Peirce’s Semiotics in the Alignment of Formal Specifications Using Shared Concepts

In To Pragmaticism and Beyond I describe an ambitious plan to develop an emergent theory of meaning. I begin that plan here by describing how introducing semiotics into the alignment and unification of domain specific ontologies, also called local ontologies, serves to better specify implicit relationships among those ontologies.

Post-hoc ontology alignment has recently and will continue to gain prominence in response to design principles of complex systems. Approaches to post-hoc alignment include automated mapping using a variety of approaches most notably the IF-Map approach and the alignment and unification approach described in Robert Kent’s Information Flow Framework. Other approaches include alignment of the object and metalanguages based on matching, mapping, distance measures and Galois connections.

All very cool stuff, however the results of ontology alignment and unification are often perceived as underwhelming for two reasons: 1. there’s insufficient information in domain ontologies on which to base alignment because they were conceived and specified separately; and 2. the model theory on which the alignment is based is grounded in a semantic theory of truth, not meaning. I already describe #2 in State of the Semantic Web:Representation and Realism and I’ll return to #2 in a later post. Regarding #1, standardization may cause our representations to converge locally. Public initiatives such as Dublin Core Metadata Initiative is a good example as are the ongoing Linked Data efforts related to Semantic Web based repositories such as DBPedia and Science Commons as are private initiatives such as MetaWeb‘s Freebase. Given this list of standardization initiatives even casual observers ask the obvious question: How then would one align ontologies from Dublin Core, DBPedia, Science Commons and Freebase? Unfortunately, any standardization approach reveals the paradox that because the scope and reach of universality is unachievable in standardization, especially ontology specification, standardization implies opposition and mediation.

Faced with this paradox of standardization, ontologists can perform post-hoc annotations in which humans interpret the meaning of local terms and specify global ontologies that establish relations between local ontologies. This approach can be very effective presuming the availability of resources and cash. A casual observer would recognize again that this approach does not scale, but post-hoc alignment offers benefits over certain limitations implied by a Common Upper Ontology where local ontologies can only be defined once the global ontology has been defined.

One approach that has gained interest recently is the introduction of a global semiotic ontology based on the work of Charles Sanders Peirce. Peirce’s semiotics includes a) a system of signs that describes how language functions in human understanding; b) a system of triadic relations which exist within the system of signs; and c) an approach to categorization through which one can abstract the function of tokens in an object language into a useful types in a metalanguage. By wide interest I mean leading thinkers such as Joseph Goguen, John Sowa, Robert Kent and many others. Presumably this approach offers no advantages or disadvantages in automation. The value is in Peirce’s specification of the semiotic domain, its function in explaining how humans understand the world and its corollary in building more sophisticated models of machine understanding.

To explain this approach I’ll work out an example in OWL, but there’s no dependency on OWL in using this approach. I just so happened to be working with OWL a few years ago when I first developed the example. I encourage you to work out an example in your favorite language and post a comment.

Shared Concept Alignment of Functional Decomposition The figure illustrates the approach. Consider two specifications: first, the Federal Enterprise Architecture Business Reference Model defined by the Office of Management and Budget and second, the Business Enterprise Architecture defined by the Office of the Secretary of Defense. The naive Enterprise Architect as the question: How are these specifications aligned?

Simply put, BusinessArea and MissionArea are both functional areas specific to the domain of discourse. The green circle FunctionalArea acts as a symbol that represents the blue circle FunctionalDecomposition which is a concept shared between the specifications. In the example, the concept serves as an interpretant, the symbol as its representation and the terms BusinessArea and MissionArea as objects. The large blue ellipse indicates the boundary that separates the terminological space from the conceptual space.

The astute observer will recognize that using OWL SameAs is a degenerate case of the approach defined here. The SameAs relation established between BusinessArea and MissionArea serves as a clear example of Peirce’s thirdness or mediation. In fact, Tim Berner’s Lee describes and approach that he calls shared concept here. Tim’s example focuses strongly on the value of the URI – what a surprise – and importing Dublin Core. Feel free to share how you think the approaches compare.

The files that I specified to prove this approach are:

http://www.rickmurphy.org/fea-osd.owl

http://www.rickmurphy.org/fea-brm.owl

http://www.rickmurphy.org/dod-bea.owl

http://www.rickmurphy.org/categories.owl

I used Swoop and Pellet as the reference implementation, but you can probably use tools like Top Braid Composer and others. In terms of instructions, just point Swoop here. This is the fea-osd ontology, one of two that contains assertions and axioms derived from Peirce’s semiotics. The other is the categories ontology based on Peirce’s On a New List of Categories. Before you run Pellet, notice the categories import and the assertion that FunctionalDecomposition is a subclass of UniversalConception from categories. Then select FunctionalArea and notice the axiom that says that FunctionalArea is defined as the intersection of FunctionalDecomposition and the property called representation restricted to the value symbol. As above, this axiom means that FunctionalArea is the symbol representing the concept FunctionalDecomposition. When you turn on the Pellet reasoner the standard reasoning services (classification, realization, subsumption and consistency checks) begin to execute. When execution terminates, the type of FunctionalArea is inferred as a subclass of FunctionalDecomposition. In addition to demonstrating the value of Peirce’s semiotics, this example also serves to illustrate the use of a Curry-Howard correspondence of sorts for the Semantic Web.

So, I hope you enjoy the approach I’ve shown here. It demonstrates the value of Perice’s semiotics in ontology alignment and unification. It shows that a) OWL SameAs is a degenerate case of using a global semiotic domain ontology based on Peirce’s thirdness or mediation; b) the semiotic domain provides deeper insights into how machine understanding can model human understanding; and c) how to use type inferencing with the Pellet description logic reasoner. There’s much more to be done than what this small example demonstrates. This example is just the beginning of developing a semiotic domain. The example should be extended and I look forward to your comments.

I’ll be discussing this approach at the Washington, DC Semantic Web Meetup on December 11, 2008 and I hope to see you there !

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