  The triple language RDFS is designed to represent and reason with
\emph{positive} statements only (e.g."antipyretics are drugs").
  In this paper we show how to extend RDFS to express and reason with various
forms of negative statements under the Open World Assumption (OWA). To do so,
we start from $\rho df$, a minimal, but significant RDFS fragment that covers
all essential features of RDFS, and then extend it to $\rho df_\bot^\neg$,
allowing express also statements such as "radio therapies are non drug
treatments", "Ebola has no treatment", or "opioids and antipyretics are
disjoint classes". The main and, to the best of our knowledge, unique features
of our proposal are: (i) $\rho df_\bot^\neg$ remains syntactically a triple
language by extending $\rho df$ with new symbols with specific semantics and
there is no need to revert to the reification method to represent negative
triples; (ii) the logic is defined in such a way that any RDFS reasoner/store
may handle the new predicates as ordinary terms if it does not want to take
account of the extra capabilities; (iii) despite negated statements, every
$\rho df_\bot^\neg$ knowledge base is satisfiable; (iv) the $\rho df_\bot^\neg$
entailment decision procedure is obtained from $\rho df$ via additional
inference rules favouring a potential implementation; and (v) deciding
entailment in $\rho df_\bot^\neg$ ranges from P to NP.
