Temporally Qualified Continuants to Simplify Temporalized Relations

[zhengj2007]

From steschu@gmail.com on February 04, 2013 10:54:49

Following up several discussions we had in the past, and in light of the acceptance problems of the current temporalized BFO2 relations I would like to suggest the "Temporally Qualified Continuants" approach as a possible alternative (thanks: Niels Grewe, Janna Hastings, Fabian Neuhaus).

I uploaded a SAMPLE ONTOLOGY: http://bfo.googlecode.com/svn/trunk/src/ontology/owl-schulz/tqc2.owl The key idea is that a subclass is added to Continuant: Temporally qualified continuant = Time-stamped continuant.

"Temporally qualified continuant" is NOT an ontologically relevant category. For TBox reasoning it is irrelevant. But it matters when it comes to represent individuals, because it requires that a timestamp be added to the each instance.

The idea is the following:

Rel (a, b, t)

cannot be expressed in OWL.

But we could state the same by

Rel (a@t, b@t)

with a@t , b@t being temporally qualified continuants.

By adding domain / range constraints it can be easily assured that wherever a relation is asserted between two continuants the relata are classified as temporally qualified continuants.

The notion of "at some time" can be added by chaining with the object property "at some time", which related a continuant with each of its temporalized aspects.

In case of transitive relations, the approach maintains transitivity between temporally qualified continuants, but blocks transitivity as soon as there is a chaining with the relation "at some time".

It also seems that this approach addresses the needs for using OWL relations related to triple-based instance data.

An assertion of the type continuant1 rel continuant2 entails that both relata must be temporally qualified:

continuant1 rel continuant2
continuant1 hasTimestamp T1 continuant2 hasTimestamp T1

However, OWL cannot avoid invalid statements such as

rel (continuant1@T1, continuant2@T2) with T1 =/= T2 http://bfo.googlecode.com/svn/trunk/src/ontology/owl-schulz/tqc2.owl

Original issue: http://code.google.com/p/bfo/issues/detail?id=149

[zhengj2007]

From alanruttenberg@gmail.com on February 04, 2013 08:03:08

Can you detail how it simplifies things? Do we still need occurrent versus continuants relations? What Kinds of inference and queries does it support? How is continuity between a@t1 and a@t2 established at the instance level - I.e how do we know they are both 'a' and determine rigid values, such as name or species.

[zhengj2007]

From steschu@gmail.com on February 04, 2013 15:18:14

It simplifies things because if we assume generical relatedness as the default in existing OBO ontologies (according to the interpretation of relations in OBO syntax), then the migration would be straightforward. Whoever wants to restrict the relation to "at some time" can do it by postcoordination as demonstrated in the example.

In my opinion this approach is compatible with one, e.g. part-of relation. It is always binary, as between continuants it can only be used if the continuants are temporally qualified. To prevent the linkage between continuants and occurrent, one axiom suffices: Occurrent subClassOf part-of only Occurrent

It supports transitivity in its standard use case, but the combination of a transitive relation with the "at some time" relation is no longer transitive, as expected.

Continuity between a@t1 and a@t2 at the instance level assured because the instances are not referred to as a@t1 or a@t2 but just as a

In a triplet representation it would look like < a has-timestamp t1> < a has-timestamp t2>

But it is not straightforward. I don't have a clear solution - but it is also unclear how it should look like if we use temporalized relations, e.g.

< a has-part-at-some-time b> < a has-part-at-some-time c>

How would you introduce timestamps here? I think in both cases we need to introduce blank nodes which would correspond to sth like a@t1

I haven't tested it, but one could make the following assertions (using the standard example human as a rigid class and student as an anti-rigid class):

Student subClassOf Human Student subClassOf 'at some time' some (not Student)

Not sure what are the consequences of it, I haven't tested it. But I guess nobody expects that we solve the rigidity problem with a simple OWL formalism. Perhaps if we move further to some kind of fourdimensionalism, but I guess that this is not agreeable

[zhengj2007]

From alanruttenberg@gmail.com on February 04, 2013 20:04:52

It doesn't support sound inference of transitivity. Any entailment of transitivity is unsound unless the times align in all models. Since transitivity is inferred whether or not that is known, and as in any case in which it is unknown it is possible to create a set of assertions in which the times do not align, an entailment of transitivity in such a case would be unsound.

It would be as if in the current BFO2 draft part-of-at-some-times was asserted to be transitive.

[zhengj2007]

From cmung...@gmail.com on February 04, 2013 21:09:46

I think this approach is promising. Maybe Stefan could flesh out some more examples (tqc2.owl is a little abstract!).

It would be great to this proposal embedded in CLIF somehow. This would be for purposes of clarification and validation, users would not see the CLIF.

Failing that examples and counterexamples are good. Alan, can you give an example of unsound inference of transitivity entailed by this model.

My intuition is that this proposal aligns well with the RO 2005 paper (I think this is what Stefan means when he says "interpretation of relations in OBO syntax").

[zhengj2007]

From alanruttenberg@gmail.com on February 04, 2013 22:05:14

Failing that examples and counterexamples are good. Alan, can you give an example of unsound inference of transitivity entailed by this model.

Add

TimeInstant subClassOf TemporalInterval t1 instanceOf TimeInstant t2 instanceOf TimeInstant t1 differentFrom t2 a1 hasTimeStamp t1 b1 hasTimeStamp t2 A = {a1} B = {b1}

Now despite the fact that we have said that

• There is only one instance of A:a1
• There is only one instance of B:b1
• a1 doesn't exist at the same time as b1 (they are atSomeTime distinct time instants)

The same inference as before is found: A is determined to be a subclass of HAS_CONTINUANT_PART_SOME_C This inference disappears (and the ontology makes sense again) if you remove the transitivity axioms on has_part, part_of

So: The transitivity is incorrectly inferred in this case.

[zhengj2007]

From cmung...@gmail.com on February 04, 2013 22:30:32

These axioms extend tqc2.owl, correct?

Is it not the case that the inference is valid but the ontology is inconsistent? Unfortunately we can't detect the inconsistency, noted by Stefan: "However, OWL cannot avoid invalid statements such as rel (continuant1@T1, continuant2@T2) with T1 =/= T2"

[there may be some practical techniques we can use detect some of these inconsistencies]

Are there examples of incorrect inferences that start from a coherent set of axioms?

You say "This inference disappears (and the ontology makes sense again) if you remove the transitivity axioms on has_part, part_of" - but how does the ontology make sense, if two TQCs from different times are connected via part_of?

[zhengj2007]

From steschu@gmail.com on February 04, 2013 23:42:50

BFO OWL cannot solve all temporal reasoning problems when dealing with instance data.

Also temporally qualified relations relating instance data are problematic, e.g.

NOW: StefansHeart part-of-all-times StefansBody

This statement has no timestamp attached. It will be invalid if I die tomorrow and my heart is transplanted.

With TQCs, we would get from the upper level ontology 'x rdf:Type bfo:TQC' for each instane x that is used with some continuant-to-continuant relation. The test for temporal consistency would have to occur outside DL, anyway.

[zhengj2007]

From steschu@gmail.com on February 05, 2013 00:10:23

See a draft version of the pre-Graz BFO2 (without temporalized relations) enhanced by 'temporally qualified continuant', 'at some time', and a value restriction for entity https://code.google.com/p/bfo/source/browse/trunk/src/ontology/owl-schulz/bfo_tqc.owl

[zhengj2007]

From alanruttenberg@gmail.com on February 05, 2013 04:13:49

However, OWL cannot avoid invalid statements such as rel (continuant1@T1, continuant2@T2) with T1 =/= T2"

Are there examples of incorrect inferences that start from a coherent set of axioms?

You say "This inference disappears (and the ontology makes sense again) if you remove the transitivity axioms on has_part, part_of" - but how does the ontology make sense, if two TQCs from different times are connected via part_of?

This is a somewhat fair criticism. I will construct an example that doesn't have this problem - it only needs to arrange temporal regions in which misalign

a

b

c -----------

This is not an implausible biological scenario during development.

There is a difference between not being able to detect inconsistencies (incompleteness) and deriving incorrect entailments (unsoundness)

As an example, inconsistent OWL will not be detected by RDF reasoning. But entailment in OWL will not derive any unsound by RDF inferences.

We may accept incompleteness. We can't accept unsoundness.

Regarding transplantation, this is a problem with the assertions made by canonical anatomy ontologies. If you are suggesting that the TQC approach allows a straightforward way to design anatomy ontologies that both preserve transitive part hood, and also allow for transplantation, please show how.

[zhengj2007]

From dosu...@gmail.com on February 05, 2013 05:28:22

Surely the issue is one of specifying the circumstances for which a modelling approach is applicable. Transitive 'part of' + inverse 'has part' make perfect sense, but only if modelling the aspects of some class of continuant that do not change over time.

As an example: VFB currently only models static aspects of (canonical) adult Drosophila brain anatomy. Our queries rely on transitivity of parthood, both directly and in the derivation of axioms on relations. We would lose lots of perfectly correct and useful inference if we eliminated transitivity of parthood.

[zhengj2007]

From steschu@gmail.com on February 05, 2013 06:06:38

Important: in terms of OWL (I wouln’t make an ontological claim here), if x is an non-TQC continuant and x@t1 a temporally qualified one then x =/= x@t1

In RDF:

<x; rdf:Type; X> <x; 'at some time'; x@t1> <x; 'at some time'; x@t2> < x@t1; 'has timestamp'; t1> < x@t2; 'has timestamp'; t2>

Part-of transitivity, in its most general form can be expressed by the following rule using temporalized triples:

<x@t1; 'part of';y@t1> <y@t1; 'part of';z@t1>

---

<x@t1; 'part of';z@t1>

Outside OWL we need to check the validity rule: IF <x@t1; rel ; y@t2> and t1=/=t2, THEN triplet is invalid

The reason ist that the triplet corresponds to the quadruple < rel, x, y, t1> This quadruple has only one time argument

Re: consistency check of temporalized triplets: tentative OWL axiom:

TemporalInstant subClassOf isTimeStampOf only ((not TQC) or TQC and (rel some (TQC and hasTimestamp Self)))

(not tested yet)

[zhengj2007]

From alanruttenberg@gmail.com on February 05, 2013 08:07:45

I'm wondering about whether this axiom

entity subClassOf topObjectProperty only ('temporally qualified continuant' or occurrent)

is valid OWL2.

If it is note that this precludes having inverses of relations that go from (continuant and not tqc) -> tqc, as the inverse would violate the global restriction on topobjectproperty.

I suspect there will be other issues around that.

I've asked Uli Sattler about this, and to discuss the two approaches - she should be available next week,

[zhengj2007]

From alanruttenberg@gmail.com on February 05, 2013 08:08:45

AR: The condition is too strong.

SC: Part-of transitivity, in its most general form can be expressed by the following rule using temporalized triples:

<x@t1; 'part of';y@t1> <y@t1; 'part of';z@t1>

---

<x@t1; 'part of';z@t1>

AR: You aren't specifying what it means to say x@t1. If t1 is an interval, do you mean x@t1 'part of' z@t2 is true a) Only when t1 and t2 are the same? b) as long as t1 part of t2? (this is the sense of RO 2005) c) at any ti that is part of t1 and part of t2?

The general case is: <x@t1; 'part of';y@t2> <y@t3; 'part of';z@t4>

---

According to a) t1=t2 and t3=t4 else invalid. only if t1=t3 is it the case that <x@t1; 'part of';z@t1>

according to b) Notation: '<' = 'part of' t1 < t2 or invalid t3 < t4 or invalid

If t2 < t3 then <x@t1; 'part of';z@t1> otherwise there is nothing inferred.

According to c) if not exists(ti) ti < t1 and t1< t2 then invalid (t1 and t2 don't intersect) if not exists(ti) ti < t3 and t1< t4 then invalid (t3 and t4 don't intersect) Otherwise if exists(ti) z < z < t1 and z< t2 and z< t3 and z < t4 then x@ti 'part of' y@ti otherwise no inference should be made.

SC: Outside OWL we need to check the validity rule: IF <x@t1; rel ; y@t2> and t1=/=t2, THEN triplet is invalid

AR: It looks to me that the check is more complicated than that. Also, if you always have to have t1=t2 then that severely limits the biology you can describe, no?

[zhengj2007]

From cmung...@gmail.com on February 05, 2013 08:26:37

SC: Outside OWL we need to check the validity rule: IF <x@t1; rel ; y@t2> and t1=/=t2, THEN triplet is invalid

AR: It looks to me that the check is more complicated than that. Also, if you always have to have t1=t2 then that severely limits the biology you can describe, no?

CM: probably. E.g. we probably only want to perform this test for some rel in a set of temporally qualified relations. E.g. it would be valid to have some relations (e.g. transormation_of) connect across times.

[zhengj2007]

From steschu@gmail.com on February 06, 2013 06:01:34

STEFAN: I was looking for literature about the problem how instance data can be temporalized. The only approach which is referred to repeatedly is to reify object properties. In our case it would mean:

<p1; rdf:Type; Parthood> <p1; Whole; y> <p1; Part; x> <p1; Time; t1> <p2; rdf:Type; Parthood> <p2; Whole; z> <p2; Part; y> <p2; Time; t1>

I don't see any way do get the desired inference be DL reasoning here.

[zhengj2007]

From steschu@gmail.com on February 26, 2013 11:44:55

It seems that this thread is no longer active, but I suppose the issue is not settled. Would TQC be a reasonable feature to include into the OWL version of BFO 2? Or can the OBO community cope with the temporally qualified relations suggested thus far?

[zhengj2007]

From cmung...@gmail.com on February 27, 2013 18:25:39

The OBO community is fairly diverse. I think the reification approach would not be acceptable but this may not be required for TQCs. I'm not sure the tracker is the best place to hash this out - I'd like to see more concrete examples in OWL and some FOL showing the translation.

[zhengj2007]

From steschu@gmail.com on March 04, 2013 02:17:32

The reification approach would not be required for TQCs. I just mentioned it because it is often regarded as the standard approach for expressing n-ary relations in OWL. It has the problem that it is complex (especially in case it is expected to support transitivity) and will probably not be well accepted by the user community.