Proposed strategy for semantics in RDF* and Property Graphs

Graph databases such as Neo4J are gaining in popularity. These are in many ways comparable to RDF databases (triplestores), but I will highlight three differences:

  1. The underlying datamodel in most graph databases is a Property Graph (PG). This means that information can be directly attached to edges. In RDF this can only be done indirectly via reification, or reification-like models, or named graphs.
  2. RDF is based on open standards, and comes with a standard query language (SPARQL), whereas a unified set of standards have yet to arrive for PGs.
  3. RDF has a formal semantics, and languages such as OWL can be layered on providing more expressive semantics.

RDF* (and its accompanying query language SPARQL*) is an attempt to bring PGs into RDF, thus providing an answer for points 1-2. More info can be found in this post by Olaf Hartig.

You can find more info in that post and in related docs, but briefly RDF* adds syntax to add property directly onto edges, e.g

<<:bob foaf:friendOf :alice>> ex:certainty 0.9 .

This has a natural visual cognate:

Mungalls-Ontology-Design-Guidelines (7).png

We can easily imagine building this out into a large graph of friend-of connections, or connecting other kinds of nodes, and keeping additional useful information on the edges.

But what about the 3rd item, semantics?

What about semantics?

For many in both linked data/RDF and in graph database/PG camps, this is perceived as a minor concern. In fact you can often find RDF people whinging about OWL being too complex or some such. The “semantic web” has even been rebranded as “linked data”. But in fact, in the life sciences many of us have found OWL to be incredibly useful, and being able to clearly state what your graphs mean has clear advantages.

OK, but then why not just use what we have already? OWL-DL already has a mapping to RDF, and any document in RDF is automatically an RDF* document, so problem solved?

Not quite. There are two issues with continuing he status quo in the world of RDF* and PGs:

  1. The mapping of OWL to RDF can be incredibly verbose and leads to unintuitive graphs that inhibit effective computation.
  2. OWL is not the only fruit. It is great for the use cases it was designed for, but there are other modes of inference and other frameworks beyond first-order logic that people care about.

Issues with existing OWL to RDF mapping

Let’s face it, the existing mapping is pretty ugly. This is especially true for life-science ontologies that are typically construed of as relational graphs, where edges are formally SubClassOf-SomeValuesFrom axioms. See the post on obo json for more discussion of this. The basic idea here is that in OWL, object properties connect individuals (e.g. my left thumb is connected to my left hand via part-of). In contrast, classes are not connected directly via object properties, rather they are related via subClassOf and class expressions. It is not meaningful in OWL to say “finger (class) part_of hand (class)”. Instead we seek to say “all instances of finger are part_of some x, where x is an instance of a hand”. In Manchester Syntax this has compact form

Finger SubClassOf Part_of some Hand

This is translated to RDF as

Finger owl:subClassOf [

a owl:Restriction ;

owl:onProperty :part_of

owl:someValuesFrom :Hand

]

As an example, consider 3 classes in an anatomy ontology, finger, hand, and forelimb, all connected via part-ofs (i.e. every finger is part of some hand, and ever hand is part of some finger). This looks sensible when we use a native OWL syntax, but when we encode as RDF we get a monstrosity:

z

Fig2 (A) two axioms written in Manchester Syntax describing anatomical relationship between three structures (B) corresponding RDF following official OWL to RDF mapping, with 4 triples per existential axiom, and the introduction of two blank nodes (C) How the axioms are conceptualized by ontology developers, domain experts and how most browsers render them. The disconnect between B and C is an enduring source of confusion among many.

This ugliness was not the result of some kind of perverse decision by the designers of the OWL specs, it’s a necessary consequence of the existing stack which bottoms out at triples as the atomic semantic unit.

In fact, in practice many people employ some kind of simplification and bypass the official mapping and store the edges as simple triples, even though this is semantically invalid. We can see this for example in how Wikidata loads OBOs into its triplestore. This can cause confusion, for example, WD storing reciprocal inverse axioms (e.g. part-of, has-part) even though this is meaningless when collapsed to simple triples.

I would argue there is an implicit contract when we say we are using a graph-based formalism that the structures in our model correspond to the kinds of graphs we draw on whiteboards when representing an ontology or knowledge graph, and the kinds of graphs that are useful for computation; the current mapping violates that implicit contract, usually causing a lot of confusion.

It also has pragmatic implications too. Writing a SPARQL query that traverses a graph like the one in (B), following certain edge types but not others (one of the most common uses of ontologies in bioinformatics) is a horrendous task!

OWL is not the only knowledge representation language

The other reason not to stick with the status quo for semantics for RDF* and PGs is that we may want to go beyond OWL.

OWL is fantastic for the things it was designed for. In the life sciences, it is vital for automatic classification and semantic validation of large ontologies (see half of the posts in this blog site). It is incredibly useful for checking the biological validity of complex instance graphs against our encoded knowledge of the world.

However, not everything we want to say in a Knowledge Graph (KG) can be stated directly in OWL. OWL-DL is based on a fragment of first order logic (FOL); there are certainly things not in that fragment that are useful, but often we have to go outside strict FOL altogether. Much of biological knowledge is contextual and probabilistic. A lot of what we want to say is quantitative rather than qualitative.

For example, when relating a disease to a phenotype (both of which are conventionally modeled as classes, and thus not directly linkable via a property in OWL), it is usually false to say “every person with this disease has this phenotype“. We can invent all kinds of fudges for this – BFO has the concept of a disposition, but this is just a hack for not being able to state probabilistic or quantitative knowledge more directly.

A proposed path forward for semantics in Property Graphs and RDF*

RDF* provides us with an astoundingly obvious way to encode at least some fragment of OWL in a more intuitive way that preserves the graph-like natural encoding of knowledges. Rather than introduce additional blank nodes as in the current OWL to RDF mapping, we simply push the semantics onto the edge label!

Here is example of how this might look for the axioms in the figure above in RDF*

<<:finger :part-of :hand>> owlstar:hasInterpretation
owlstar:SubClassOfSomeValuesFrom .
<<:hand :part-of :forelimb>> owlstar:hasInterpretation owlstar:SubClassOfSomeValuesFrom .

I am assuming the existing of a vocabulary called owlstar here – more on that in a moment.

In any native visualization of RDF* this will end up looking like Fig1C, with the semantics adorning the edges where they belong. For example:

Mungalls-Ontology-Design-Guidelines (8)

proposed owlstar mapping of an OWL subclass restriction. This is clearly simpler than the corresponding graph fragment in 2B. While the edge properties (in square brackets) may be too abstract to show an end user (or even a bioinformatician performing graph-theoretiic operations), the core edge is meaningful and corresponds to how an anatomist or ordinary person might think of the relationship.

Maybe this is all pretty obvious, and many people loading bio-ontologies into either Neo4j or RDF end up treating edges as edges anyway. You can see the mapping we use in our SciGraph Neo4J OWL Loader, which is used by both Monarch Initiative and NIF Standard projects. The OLS Neo4J representation is similar. Pretty much anyone who has loaded the GO into a graph database has done the same thing, ignoring the OWL to RDF mapping. The same goes for the current wave of Knowledge Graph embedding based machine learning approaches, which typically embed a simpler graphical representation.

So problem solved? Unfortunately, everyone is doing this differently, and are essentially throwing out OWL altogether. We lack a standard way to map OWL into Property Graphs, so everyone invents their own. This is also true for people using RDF stores, people often have their own custom OWL mapping that is less verbose. In some cases this is semantically dubious, as is the case for the Wikipedia mapping.

The simple thing is for everyone to get around a common standard mapping, and RDF* seems a good foundation. Even if you are using plain RDF, you could follow this standard and choose to map edge properties to reified nodes, or to named graphs, or to the Wikidata model. And if you are using a graph database like Neo4J, there is a straightforward mapping to edge properties.

I will call this mapping OWL*, and it may look something like this:

RDF* OWL Interpretation
<<?c ?p ?d>> owlstar:interpretation owlstar:subClassOfSomeValuesFrom ?c SubClassOf ?p some ?d
<<?c ?p ?d>> owlstar:interpretation owlstar:subClassOfQCR, owlstar:cardinality ?n ?c SubClassOf ?p exactly 5 ?d
<<?c ?p ?d>> owlstar:interpretation owlstar:subjectContextProperty ?cp, owlstar:subjectContextFiller ?cf, owlstar:interpretation owlstar:subClassOfSomeValuesFrom (?c and ?cp some cf?) SubClassOf ?p some ?d

Note that the code of each of these mappings is a single edge/triple between class c, class d, and an edge label p. The first row is a standard existential restriction common to many ontologies. The second row is for statements such as ‘hand has part 5 fingers’, which is still essentially a link between a hand concept and a finger concept. The 3rd is for a GCI, an advanced OWL concept which turns out to be quite intuitive and useful at the graph level, where we are essentially contextualizing the statement. E.g. in developmentally normal adult humans (context), hand has-part 5 finger.

When it comes to a complete encoding of all of OWL there may be decisions to be made as to when to introduce blank nodes vs cramming as much into edge properties (e.g. for logical definitions), but even having a standard way of encoding subclass plus quantified restrictions would be a huge boon.

Bonus: Explicit deferral of semantics where required

Many biological relationships expressed in natural language in forms such as “Lmo-2 binds to Elf-2” or “crocodiles eat wildebeest” can cause formal logical modelers a great deal of trouble. See for example “Lmo-2 interacts with Elf-2”On the Meaning of Common Statements in Biomedical Literature (also slides) which lays out the different ways these seemingly straightforward statements about classes can be modeled. This is a very impressive and rigorous work (I will have more to say on how this aligns with GO-CAM in a future post), and ends with an impressive Wall of Logic:

Screen Shot 2019-07-08 at 10.16.38 PM.png

Dense logical axioms proposed by Schulz & Jansen for representing biological interactions

this is all well and good, but when it comes to storing the biological knowledge in a database, the majority of developers are going to expect to see this:

Mungalls-Ontology-Design-Guidelines (6).png

protein interaction represented as a single edge connecting two nodes, as represented in every protein interaction database

And this is not due to some kind of semantic laziness on their part: representing biological interactions using this graphical formalism (whether we are representing molecular interactions or ecological interactions) allows us to take advantage of powerful graph-theoretic algorithms to analyze data that are frankly much more useful than what we can do with a dense FOL representation.

I am sure this fact is not lost on the authors of the paper who might even regard this as somewhat trivial, but the point is that right now we don’t have a standard way of serializing more complex semantic expressions into the right graphs. Instead we have two siloed groups, one from a formal perspective producing complex graphs with precise semantics, and the other producing useful graphs with no encoding of semantics.

RDF* gives us the perfect foundation for being able to directly represent the intuitive biological statement in a way that is immediately computationally useful, and to adorn the edges with additional triples that more precisely state the desired semantics, whether it is using the Schulz FOL or something simpler (for example, a simple some-some statement is logically valid, if inferentially weak here).

Beyond FOL

There is no reason to have a single standard for specifying semantics for RDF* and PGs. As hinted in the initial example, there could be a vocabulary or series of vocabularies for making probabilistic assertions, either as simple assignments of probabilities or frequencies, e.g.

<<:RhinovirusInfection :has-symptom :RunnyNose>> probstar:hasFrequency
0.75 .

or more complex statements involving conditional probabilities between multiple nodes (e.g. probability of symptom given disease and age of patient), allowing encoding of ontological Bayesian networks and Markov networks.

We could also represent contextual knowledge, using a ‘that’ construct borrowed from ILK:

<<:clark_kent owl:sameAs :superman>> a ikl:that ; :believed-by :lois_lane .

which could be visually represented as:

Mungalls-Ontology-Design-Guidelines (10)

Lois Lane believes Clark Kent is Superman. Here an edge has a link to another node rather than simply literals. Note that while possible in RDF*, in some graph databases such as Neo4j, edge properties cannot point directly to nodes, only indirectly through key properties. In other hypergraph-based graph DBs a direct link is possible.

Proposed Approach

What I propose is a series of lightweight vocabularies such as my proposed OWL*, accompanied by mapping tables such as the one above. I am not sure if W3C is the correct approach, or something more bottom-up. These would work directly in concert with RDF*, and extensions could easily be provided to work with various ways to PG-ify RDF, e.g. reification, Wikidata model, NGs.

The same standard could work for any PG database such as Neo4J. Of course, here we have the challenge of how to best to encode IRIs in a framework that does not natively support these, but this is an orthogonal problem.

All of this would be non-invasive and unobtrusive to people already working with these, as the underlying structures used to encode knowledge would likely not change, beyond an additional adornments of edges. A perfect stealth standard!

It would help to have some basic tooling around this. I think the following would be straightforward and potentially very useful:

  • Implementation of the OWL* mapping of existing OWL documents to RDF* in tooling – maybe the OWLAPI, although we are increasingly looking to Python for our tooling (stay tuned to hear more on funowl).
  • This could also directly bypass RDF* and go directly to some PG representation, e.g. networkx in Python, or stored directly into Neo4J
  • Some kind of RDF* to Neo4J and SPARQL* to OpenCypher [which I assume will happen independently of anything proposed here]
  • And OWL-RL* reasoner that could demonstrate simple yet powerful and useful queries, e.g. property chaining in Wikidata

A rough sketch of this approach was posted on public-owl-dev to not much fanfare, but, umm, this may not be the right forum for this.

Glossing over the details

For a post about semantics, I am glossing over the semantics a bit, at least from a formal computer science perspective. Yes of course, there are some difficult details to be worked out regarding the extent to which existing RDF semantics can be layered on, and how to make these proposed layers compatible. I’m omitting details here to try and give as simple an overview as possible. And it also has to be said, one has to be pragmatic here. People are already making property graphs and RDF graphs conforming to the simple structures I’m describing here. Just look at Wikidata and how it handles (or rather, ignores) OWL. I’m just the messenger here, not some semantic anarchist trying to blow things up. Rather than worrying about whether such and such a fragment of FOL is decidable (which lets face it is not that useful a property in practice) let’s instead focus on coming up with pragmatic standards that are compatible with the way people are already using technology!

 

 

 

 

 

 

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