Contrary‐to‐duty reasoning with preference‐based dyadic obligations

  • Leendert van der Torre
  • Yao‐Hua Tan

DOI: 10.1023/A:1018975332469

Cite this article as:
van der Torre, L. & Tan, Y. Annals of Mathematics and Artificial Intelligence (1999) 27: 49. doi:10.1023/A:1018975332469


In this paper we introduce Prohairetic Deontic Logic (PDL), a preference‐based dyadic deontic logic. In our preference‐based interpretation of obligations “α should be (done) if β is (done)” is true if (1) no ¬α ∧ β state is as preferable as an α ∧ β state and (2) the preferred β states are α states. We show that this representation solves different problems of deontic logic. The first part of the definition is used to formalize contrary‐to‐duty reasoning, which, for example, occurs in Chisholm’s and Forrester’s notorious deontic paradoxes. The second part is used to make deontic dilemmas inconsistent.

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Leendert van der Torre
    • 1
  • Yao‐Hua Tan
    • 2
  1. 1.Department of Artificial Intelligence, Faculty of SciencesVrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.EuridisErasmus University RotterdamRotterdamThe Netherlands