edu>phis...@buffalo.edu> wrote:
> > >
> > > At 11:18 AM 5/5/2009, Colin Batchelor wrote:
> > >>Barry Smith writes:
> > >>
> > >> > At the same time I have been
> > >> > convinced that all the other seeming examples of 1-to-1 derivation do
> > >> > not work. Hence -- with general agreement, I think -- in the new
> > >> > version of RO we plan to insist that derivation is always either
> > >> > n-to-1 or 1-to-n, for n > 1 -- i.e. that all derivation is either
> > >> > fission or budding, or fusion or capture.
> > >>
> > >>I've been looking recently at mechanisms of chemical
> > >>reactions. This all goes back to Ingold's work in the 20s and 30s,
> > >>but it seems to hold good today.
> > >>
> > >>Most of the reactions are 2-to-1 or 1-to-2 as you say, but there are
> > >>some concerted processes which I would like to model as 2-to-2. One
> > >>of them is the SN2 reaction:
> > >><http://en.wikipedia.org/wiki/Sn2>http://en.wikipedia.org/wiki/Sn2
> > >
> > > I have no objection to 2-to-2, too.
> > > We can just say: transformation is always
> > 1-1; everything else is derivation.
> >
> >"everything else"
> >
> >In the puzzle I posed the other day
> (<http://tinyurl.com/dasyrw>http://tinyurl.com/dasyrw), one
> >of the things buzzing around the back of my head was that it feels
> >like neither derivation nor transformation is appropriate at the
> >molecular level.
> >
> >The problem with derivation is that it posits that after some point in
> >time the previous entities cease to exist. However, in (perhaps only
> >some) chemical reactions, at molecular granularity, it seems to me
> >that entities retain identity even as they come together because they
> >can later come apart and be what they were before.
> >
> >I assume that existence is such that there can't be temporal gaps.
>
>there is a good case to be made to the effect
>that the existence of artifacts can have temporal gaps:
>Poland in the era 1795–1918
>your watch when it is lying in bits in different places in the repair shop
>BS
>
>
>What happens if you pick up different parts than
>you had before? In only a select few cases
>would the same atoms actually be reincorporated into the molecule...
I can well imagine that artifacts have special features in this respect;
BS
Derivation on the instance-level is a relation holding between
non-identicals. More precisely, it holds between distinct
material continuants when one succeeds the other across a
temporal divide in such a way that at least a biologically sig-
nificant portion of the matter of the earlier continuant is
inherited by the later. Thus we will have axioms to the effect
that from c derives_from c1 we can infer that c and c1 are
not identical and that there is some instant of time t such that
c1 exists only prior to and c only subsequent to t. We will also
be able to infer that the spatial region occupied by c as it
begins to exist at t overlaps with the spatial region occupied
by c1 as it ceases to exist in the same instant.
Alan Ruttenberg writes:
> However for many other entities this will not happen. The orange I eat
> will not sometimes appear back as a whole orange. Statistically
> speaking, it is possible, but very unlikely. Therefore I conclude that
> questions of when identity is lost have something to do with entropy
> and thermodynamics.
I wonder whether the important quantity here isn't kT. What counts as a chemical entity at 3 K certainly doesn't count as a chemical entity at body temperature, and very little inside me would count as a chemical entity inside a star.
The only difference between changes that break bonds and changes that rearrange atoms in space but preserve bonding is one of energy, and what we think of as a bond is conditioned by the temperature we do our experiments at.
This is a bit like granularity. Could it even be a different sort granularity?
> Doesn't quite feel the same. With granularity we have different
> perspectives on the same stuff, whereas with temperature you are
> either hot or cold, so to speak, but not both at the same time.
> The arrangements of matter can be different at different temperatures
> (or in solution), and as objects are subjected to these different
> conditions, changes to them may occur.
Agreed.
The conundrum as I see it is that, disregarding the thermal background, at the molecular granularity, all changes are reversible. Irreversibility only arises when we start looking at ensembles. But if we pick a temperature then we can look at the energy landscape for a particular system and point to relatively-shallow, symmetric barriers which we expect to be recrossed all the time, like tautomerisms, and barriers which are asymmetric and relatively steep on one side which we don't expect to be recrossed. I'm not suggesting this is a good way of modelling this! But I am suggesting that this might be one of the many unstated assumptions in the way that people try to model molecular entities in biological systems.
Best wishes,
Colin.
--
Dr Colin Batchelor MChem MRSC, Team Leader, Informatics R&D
Informatics Department,
Royal Society of Chemistry, Thomas Graham House, Cambridge UK CB4 0WF
batch...@rsc.org t: +44 1223 432280
I think South Korea is derived from Korea
I think East Germany, God bless its soul, derived from Germany
>I was hoping that I was getting clearer on what
>the problem is, and that you might address it
>more directly. But I'll try again. We have two
>types of relations for representing temporal
>change in entities in an overall process where
>total material is approximately conserved:
>derivation and transformation. According to the
>documentation of these relations, each has
>consequences - in transformation there is a
>class change and in derivation entities cease to exist and come into existence.
>
>Neither of these seem appropriate for
>representing the kind of change where something
>becomes a part and yet retains its identity, as
>evidenced by the ability to have the part later
>become dissociated and be the same thing as it was before.
I think on the instance level (where we can talk
simply of identity, rather than transformation), the matter is clear:
A heart undergoes two successive transplants; the
same heart (instance) in 3 successive ; so
identity. Can you think of a case where the story
you tell above would not realizably be described in terms of identity?
BS
>Given the above, I see two choices currently.
>Either a) such a change is not represented by a
>relation at all, as neither derives_from or
>transformation_of appears appropriate or b)
>There is some other relation to be used.
>
>If the choice is v, the other relation should
>imply (at least) that one of the relata goes
>from being a part to being not a part, and that
>the now-not-part-then-part continues to exist
>and retain identity. Subtypes of this relation
>could be created for the case where the other
>relatum a) comes into existence during the
>transition, as is the case with the synthesis of
>small molecules or b) retains identity during
>the transition, as is the case with cars and
>wheels, or c) Undergoes a transformation (not
>coming up with a good example atm, but I suspect this is a valid case).
>
>There would be a corresponding relation going in
>the other direction, for the now-part-then-not-part case.
>
>-Alan
>
>
>
>BS
I think on the instance level (where we can talk simply of identity, rather than transformation), the matter is clear:I was hoping that I was getting clearer on what the problem is, and that you might address it more directly. But I'll try again. We have two types of relations for representing temporal change in entities in an overall process where total material is approximately conserved: derivation and transformation. According to the documentation of these relations, each has consequences - in transformation there is a class change and in derivation entities cease to exist and come into existence.
Neither of these seem appropriate for representing the kind of change where something becomes a part and yet retains its identity, as evidenced by the ability to have the part later become dissociated and be the same thing as it was before.
A heart undergoes two successive transplants; the same heart (instance) in 3 successive ; so identity. Can you think of a case where the story you tell above would not realizably be described in terms of identity?
assembled_from holds between material continuants when one comes into existence at a certain time in such a way that it has the others as parts. Thus we will have axioms to the effect
that from c assembled_from c1 and c2 we can infer that c1 part_of c at t, c2 part_of c at t, etc, and that the spatial region occupied by c contains the spatial regions of c1.. cn at t
c gains_part c1
gains_part holds between material continuants when one becomes part of the other at a certain time. Thus we will have axioms to the effect that from c gains_part c1 we can infer that c1 part_of c at t, that the spatial region occupied by c contains the spatial region of c1 at t , and that for any e > 0, there exists a time te st. t-te < e and it is not the case that c1 part_of c at te and the spatial region occupied by c does not overlap the spatial region of c1 at te.
loses_part holds between material continuants when one ceases being part of the other at a certain time, but both entities continue to exist. Thus we will have axioms to the effect that from c loses_part c1 we can infer that not(c1 part_of c at t), that the spatial region occupied by c does not overlap the spatial region of c1 at t , and that for any e > 0, there exists a time te st. t-te < e and c1 part_of c at te and the spatial region occupied by c contains the spatial region of c1 at te.
-Alan
breaks_into holds between material continuants when one ceases to exist at a
certain time and some of its parts come to be self standing.
Thus we will have axioms to the effect that from c disassembles_into
c1 and c2 we can
infer that c1 part_of c just before t, c2 part_of c just before t,
etc, that the spatial region
occupied by c contains the spatial regions of c1.. cn just before t,
that c does not exist
after t, and c1, c2.. exist at t.
-Alan
-Alan
On Fri, May 8, 2009 at 3:58 PM, Werner Ceusters <ceus...@buffalo.edu> wrote:
> Sound all more like processes to me, rather than relations.
I guess my proposal is that derivation should be viewed as the
superordinate relation, of which all cases except transformation [and
(perhaps) loses part and gains part] would be subcases.
BS