Introducing grades in deontic logics

Pilar Dellunde*, Lluís Godo

*Corresponding author for this work

Research output: Chapter in BookChapterResearchpeer-review

10 Citations (Scopus)


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 r → NΦ or r → PΦ, 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.

Original languageEnglish
Title of host publicationDeontic Logic in Computer Science - 9th International Conference, DEON 2008, Proceedings
Number of pages15
Publication statusPublished - 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5076 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Deontic Logic
  • Fuzzy Logic
  • Institutions
  • Norms


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