Friday, March 17, 2006

Math is hard!

I was complaining before about semantic web stuff being heavyweight? Here's a section from the SPARQL (RDF query language) specification:

2.5 Basic Graph Patterns

A basic graph patterns is a set of triple patterns and forms the basis of SPARQL query matching. Matching a basic graph pattern is defined in terms of generic entailment to allow for future extension of the language.

Definition: Basic Graph Pattern

A Basic Graph Pattern is a set of Triple Patterns.

Definition: E-entailment Regime

An E-entailment regime is a binary relation between subsets of RDF graphs.

A graph in the range of an E-entailment is called well-formed for the E-entailment.

This specification covers only simple entailment [RDF-MT] as E-entailment. Examples of other E-entailment regimes are RDF entailment [RDF-MT], RDFS entailment [RDF-MT], OWL entailment [OWL-Semantics].

Definition: Basic Graph Pattern equivalence

Two basic graph patterns are equivalent if there is a bijection M between the terms of the triple patterns that maps blank nodes to blank nodes and maps variables, literals and IRIs to themselves, such that a triple ( s, p, o ) is in the first pattern if and only if the triple ( M(s), M(p) M(o) ) is in the second.

This definition extends that for RDF graph-equivalence to basic graph patterns by preserving variables names across equivalent graphs

Now, this is not all that abstruse, but then I have a math degree and am used to it. Way back then I studied mathematical logic, thought it was fun but a lousy way to describe the world and a lousy model for computation. It seems to have triumphed, however, and now people are expected to speak that language (the RDF semantics spec is even worse). I have a hard time believing that working programmers (a set of which I myself am a member of, nowadays) are going to be gleefully soaking up all the model-theoretic semantic theory behind the semantic web.

Maybe I'm wrong, there are people willing to boil things down into understandability. This well-written article doesn't cover any sort of non-trivial queries however.

There seems to be a big gap between RDF-as-first-order-predicate-logic-with-model-theoretic-semantics and RDF-as-useful-flexible-emerging-data-standard. Looked at positively, it's a two-pronged thrust, from academia and hackerdom acting together.

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