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

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• 作者：Mathijs de Boer (3)
  Dov M. Gabbay (123) dov.gabbay@kcl.ac.uk
  Xavier Parent (3)
  Marija Slavkovic (3)
• 关键词：Deontic Logic – Contrary to Duties – Chisholm paradox – Two dimensional temporal logic
• 刊名：Synthese
• 出版年：2012
• 出版时间：July 2012
• 年：2012
• 卷：187
• 期：2
• 页码：623-660
• 全文大小：378.7 KB
• 参考文献：1. Aqvist, L. (1965). A new approach to the logical theory of interrogatives, Part I, Analysis. Philosophical Society and Department of Philosophy, University of Uppsala, Sect. 6.2.
  2. Aqvist L. (1966) “Next” and “Ought”, alternative foundations for Von Wrights’s tense-logic, with an application to deontic logic. Logique et Analyse 9: 231–251
  3. Carmo J., Jones A. J. I. (2002) Deontic logic and contrary to duties. In: Gabbay D., Guenther F. (eds) Handbook of philosophical logic, 2nd ed. Springer, Heidelberg, pp 256–344
  4. Chellas B. F. (1980) Modal logic—an introduction. Cambridge University Press, Cambridge, UK
  5. Chisholm R.M. (1963) Contrary-to-duty imperatives and deontic logic. Analysis 24: 33–36
  6. Forrester J. W. (1984) Gentle murder, or the adverbial samartian. The Journal of Philosophy 81(4): 193–197
  7. Gabbay D. (1970) Selective filtration in modal logics I. Theoria 36: 323–330
  8. Gabbay D. (1974) Tense logics and the tenses of English. In: Moravcsik J. M. E. (Ed.) Readings in logic. Mouton Publishing Co., The Hague, pp 177–186
  9. Gabbay D. M. (1976a) Modal and tense logics. D Reidel, Dordrech
  10. Gabbay D. (1976b) Investigations in modal and tense logic with applications, Synthese Volume 92. D Reidel, Dordrech
  11. Gabbay, D. (2008a). Reactive Kripke semantics and arc accessibility. In A. Avron, N. Dershowitz, & A. Rabinovich (Eds.), Pillars of computer science: Essays dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday (pp. 292–341). Lecture notes in computer science, Vol. 4800. Berlin: Springer-Verlag.
  12. Gabbay D. M. (2008b) Reactive Kripke models and contrary-to-duty obligations. In: Meyden R., Torre L. (eds) DEON-2008, Deontic logic in computer science, LNAI 5076. Springer, Berlin, pp 155–173
  13. Gabbay, D. M. (2010). Reactive standard deontic logic. Draft, February.
  14. Gabbay, D. (2011). Reactive Kripke models and contrary-to-duty obligations. Expanded version. Journal of Applied Logic. (to appear)
  15. Gabbay D. M., Marcelino S. (2009) Modal logics of reactive frames. Studia Logica 93: 403–444
  16. Gabbay, D., & Schlechta, K. (2009). Critical analysis of the Carmo–Jones model of contrary-to-duty obligations. Draft paper 358.
  17. Hansson S. O. (1989) A note on the Deontic System DL of Jones and P?rn. Synthese 80: 427–428
  18. Jones A. J. I. (1993) Towards a formal theory of defeasible deontic conditionals. Annals of Mathematics and Artificial Intelligence 9: 151–166
  19. Jones A.J.I., P?rn I. (1985) Ideality, sub-ideality and deontic logic. Synthese 65: 275–290
  20. Jones A.J.I., P?rn I. (1986) “Ought” and “must”. Synthese 66: 89–93
  21. Jones A. I. J., P?rn I. (1989) A rejoinder to Hansson. Synthese 80: 429–432
  22. Jones, A. J. I., & P?rn, I. (1991). On the logic of deontic conditionals. In J.-J. Ch. Meyer & R. J. Wieringa (Eds.) DEON91—Proceedings of Ist international workshop on deontic logic in computer science. Amsterdam.
  23. Kamp H. (1971) Formal properties of ‘Now’. Theoria 37: 227–274
  24. Kanger, S. (1971). New foundations for ethical theory, 1957. Reprinted In R. Hilpinen & D. Follesdal (Eds.), Deontic logic: Introductory and systematic readings (pp. 36–58). Dordrecht: D. Reidel.
  25. Lewis D. (1970) Anselm and actuality. Nous 4: 175–188
  26. Loewer B., Belzer M. (1983) Dyadic deontic detachment. Synthese 54: 295–318
  27. Prakken H., Sergot M. (1996) Contrary to duty obligations. Studia Logica 57: 91–115
  28. Prior A. N. (1958) Escapism: The logical basis of ethics. In: Melden A. I. (Ed.) Essays in moral philosophy. University of Washington Press, Washington, pp 135–146
  29. Prior A. N. (1968) Now. Nous 2: 101–119
  30. Reichenbach, H. (1947). Elements of symbolic logic. New York: McMillan. Republished, Free Press (1966).
  31. Ross A. (1941) Imperatives and logic. Theoria 7: 53–71
  32. Segerberg K. (1967) On the logic of ‘Tomorrow’. Theoria 33: 46–52
  33. Segerberg K. (1973) Two-dimensional modal logic. Journal of Philosophical Logic 2: 77–96
  34. van der Torre L., Tan Y.-H. (1999) Contrary-to-duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27: 49–78
• 作者单位：1. King’s College, London, UK2. Bar Ilan University, Ramat Gan, Israel3. Individual and Collective Reasoning Group, Computer Science and Communications, University of Luxembourg, Luxembourg, UK
• ISSN：1573-0964

文摘

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 P?rn 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.