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Prohairetic Deontic Logic (PDL)

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Logics in Artificial Intelligence (JELIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1489))

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Abstract

In this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based dyadic deontic logic. An obligation ‘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 the different elements of this mixed representation solve different problems of deontic logic. The first part of the definition is used to formalize contrary-to-duty reasoning, that for example occurs in Chisholm’s and Forrester’s notorious deontic paradoxes. The second part is used to make dilemmas inconsistent. PDL shares the intuitive semantics of preference-based deontic logics without introducing additional semantic machinery such as bi-ordering semantics or ceteris paribus preferences.

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References

  1. C.E. Alchourrón. Philosophical foundations of deontic logic and the logic of defeasible conditionals. In J.-J. Meyer and R. Wieringa, editors, Deontic Logic in Computer Science: Normative System Specification, pages 43–84. John Wiley & Sons, 1993.

    Google Scholar 

  2. L. Åqvist. Good Samaritans, contrary-to-duty imperatives, and epistemic obligations. Noûs, 1:361–379, 1967.

    Article  Google Scholar 

  3. C. Boutilier. Conditional logics of normality: a modal approach. Artificial Intelligence, 68:87–154, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  4. A.L. Brown, S. Mantha, and T. Wakayama. Exploiting the normative aspect of preference: a deontic logic without actions. Annals of Mathematics and Artificial Intelligence, 9:167–203, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  5. B.F. Chellas. Modal Logic: An Introduction. Cambridge University Press, 1980.

    Google Scholar 

  6. R.M. Chisholm. Contrary-to-duty imperatives and deontic logic. Analysis, 24:33–36, 1963.

    Article  Google Scholar 

  7. R. Conte and R. Falcone. ICMAS’96: Norms, obligations, and conventions. AI Magazine, 18,4:145–147, 1997.

    Google Scholar 

  8. B.S. Firozabadhi and L.W.N. van der Torre. Towards an analysis of control systems. In H. Prade, editor, Proceedings of the ECAI’98, pages 317–318, 1998.

    Google Scholar 

  9. J.W. Forrester. Gentle murder, or the adverbial Samaritan. Journal of Philosophy, 81:193–197, 1984.

    Article  MathSciNet  Google Scholar 

  10. L. Goble. A logic of good, would and should, part 2. Journal of Philosophical Logic, 19:253–276, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. Goble. Murder most gentle: the paradox deepens. Philosophical Studies, 64:217–227, 1991.

    Article  Google Scholar 

  12. B. Hansson. An analysis of some deontic logics. In R. Hilpinen, editor, Deontic Logic: Introductionary and Systematic Readings, pages 121–147. D. Reidel Publishing Company, Dordrecht, Holland, 1971. Reprint from Noûs, 1969.

    Google Scholar 

  13. S.O. Hansson. A new semantical approach to the logic of preference. Erkenntnis, 31:1–42, 1989.

    Article  Google Scholar 

  14. S.O. Hansson. Defining “good” and “bad” in terms of “better”. Notre Dame Journal of Formal Logic, 31:136–149, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  15. S.O. Hansson. Preference-based deontic logic (PDL). Journal of Philosophical Logic, 19:75–93, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  16. S.O. Hansson. Situationist deontic logic. Journal of Philosophical Logic, 26:423–448, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  17. Z. Huang and M. Masuch. The logic of permission and obligation in the framework of ALX3: how to avoid the paradoxes of deontic logic. Logique et Analyse, 149, 1997.

    Google Scholar 

  18. H.G. Hughes and M.J. Creswell. A Companion to Modal Logic. Methuen, London, 1984.

    Google Scholar 

  19. F. Jackson. On the semantics and logic of obligation. Mind, 94:177–196, 1985.

    Article  MathSciNet  Google Scholar 

  20. R.E. Jennings. Can there be a natural deontic logic? Synthese, 65:257–274, 1985.

    Article  MathSciNet  Google Scholar 

  21. P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the KR’91, pages 357–367, 1991.

    Google Scholar 

  22. D. Lewis. Counterfactuals. Blackwell, Oxford, 1973.

    Google Scholar 

  23. D. Lewis. Semantic analysis for dyadic deontic logic. In S. Stunland, editor, Logical Theory and Semantical Analysis, pages 1–14. D. Reidel Publishing Company, Dordrecht, Holland, 1974.

    Google Scholar 

  24. B. Loewer and M. Belzer. Dyadic deontic detachment. Synthese, 54:295–318, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  25. J. Pearl. From conditional oughts to qualitative decision theory. In Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI’93), pages 12–20, 1993.

    Google Scholar 

  26. H. Prakken and M.J. Sergot. Contrary-to-duty obligations. Studia Logica, 57:91–115, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  27. H. Prakken and M.J. Sergot. Dyadic deontic logic and contrary-to-duty obligations. In D. Nute, editor, Defeasible Deontic Logic, pages 223–262. Kluwer, 1997.

    Google Scholar 

  28. Y. Moses R. Fagin, J.Y. Halpern and M.Y. Vardi. Reasoning About Knowledge. MIT press, 1995.

    Google Scholar 

  29. S.-W. Tan and J. Pearl. Specification and evaluation of preferences under uncertainty. In Proceedings of the KR’94, pages 530–539, 1994.

    Google Scholar 

  30. Y.-H. Tan and L.W.N. van der Torre. How to combine ordering and minimizing in a deontic logic based on preferences. In Deontic Logic, Agency and Normative Systems. Proceedings of the ΔEON’96, Workshops in Computing, pages 216–232. Springer Verlag, 1996.

    Google Scholar 

  31. L.W.N. van der Torre. Violated obligations in a defeasible deontic logic. In Proceedings of the ECAI’94, pages 371–375, 1994.

    Google Scholar 

  32. L.W.N. van der Torre. Reasoning About Obligations: Defeasibility in Preference-based Deontic Logics. PhD thesis, Erasmus University Rotterdam, 1997.

    Google Scholar 

  33. L.W.N. van der Torre and Y.-H. Tan. Cancelling and overshadowing: two types of defeasibility in defeasible deontic logic. In Proceedings of the IJCAI’95, pages 1525–1532, 1995.

    Google Scholar 

  34. L.W.N. van der Torre and Y.-H. Tan. Contextual deontic logic. In Proceedings of the First International Conference on Modeling and Using Context (CONTEXT’ 97), pages 1–12, Rio de Janeiro, Brazil, 1997.

    Google Scholar 

  35. L.W.N. van der Torre and Y.-H. Tan. The many faces of defeasibility in defeasible deontic logic. In D. Nute, editor, Defeasible Deontic Logic, pages 79–121. Kluwer, 1997.

    Google Scholar 

  36. L.W.N. van der Torre and Y.-H. Tan. Diagnosis and decision making in normative reasoning. Artificial Intelligence and Law, 1998.

    Google Scholar 

  37. L.W.N. van der Torre and Y.-H. Tan. The temporal analysis of Chisholm’s paradox. In Proceedings of the AAAI’98, 1998.

    Google Scholar 

  38. L.W.N. van der Torre and Y.-H. Tan. An update semantics for deontic reasoning. In P. McNamara and H. Prakken, editors, Norms, Logics and Information Systems. New Studies on Deontic Logic and Computer Science. IOS Press, 1998.

    Google Scholar 

  39. L.W.N. van der Torre and Y.-H. Tan. An update semantics for prima facie obligations. In H. Prade, editor, Proceedings of the ECAI’98, pages 38–42, 1998.

    Google Scholar 

  40. B.C. van Fraassen. Values and the heart command. Journal of Philosophy, 70:5–19, 1973.

    Article  Google Scholar 

  41. G.H. von Wright. The Logic of Preference. Edinburgh University Press, 1963.

    Google Scholar 

  42. G.H. von Wright. A new system of deontic logic. In R. Hilpinen, editor, Deontic Logic: Introductory and Systematic Readings, pages 105–120. D. Reidel Publishing company, Dordrecht, Holland, 1971.

    Google Scholar 

  43. E. Weydert. Hyperrational conditionals. monotonic reasoning about nested default conditionals. In Foundations of Knowledge Representation and Reasoning, LNAI 810, pages 310–332. Springer, 1994.

    Google Scholar 

  44. R.J. Wieringa and J.-J.Ch. Meyer. Applications of deontic logic in computer science: A concise overview. In Deontic Logic in Computer Science, pages 17–40. John Wiley & Sons, Chichester, England, 1993.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IRIT, Paul Sabatier University, Toulouse, France

    Leendert W. N. van der Torre

  2. Euridis, Erasmus University Rotterdam, The Netherlands

    Yao-Hua Tan

Authors
  1. Leendert W. N. van der Torre
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  2. Yao-Hua Tan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, Maryland, 20742, USA

    Jürgen Dix

  2. I.R.I.T. Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex, France

    Luís Fariñas del Cerro

  3. Fachbereich 4: Informatik, Universität Koblenz, Rheinau 1, D-56075, Koblenz, Germany

    Ulrich Furbach

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© 1998 Springer-Verlag Berlin Heidelberg

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van der Torre, L.W.N., Tan, YH. (1998). Prohairetic Deontic Logic (PDL). In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_6

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  • DOI: https://doi.org/10.1007/3-540-49545-2_6

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  • Print ISBN: 978-3-540-65141-3

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