Synthese

, Volume 187, Issue 2, pp 623–660

Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]

  • Mathijs de Boer
  • Dov M. Gabbay
  • Xavier Parent
  • Marija Slavkovic
Article

DOI: 10.1007/s11229-010-9866-4

Cite this article as:
de Boer, M., Gabbay, D.M., Parent, X. et al. Synthese (2012) 187: 623. doi:10.1007/s11229-010-9866-4

Abstract

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985.

Keywords

Deontic LogicContrary to DutiesChisholm paradoxTwo dimensional temporal logic

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Mathijs de Boer
    • 3
  • Dov M. Gabbay
    • 1
    • 2
    • 3
  • Xavier Parent
    • 3
  • Marija Slavkovic
    • 3
  1. 1.King’s CollegeLondonUK
  2. 2.Bar Ilan UniversityRamat GanIsrael
  3. 3.Individual and Collective Reasoning Group, Computer Science and CommunicationsUniversity of LuxembourgLuxembourgUK