Linked data got some attention over the past year. Both leading technologists and policy makers are coming to recognize that a smarter Web is a better Web. As I recently wrote in Linking Open Data: An Emerging Practice Area for the Semantic Web today’s open government initiatives in both the US and the UK share common values. When a technology becomes available to advance public policy great things can happen.
At O’Reilly Media’s recent Gov2.0 Summit Beth Noveck explained three areas of President Obama’s Open Government Directive: transparency, participation and collaboration. What Beth said that was especially relevant to Linked Data was to relate collaboration to platforms. Beth’s examples like iTunes were compelling, but as we know from Sir Tim Berners-Lee’s appointment to advise policy makers in the UK Cabinet Office on public information delivery, Linked Data is THE platform for internet-scale collaboration.
But this post isn’t about technology policy, it’s about interpretants and interpretation. If we expect Linked Data to become highly effective it will be essential to develop a much richer understanding of interpretants and interpretation on the Web. So in this post I’ll: 1) elaborate on the Triangle of Meaning (the Triangle) first clarifying its terminology by introducing the interpretant and explaining the meaning of each edge of the Triangle; 2) suggest a few refinements to the language used in W3C’s Architecture of the World Wide Web and Cool URIs for the Semantic Web that are especially relevant to Linked Data; 3) explain the relevance of the Triangle to current RDF Model Theory; and 4) propose further elaboration of the Triangle using Category Theory, Haskell and Higher Order Logic using Isabelle/HOL to advance the state of Linked Data. Sound ambitious? Read on brave traveler, but don’t forget to bring a towel.
For a primer on the following material read my recent post titled RDFS Idioms for the Working Semiotician in which I propose a useful idiom in the semiotic domain using the Typing Data by Usage and Mutual SubPropertyOf patterns from Dean Allemang and Jim Hendler’s Semantic Web for the Working Ontologist to infer that an Icon which is an instance of a Sign of an Object is the equivalent of an Icon which is an instance of its Conception.
Figure 1.
The term Conception implies the interpretation of a Sign by a human or animal, but Linked Data requires the interpretation of Signs by machines. In his later work instead of the term Conception, Peirce uses the term Interpretant: “I define a sign as something, A, which brings something, B, its interpretant, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. In this definition I make no more reference to anything like the human mind than I do when I define a line as the place within which a particle lies during a lapse of time.” Figure 1 illustrates the Triangle with Interpretant substituted for Conception. It also elaborates on prior illustrations by listing its edges. Each edge is comprised of two inverse functions. The inverse functions form outer and inner paths. The clockwise outer path traces the metaphysics of the Triangle. The counter-clockwise inner path traces an existent.
I’ll return to the edges of the Triangle shortly. For now I’ll use the nodes of the Triangle substituting Interpretant for Conception to suggest refinements to the language used in W3C’s Architecture of the World Wide Web (AWWW) and Cool URIs for the Semantic Web (CUSW). The following suggestions will serve to inform a long standing discussion among members of W3C about URIs and resources.
There’s no doubt the URI serves as useful syntax for identification on the Web. But, the term resource does not serve us well. Because URIs serve various purposes on the Web, we need to understand them according to their purpose. AWWW and CUSW already do some of that, but it can be done better. Calling everything a resource doesn’t help. Here are a few important refinements stated in terms of the Triangle:
Information resources are really Objects: bits and bytes that exist in the machine. To precisely express their extent, they would be better called Information Objects. But before I continue here’s what I mean when I use the term extent. Extent defines the boundaries where an Interpretant, Sign or Object can exist. Extent can be either machine, external world or consciousness. So the extent of Information Objects is machine. Their metaphysics and existence is represented in the machine by both the outer and inner paths of the Triangle. Non-Information Resources are Objects too, but they cannot be materialized inside the machine. Their extent is external world: they exist in the external world. They can only be represented in the machine.
303 redirects do nothing to change the extent of objects. There’s no way to overcome our inability to materialize non-Information Objects inside the machine. A redirect to a description of an object is simply another Sign or representation of the Object. Science fiction intentionally blurs this distinction and that makes great entertainment, but fuzzy thinking. Remember Neo in The Matrix? Neo is shown to be reading Baudrillard’s Simulacra and Simulation (SS). In SS Baudrillard warns against what he calls the Precession of the Simulacra. The precession is more dangerous than fuzzy thinking. Failing to understand this distinction disconnects us from reality and truth.
The term Information Object should replace Information Resource, then we can call plain old objects just that: Objects. Also, this replacement allows us to drop the awkward term Indirect Identification which actually means represents which is precisely what the Sign does for the Object.
The description logic community has a long standing practice of using the term Concept in both constructors and language classification. However, this community neither differentiates concepts from signs or from objects. Nor does it distinguish concepts from interpretants. Of course the extent of concept is the Consciousness. Signs exist in the machine and the external world. Interpretants exist in the machine and the Consciousness.
Now that I’ve introduced interpretants and suggested refinements to the current language in AWWW and CUSW, how could the Triangle apply to an interpretation in RDF? First, the interpretation in model theory is not the interpretant of the Triangle. In RDF, as in classical logic, interpretation is defined as follows: An interpretation for a language L is a structure in a domain and a function that preserves truth between symbols in the language L and the objects to which they refer. For model theory, the objects to which the symbols refer are the objects in the formal system. See Tarski’s system T in his Semantical Conception of Truth. Because RDF model theory implies a denotational semantics with a boolean valuation.
To advance Linked Data we need to extend an interpretation based on a boolean valuation to include meaning. To extend truth with meaning we could use the symbols of logic – connectives, constants, predicates and function, etc – AND add the nodes of the Triangle – Interpretant, Sign and Object according to their proper extent AND add the edges of the Triangle.
However, even with this addition we require further analysis before we conclude that we’ve extended truth, or boolean valuation, with meaning. Does this extension refute Searle’s Chinese Room Argument? Does it provide something new in relation to the Turing Test? Does a signature enhanced with the Triangle allow Semiotic Morphisms under Goguen’s Theory of Institutions? I believe it is too early to answer these questions, but we can recognize the value of a separate semiotic domain and its role in recognizing well defined extents for Linked Data.
To wrap up this post, there are additional characteristics of the Triangle to be explained to satisfy Peirce’s definition. To paraphrase, A brings something B into correspondence with something C in which itself stands to C. So, these additional characteristics are most likely commutativity of the Triangle and the composition of the relations that make up the edges. Specifically, each edge is the composition of the two complementary edges of the Triangle. Category Theory provides a useful mechanism to explore these characteristics. Over the next few months I will develop exercises in Haskell to demonstrate these characteristics of the Triangle. Isabelle/HOL looks like a great prover and it now comes with a new utility called Haskabelle that translates Haskell into ML.
That pretty much covers interpretants and interpretation. Stay tuned for interim results in Category Theory, Haskell and Isabelle/HOL.
