Triadic Relations: An Algebra for the Semantic Web

Abstract

This paper introduces and develops an algebra over triadic relations (relations whose contents are only triples). In essence, the algebra is a severely restricted variation of relational algebra (RA) that is de.ned over relations with exactly three attributes and is closed for the same set of relations. In particular, arbitrary joins and Cartesian products are replaced by a single three-way join. Ternary relations are important because they provide the minimal, and thus most uniform, way to encode semantics wherein metadata may be treated uniformly with regular data; this fact has been recognized in the choice of triples to formalize the Semantic Web via RDF. Indeed, algebraic de.nitions corresponding to certain of these formalisms will be shown as examples.

An important aspect of this algebra is an encoding of triples, implementing a kind of rei.cation. The algebra is shown to be equivalent, over non-rei.ed values, to a restriction of Datalog and hence to a fragment of .rst order logic. Furthermore, the algebra requires only two operators if certain .xed in.nitary constants (similar to Tarski’s identity) are present. In this case, all structure is represented only in the data, that is, in the encodings that these in.nitary constants represent.