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Ruben Verborgh

Semantics of Notation3 Logic: A solution for implicit quantification

by Dörthe Arndt, Ruben Verborgh, Jos De Roo, Hong Sun, Erik Mannens, and Rik Van de Walle

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.

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Published in 2015 in Proceedings of the 9th International RuleML Symposium.

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Cite this article easily using its BibTeX entry:

@inproceedings{arndt_ruleml_2015,
  author = {Arndt, D\"orthe and Verborgh, Ruben and De Roo, Jos and Sun, Hong and Mannens, Erik and Van de Walle, Rik},
  title = {Semantics of {Notation3} Logic: A solution for implicit quantification},
  booktitle = {Proceedings of the 9th International RuleML Symposium},
  series = {Lecture Notes in Computer Science},
  editor = {Bassiliades, Nick and Gottlob, Georg and Sadri, Fariba and Paschke, Adrian and Roman, Dumitru},
  volume = 9202,
  pages = {127--143},
  publisher = {Springer},
  year = 2015,
  month = jul,
  url = {http://link.springer.com/chapter/10.1007/978-3-319-21542-6_9},
}

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IEEE
D. Arndt, R. Verborgh, J. De Roo, H. Sun, E. Mannens, and R. Van de Walle, “Semantics of Notation3 Logic: A solution for implicit quantification,” in Proceedings of the 9th International RuleML Symposium, 2015, vol. 9202, pp. 127–143.
ACM
Dörthe Arndt, Ruben Verborgh, Jos De Roo, Hong Sun, Erik Mannens, and Rik Van de Walle. 2015. Semantics of Notation3 Logic: A solution for implicit quantification. In Nick Bassiliades, Georg Gottlob, Fariba Sadri, Adrian Paschke, & Dumitru Roman, eds. Proceedings of the 9th International RuleML Symposium. Lecture Notes in Computer Science. Springer, 127–143.
LNCS
Arndt, D., Verborgh, R., De Roo, J., Sun, H., Mannens, E., Van de Walle, R.: Semantics of Notation3 Logic: A solution for implicit quantification. In: Bassiliades, N., Gottlob, G., Sadri, F., Paschke, A., and Roman, D. (eds.) Proceedings of the 9th International RuleML Symposium. pp. 127–143. Springer (2015).
APA
Arndt, D., Verborgh, R., De Roo, J., Sun, H., Mannens, E., & Van de Walle, R. (2015). Semantics of Notation3 Logic: A solution for implicit quantification. In N. Bassiliades, G. Gottlob, F. Sadri, A. Paschke, & D. Roman (Eds.), Proceedings of the 9th International RuleML Symposium (Vol. 9202, pp. 127–143). Springer.
MLA
Arndt, Dörthe et al. “Semantics of Notation3 Logic: A Solution for Implicit Quantification.” Proceedings of the 9th International RuleML Symposium. Ed. Nick Bassiliades et al. Vol. 9202. Springer, 2015. 127–143. Print. Lecture Notes in Computer Science.

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