RDFS Idioms for the Working Semiotician

I’m fresh back from Spain where I enjoyed the last few weeks on my honeymoon. I had some time to read Dean Allemang and Jim Hendler’s Semantic Web for the Working Ontologist (SWWO). Great book, highly recommended! SWWO provides some nice insights into RDFS patterns and I wanted to develop a worked example in RDFS that complements the previous example here in OWL-DL.

Like the previous example, the problem is to specify an ontology in the semiotic domain where the reasoner infers meaning from the model. By introducing the semiotic domain into our model we get more than interpretation based on RDF model theory and classical logic. We get meaning it in its fullest sense because the reasoner infers membership of an individual in the class conception from its the representation of an object by a sign. Unlike the prior example, this time I avoid inferring Sign as a sub class of Conception by using a few of Dean’s neat patterns and restricting the reasoning to RDFS.

To introduce the semiotic domain into the model I specify Object, Sign and Conception as sub classes of rdfs:Resource, then I specify relations between pairs of these resources as follows:

sem:Object sem:resolves sem:Conception

sem:Sign sem:represents sem:Object

sem:Conception sem:signifies sem:Sign

This most simple expression of the semiotic domain says that a sign represents an object, the conception signifies the meaning of the sign and the object resolves the conception. For more on what is commonly known as the Triangle of Meaning, see Ogden and Richards here.

To introduce the first idiom, Typing Data by Usage (see page 98), I assert the triples

sem:represents rdf:type rdf:Property

sem:represents rdfs:domain sem:Sign

then assert the individual

sem:Icon sem:represents sem:Likeness

from which the reasoner infers, that

sem:Icon rdf:type sem:Sign

We know from Peirce’s What is a Sign? that Icons are just one example of a Sign. Icons resemble, or represent, the likeness of an object. As is appropriate, I assert that Icon has the property represents and the RDFS reasoner appropriately infers that Icon is an instance of Sign. Nice!

The next idiom uses the Mutual SubPropertyOf pattern (see page 118). I justify the use of this pattern below, but first, here are the triples themselves.

sem:represents rdfs:subClassOf sem:signifies

sem:signifies rdfs:subClassOf sem:represents

So how do I justify Mutual SubPropertyOf? Consider Peirce’s relate and correlate. Peirce describes an interpretant as a mediating representation of correspondence between the relate and correlate where correspondence includes both concurrence and opposition. To keep the inferences withing RDFS, here I make the strong commitment of equivalence, just one of the possible relations implied by Peirce’s interpretant. For more on interpretants, see On a New list of Categories Sections 9 – 14.

All we need to do now is apply the Typing Data by Usage pattern again. This time I assert Conception as the domain of signifies.

sem:signifies rdfs:domain sem:Conception

As expected the RDFS reasoner infers the following new triples:

1. Through Mutual SubPropertyOf the equivalence relation expressed as owl:equivalentProperties.

sem:represents owl:equivalentProperty sem:signifies

sem:signifies owl:equivalentProperty sem:represents

2. Also through Mutual SubPropertyOf the reasoner infers the domains of the respective subProperties:

sem:signifies rdfs:domain sem:Sign

sem:represents rdfs:domain sem:Conception

3. Most importantly, the reasoner infers both that Icon signifies Likeness and that Icon is an instance of Conception.

sem:Icon sem:signifies sem:Likeness

This is our first glimpse of an important result. Icon, an instance of Sign by the property represents, now signifies the meaning of Likeness.

And finally

sem:Icon rdf:type sem:Conception

This inference demonstrates a fundamental result: the meaning of a Sign is inferred when Icon, an instance, is inferred to be a member of the class Conception.

This example was developed in TopBraid Composer. After a brief orientation Composer has become a very important part of my modeling toolkit. I highly recommend it! Though because these results are standard RDFS inferencing your Sesame and other open source tools should do the trick as well. You can find the sample ontology here.

So, how can this be used? Recall from SWWO that the Simple Knowledge Organization System models meaningby simply asserting a preferred and alternate symbol for a concept. The idioms defined above offer the advantages over SKOS of using RDFS inferencing to infer the meaning of a sign through the semiotic domain which SKOS does not. In fact, most knowledge representation approaches today do not effectively differentiate Sign and Conception. So, these RDFS idioms can be used to advance the state of vocabulary and thesaurus management. Also, information technology architects are often called on to manage models in different languages at Enterprise scale. The idioms above are also useful in Enterprise-wide model management and the discovery of relationships among disparate model throughout the enterprise.  This result is also significant to mashups in general and Linked Data specifically, so I have added a recipe to my mashup cookbook, check the mashup cookbook for recipe #2!

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