Form n3

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Description: This article gives an operational semantics for Notation3 (N3) and some RDF properties for expressing logic. These properties, together with N3's extensions of RDF to include variables and nested

This article gives an operational semantics for Notation3 (N3) and some RDF properties for expressing logic. These properties, together with N3's extensions of RDF to include variables and nested graphs, allow N3 to be used to express rules in a web environment.

This is an informal semantics in that should be understandable by a human being but is not a machine readable formal semantics. This document is aimed at a logician wanting to a reference by which to compare N3 Logic with other languages, and at the engineer coding an implementation of N3 Logic and who wants to check the detailed semantics.

These properties are not part of the N3 language, but are properties which allow N3 to be used to express rules, and rules which talk about the provenance of information, contents of documents on the web, and so on. Just as OWL is expressed in RDF by defining properties, so rules, queries, differences, and so on can be expressed in RDF with the N3 extension to formulae.

The prefix log: is used below as shorthand for the namespace < >. See the schema for a summary.

The motivation of the logic was to be useful as a tool in in open web environment. The Web contains many sources of information, with different characteristics and relationships to any given reader. Whereas a closed system may be built based on a single knowledge base of believed facts, an open web-based system exists in an unbounded sea of interconnected information resources. This requires that an agent be aware of the provenance of information, and responsible for its disposition. The language for use in this environment typically requires the ability to express what document or message said what, so the ability to quote subgraphs and match them against variable graphs is essential. This quotation and reference, with its inevitable possibility of direct or indirect self-reference, if added directly to first order logic presents problems such as paradox traps. To avoid this, N3 logic has deliberately been kept to limited expressive power: it currently contains no general first order negation. Negated forms of many of the built-in functions are available, however.

A goal is that information, such as but not limited to rules, which requires greater expressive power than the RDF graph, should be sharable in the same way as RDF can be shared. This means that one person should be able to express knowledge in N3 for a certain purpose, and later independently someone else reuse that knowledge for a different unforeseen purpose. As the context of the later use is unknown, this prevents us from making implicit closed assumptions about the total set of knowledge in the system as a whole.

Further, we require that other users of N3 in the web can express new knowledge without affecting systems we have already built. This means that N3 must be fundamentally monotonic: the addition of new information from elsewhere, while it might cause an inconsistency by contradicting the old information (which would have to be resolved before the combined system is used), the new information cannot silently change the meaning of the original knowledge.

The non-monotonicity of many existing systems follows from a form of negation as failure in which a sentence is deemed false if it not held within (or, derivable from) the current knowledge base. It is this concept of current knowledge base, which is a variable quantity, and the ability to indirectly make reference to it which causes the non-monotonicity. In N3Logic, while a current knowledge base is a fine concept, there is no ability to make reference to it implicitly in the negative. The negation provided is the ability only for a specific given document (or, essentially, some abstract formula) to objectively determine whether or not it holds, or allows one to derive, a given fact. This has been called Scoped Negation As Failure (SNAF).

The syntax of N3 is defined by the context-free grammar This is available in machine-readable form in Notation3 and RDF/XML.

The top-level production for an N3 document is <>.

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