Current Slide

Small screen detected. You are viewing the mobile version of SlideWiki. If you wish to edit slides you will need to use a larger device.

RDFS Semantic Conditions (1)

Define (for a given RDF Interpretation \(\mathcal{I}\)):

  • \(\mathrm{I_{CEXT}} : \mathit{IR} \longrightarrow 2^\mathit{IR}\)—we define \(\mathrm{I_{CEXT}}(y)\) to contain exactly those elements \(x\) for which \(\langle x, y \rangle\) is contained in \(\mathrm{I_{EXT}}(\verb|rdf:type|)^\mathcal{I}\). The set \(\mathrm{I_{CEXT}}(y)\) is then also called the (class) extension of \(y\).
  • \(\mathit{IC}=\mathrm{I_{CEXT}}(\verb|rdfs:Class|^\mathcal{I})\)
  • \(\mathit{IR}=\mathrm{I_{CEXT}}(\verb|rdfs:Resource|^\mathcal{I})\)
  • \(\mathit{LV}=\mathrm{I_{CEXT}(\verb|rdfs:Literal|^\mathcal{I})}\)
  • If \(\langle x, y\rangle\ \in \mathrm{I_{EXT}}(\verb|rdfs:domain|^\mathcal{I})\) and \(\langle u, v \rangle \in \mathrm{I_{EXT}}(x)\), then \(u \in \mathrm{I_{CEXT}}(y)\)
  • If \(\langle x, y\rangle\ \in \mathrm{I_{EXT}}(\verb|rdfs:range|^\mathcal{I})\) and \(\langle u, v \rangle \in \mathrm{I_{EXT}}(x)\), then \(v \in \mathrm{I_{CEXT}}(y)\)
  • \(\mathrm{I_{EXT}}(\verb|rdfs:subPropertyOf|^\mathcal{I})\) is reflexive and transitive on \(\mathit{IP}\).

Speaker notes:

Content Tools

Sources

There are currently no sources for this slide.