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Introducing Grades in Deontic Logics

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Deontic Logic in Computer Science (DEON 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5076))

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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 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.

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Authors and Affiliations

  1. Univ. Autònoma de Barcelona, 08193, Bellaterra, Spain

    Pilar Dellunde

  2. IIIA - CSIC, 08193, Bellaterra, Spain

    Pilar Dellunde & Lluís Godo

Authors
  1. Pilar Dellunde
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  2. Lluís Godo
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Ron van der Meyden Leendert van der Torre

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© 2008 Springer-Verlag Berlin Heidelberg

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Dellunde, P., Godo, L. (2008). Introducing Grades in Deontic Logics. In: van der Meyden, R., van der Torre, L. (eds) Deontic Logic in Computer Science. DEON 2008. Lecture Notes in Computer Science(), vol 5076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70525-3_19

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  • DOI: https://doi.org/10.1007/978-3-540-70525-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70524-6

  • Online ISBN: 978-3-540-70525-3

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