The State of the Semantic Web: Representation and Realism
Danny Ayers made a request for comments on the state of the semantic web a few weeks ago. I’ll preface this post by saying the state of the semantic web is very good by which I mean design decisions were made early on that ensured a vibrant academic research base, a broad marketplace for technology transfer and an eager community of technology providers to realize the vision of a web of meaning. I’m personally very positive overall on the state of the semantic web. That being said it’s time to sharpen my pencil a bit and offer a critique on a few of the finer points of the state of the semantic web: representation and realism.
The state of the semantic web depends on its model theory. As I describe below in my post titled Why Meaning Comes in 3s, the model theory underlying RDF semantics and therefore the semantic web is based on Alfred Tarski’s Semantic Conception of Truth. In the Semantic Conception of Truth, Tarski defines truth in terms of what he calls material adequacy. Material adequacy implies three things: 1) sentences are objects in the world; 2) formal languages like RDF fully interpret these sentences; and 3) the semantics of the web is based not only on the boolean valuation of triples in RDF that fully interpret these sentences, but also the approximation of the world by those sentences.
RDF model theory establishes a framework for web semantics, though a fragile one, in light of the Architecture of the World Wide Web (AWW) circa 2004. We use sentences as more than objects in the world. They also serve as either our denotation, or interpretation of the world, or both and often interchangeably. For more on material adequacy see Speaking About Signs. Better distinction between object, denotation and interpretation would improve the AWW. Better alignment between AWW and RDF model theory would improve the semantics of the web.
All this being said, the Semantic Conception of Truth, on which RDF model theory is based, is consistent with our mechanistic approach to science that we inherit from Descartes, Newton, etc. The general scenario is as follows: We need to understand the world, we observe phenomena, we build a model and we validate whether the model explains the phenomena. So, these assumptions, our Semantic Conception of Truth, are our mechanism for representation and realism.
Just a few more points on Tarski’s model theory.
1. In addition to material adequacy, Tarki’s model theory also defines truth in terms of what’s formally correct. Formal correctness is the foundation for inference and reasoning on the semantic web. Although this post is mostly about Tarski’s model theory in terms of material adequacy, I’ll comment that it’s important to differentiate the standard description logic reasoning services (classification, realization, subsumption and consistency checking) from the reasoning services of theorem provers: unification, resolution, skolemization and modus ponens. And hope for additional reasoning services such as defeasibility, incremental and probablistic reasoning to evolve in the description logic community to complement the standard services already available.
2. Tarski uses the term meaning throughout the Semantic Conception of Truth. He properly concludes that his definition of truth informs the theoretical foundation of semantics. But, he also acknowledges the need to better explain other semantic concepts like designates, satisfies, defines, consequence, synonymy and meaning.
3. RDF model theory also defers on establishing the meaning of an RDF term. The introduction reads: “Exactly what is considered to be the ‘meaning’ of an assertion in RDF or RDFS in some broad sense may depend on many factors, including social conventions, comments in natural language or links to other content-bearing documents. Much of this meaning will be inaccessible to machine processing and is mentioned here only to emphasize that the formal semantics described in this document is not intended to provide a full analysis of ‘meaning’ in this broad sense; that would be a large research topic. The semantics given here restricts itself to a formal notion of meaning which could be characterized as the part that is common to all other accounts of meaning, and can be captured in mechanical inference rules.”
4. Scott Soames argues that attempts to derive a theory of meaning from Tarski’s theory of truth have failed. In his paper titled Truth and Meaning in Perspective, Soames reviews the literature of Quine, Chomsky and Davidson and concludes the interpretation, not representation provides the foundation for a theory of meaning. Of course in computer science we recognize both operational and denotational semantics to establish meaning.
For some an interesting discussion regarding #3 and #4, see this thread on the ontolog-forum. Follow the thread for comments from Pat Hayes, Chris Menzel and John Sowa.
One more point on realism. Barry Smith in his Realism Approach to the Evolution of BioMedical Ontologies argues that concepts should not be used in ontologies, RDF or otherwise, because the intent of ontology is to describe things in the world: the subject of ontology is realism. What Smith argues is that introducing concepts into ontologies tends words idealism, that it is not possible to adequately define concepts and, but it is possible to define portions of reality. Smith then describes issues in information provenance and effectivity. First, I think defining concepts and reality are probably at the same level of magnitude. At least it is for me, so I think Smith’s argument against concepts should be seen in that light. Also, contrary to his assertion, there is substantial literature on defining concepts. Joseph Goguen’s What is a Concept stands as a good example and Smith’s approach directly contradicts the practice of the description logic community in which the term concept is used throughout the literature. Also if we follow Soames’s reasoning, representation and realism will not support a theory of meaning. A detailed analysis of Tarski’s Semantic Conception of Truth reveals enough challenges with representation and realism. If we follow Smith’s suggestion and disallow concepts in ontology, we disallow interpretation and a theory of meaning for the semantic web. So, I’m concerned that Smith’s realism would limit the breadth of interpretation in the semantic web.
So, what does all this mean to the state of the semantic web ?
Again, good things in general. Good decisions were made early on and the conditions are right for success. The good news is RDF has a formal model theory through which we can can properly understand the implications of truth and meaning. Representation and realism are the order of the day in science as they are on the semantic web. But, there’s much work to be done in developing an approach to meaning by adding the notion of interpretation to our model theory and that’s the work of semiotics which I’ll describe in an upcoming post !