## Algebraic Semiotics: A Relational Theory of Meaning

If you’re interested in the categories ontology mentioned in my post called “On a New List of Categories” and you’re looking for some background, check out Joseph Goguen’s work on algebraic semiotics. As described by Goguen in “On Notation” Peirce’s semiotics forms the basis for a relational theory of meaning for algebraic specifications.

Today, RDF semantics are based in model theory. Model theory defines semantics as an interpretation of the structures in RDF and OWL from which machines can make the same, or consistent, inferences. That is, the syntax of a system is formally correct. A consistent, or similarly coherent, interpretation is assumed to represent the truth in terms of a boolean valuation. But this coherence says nothing about the correspondence of the structures with, or their relation to, the world in which we live. That relation is at best an approximation. They could be totally wrong and still be consistent. (aka. not true)

One may hope to extend RDF semantics with a correspondence theory of the truth so that meaning on the semantic web squares with what us regular folks think of as meaning. That is quite a challenge. As Goguen suggestsĂ‚Â with algebraic specifications, one could hope to use Peirce’s semiotics to propose a theory of meaning on the semantic web. In Ontology, Metadata and Semiotics, John Sowa describes the Internet as a “giant semiotic system.”

The categories ontology needs a bit of work and will for some time. LBase provides the foundation from which new RDF vocabularies can be built. In the coming months I hope to extend the categories ontology with some of Peirce’s later works where his theory of semiotics is fully developed.

Stay tuned !