Introducing Grades in Deontic Logics

  • Pilar Dellunde
  • Lluís Godo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5076)


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 Φ ∈ SDL, our language contains formulas of the form \(\overline{r} \to N\Phi\) or \(\overline{r} \to P\Phi\), where r ∈ [0, 1], expressing that the preference or probability degree respectively of a norm Φ is at least r. We present sound and complete axiomatisations for these logics.


Deontic Logic Fuzzy Logic Norms Institutions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pilar Dellunde
    • 1
    • 2
  • Lluís Godo
    • 2
  1. 1.Univ. Autònoma de BarcelonaBellaterraSpain
  2. 2.IIIA - CSICBellaterraSpain

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