Introducing Grades in Deontic Logics

  • Authors:
  • Pilar Dellunde;Lluís Godo

  • Affiliations:
  • Univ. Autònoma de Barcelona, Bellaterra, Spain 08193 and IIIA - CSIC, Bellaterra, Spain 08193;IIIA - CSIC, Bellaterra, Spain 08193

  • Venue:
  • DEON '08 Proceedings of the 9th international conference on Deontic Logic in Computer Science
  • Year:
  • 2008

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Abstract

In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula 驴驴 SDL, our language contains formulas of the form $\overline{r} \to N\Phi$ or $\overline{r} \to P\Phi$, where r驴 [0, 1], expressing that the preference or probability degree respectively of a norm 驴is at least r. We present sound and complete axiomatisations for these logics.