Semantics of Notation3 Logic: A Solution for Implicit Quantification

  • Dörthe ArndtEmail author
  • Ruben Verborgh
  • Jos De Roo
  • Hong Sun
  • Erik Mannens
  • Rik Van De Walle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9202)


Since the development of Notation3 Logic, several years have passed in which the theory has been refined and used in practice by different reasoning engines such as cwm, FuXi or EYE. Nevertheless, a clear model-theoretic definition of its semantics is still missing. This leaves room for individual interpretations and renders it difficult to make clear statements about its relation to other logics such as DL or FOL or even about such basic concepts as correctness. In this paper we address one of the main open challenges: the formalization of implicit quantification. We point out how the interpretation of implicit quantifiers differs in two of the above mentioned reasoning engines and how the specification, proposed in the W3C team submission, could be formalized. Our formalization is then put into context by integrating it into a model-theoretic definition of the whole language. We finish our contribution by arguing why universal quantification should be handled differently than currently prescribed.


Notation3 Formal semantics Quantification Logic Semantic web 


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  1. 1.
    FuXi 1.4: A Python-based, bi-directional logical reasoning system for the semantic web.
  2. 2.
    Beckett, D., Berners-Lee, T., Prud’hommeaux, E., Carothers, G.: Turtle - Terse RDF Triple Language. w \(_3\) c Recommendation, February 2014.
  3. 3.
    Berners-Lee, T.: cwm (2000–2009).
  4. 4.
    Berners-Lee, T.: Notation 3 logic (2005).
  5. 5.
    Berners Lee, T.: Re: Implicit quantification in n3. Public-cwm-talk (2015).
  6. 6.
    Berners-Lee, T., Connolly, D.: Notation3 (n \(_3\)): A readable RDF syntax. w \(_3\) c Team Submission, March 2011.
  7. 7.
    Berners-Lee, T., Connolly, D., Kagal, L., Scharf, Y., Hendler, J.: nthreelogic: A logical framework for the World Wide Web. Theory and Practice of Logic Programming 8(3), 249–269 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Clocksin, W.F., Mellish, C.S.: Programming in PROLOG. Springer (1994)Google Scholar
  9. 9.
    Cyganiak, R., Wood, D., Lanthaler, M.: rdf 1.1: Concepts and Abstract Syntax. w \(_3\) c Recommendation, February 2014.
  10. 10.
    De Roo, J.: Euler yet another proof engine, (1999–2014).
  11. 11.
    Duerst, M., Suignard, M.: Internationalized Resource Identifiers (IRIs), January 2005.
  12. 12.
    Hayes, P.J., Patel-Schneider, P.F.: rdf 1.1 Semantics. w \(_3\) c Recommendation, February 2014.
  13. 13.
    Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer-Verlag New York Inc., Secaucus (1987)CrossRefzbMATHGoogle Scholar
  14. 14.
    Pérez, J., Arenas, M., Gutierrez, C.: Semantics and complexity of SPARQL. ACM Trans. Database Syst. 34(3), 16:1–16:45 (2009). CrossRefGoogle Scholar
  15. 15.
    Prud’hommeaux, E., Seaborne, A.: sparql Query Language for rdf. w \(_3\) c Recommendation, January 2008.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Dörthe Arndt
    • 1
    Email author
  • Ruben Verborgh
    • 1
  • Jos De Roo
    • 2
  • Hong Sun
    • 2
  • Erik Mannens
    • 1
  • Rik Van De Walle
    • 1
  1. 1.Ghent University – iMinds – Multimedia LabLedeberg-GhentBelgium
  2. 2.Agfa HealthcareGhentBelgium

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