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RDFS Entailment Rules (1)

\[\frac{}{u \quad a \quad x \quad .} \qquad \mathrm{rdfax}\]
for all RDFS axiomatic triples \(u \; a \; x \; .\)

\[\frac{u \quad a \quad l \quad .}{\mathit{\_\!\!:\!\!n} \quad \verb|rdf:type| \quad \verb|rdfs:Literal| \quad .} \qquad \mathrm{rdfs1}\] with \(\mathit{\_\!\!:\!\!n}\) as usual

\[\frac{a \quad \verb|rdfs:domain| \quad x \quad . \qquad u \quad a \quad y \quad .}{u \quad \verb|rdf:type| \quad x \quad .} \qquad \mathrm{rdfs2}\]
\[\frac{a \quad \verb|rdfs:range| \quad x \quad . \qquad u \quad a \quad v \quad .}{v \quad \verb|rdf:type| \quad x \quad .} \qquad \mathrm{rdfs2}\]
\[\frac{u \quad a \quad x \quad .}{u \quad \verb|rdf:type| \quad \verb|rdfs:Resource| \quad .} \qquad \mathrm{rdfs4a}\]
\[\frac{u \quad a \quad v \quad .}{v \quad \verb|rdf:type| \quad \verb|rdfs:Resource| \quad .} \qquad \mathrm{rdfs4b}\]

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