KR2022Proceedings of the 19th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning

Haifa, Israel. July 31–August 5, 2022.

Edited by

ISSN: 2334-1033
ISBN: 978-1-956792-01-0

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Copyright © 2022 International Joint Conferences on Artificial Intelligence Organization

A Minimal Deductive System for RDFS with Negative Statements

  1. Umberto Straccia(ISTI-CNR)
  2. Giovanni Casini(ISTI-CNR, CAIR, University of Cape Town)


  1. Ontology formalisms and models
  2. KR and the Web, Semantic Web
  3. Knowledge representation languages


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.