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.
Similar content being viewed by others
References
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.
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
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
Chellas B. F. (1980) Modal logic—an introduction. Cambridge University Press, Cambridge, UK
Chisholm R.M. (1963) Contrary-to-duty imperatives and deontic logic. Analysis 24: 33–36
Forrester J. W. (1984) Gentle murder, or the adverbial samartian. The Journal of Philosophy 81(4): 193–197
Gabbay D. (1970) Selective filtration in modal logics I. Theoria 36: 323–330
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
Gabbay D. M. (1976a) Modal and tense logics. D Reidel, Dordrech
Gabbay D. (1976b) Investigations in modal and tense logic with applications, Synthese Volume 92. D Reidel, Dordrech
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.
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
Gabbay, D. M. (2010). Reactive standard deontic logic. Draft, February.
Gabbay, D. (2011). Reactive Kripke models and contrary-to-duty obligations. Expanded version. Journal of Applied Logic. (to appear)
Gabbay D. M., Marcelino S. (2009) Modal logics of reactive frames. Studia Logica 93: 403–444
Gabbay, D., & Schlechta, K. (2009). Critical analysis of the Carmo–Jones model of contrary-to-duty obligations. Draft paper 358.
Hansson S. O. (1989) A note on the Deontic System DL of Jones and Pörn. Synthese 80: 427–428
Jones A. J. I. (1993) Towards a formal theory of defeasible deontic conditionals. Annals of Mathematics and Artificial Intelligence 9: 151–166
Jones A.J.I., Pörn I. (1985) Ideality, sub-ideality and deontic logic. Synthese 65: 275–290
Jones A.J.I., Pörn I. (1986) “Ought” and “must”. Synthese 66: 89–93
Jones A. I. J., Pörn I. (1989) A rejoinder to Hansson. Synthese 80: 429–432
Jones, A. J. I., & Pörn, 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.
Kamp H. (1971) Formal properties of ‘Now’. Theoria 37: 227–274
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.
Lewis D. (1970) Anselm and actuality. Nous 4: 175–188
Loewer B., Belzer M. (1983) Dyadic deontic detachment. Synthese 54: 295–318
Prakken H., Sergot M. (1996) Contrary to duty obligations. Studia Logica 57: 91–115
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
Prior A. N. (1968) Now. Nous 2: 101–119
Reichenbach, H. (1947). Elements of symbolic logic. New York: McMillan. Republished, Free Press (1966).
Ross A. (1941) Imperatives and logic. Theoria 7: 53–71
Segerberg K. (1967) On the logic of ‘Tomorrow’. Theoria 33: 46–52
Segerberg K. (1973) Two-dimensional modal logic. Journal of Philosophical Logic 2: 77–96
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Boer, M., Gabbay, D.M., Parent, X. et al. Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones–Pörn deontic logic system]. Synthese 187, 623–660 (2012). https://doi.org/10.1007/s11229-010-9866-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-010-9866-4