Giovanni Casini and Umberto Straccia.
A Minimal Deductive System for RDFS with Negative Statements .
In Proceedings of the 19th International Conference on
Principles of Knowledge Representation and Reasoning (KR 2022),
IJCAI Organization, pages 351--361, 2022.
Abstract:
The triple language RDFS is designed to represent and reason with
positive statements only (e.g., "antipyretics are drugs"). In this
paper, we extend RDFS to deal with various forms of negative
statements under the Open World Assumption (OWA). To do so, we
consider ρdf, a minimal, but significant RDFS fragment that covers
all essential features of RDFS, and then extend it to
ρdf¬⊥, 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
features of our proposal are: (i) ρdf¬⊥ remains
syntactically a triple language by extending ρdf 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 ρdf¬⊥ knowledge base is satisfiable; (iv) the ρdf¬⊥ entailment decision procedure is obtained from
ρdf via additional inference rules favouring
a potential implementation; and (v) deciding entailment in ρdf¬⊥ ranges from P to NP.