Temporal Alethic Dyadic Deontic Logic and the Contrary-to-Duty Obligation Paradox

• Authors: Rönnedal Daniel
• Languages of publication: EN

Abstracts

EN

A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic systems, i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T× W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them.

Keywords

EN

T × W logics; temporal logic; modal logic; dyadic deontic logic; semantic tableaux; conditional norms; contrary-to-duty obligations; the contrary-to-duty (obligation) paradox

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2018
• Volume: 27
• Issue: 1
• Pages: 3–52

Dates

published

2018-03-15

Contributors

author

Rönnedal Daniel

• Stockholm University, Department of Philosophy, 106 91 Stockholm, Sweden

References

• Alchourrón, C.E., and E. Bulygin, “Normative knowledge and truth”, pages 25–45 in J.J.E. Garcia et al. (eds.), Philosophical Analysis in Latin America, D. Reidel Publishing Company, 1984.
• Anderson, A.R. (1956), “The formal analysis of normativesystems”, pages 147–213 in N. Rescher (ed.), The Logic of Decision and Action, Pittsburg: University of Pittsburg Press, 1967.
• Bailhache, P., “Les normes dans le temps et sur l’action. Essai de logique déontique”, Université de Nantes, 1986.
• Bailhache, P., “Essai de logique déontique”, Paris, Librarie Philosophique, Vrin, Collection Mathesis, 1991.
• Bailhache, P., “The deontic branching time: Two related conceptions”, Logique et Analyse 36 (1993): 159–175.
• Bailhache, P., “Canonical models for temporal deontic logic”, Logique et Analyse 149 (1995): 3–21.
• Bartha, P., “Moral preference, contrary-to-duty obligation and defeasible oughts”, pages 93–108 in [37].
• Belnap, N., M. Perloff, and M. Xu, Facing the Future: Agents and Choices in Our Indeterminist World, Oxford, Oxford University Press, 2001.
• Brown, M.A., “Agents with changing and conflicting commitments: A preliminary study”, page 109–125 in [37].
• Brown, M.A., “Conditional obligation and positive permission for agents in time”, Nordic Journal of Philosophical Logic 5, 2 (2000): 83–112.
• Brown, M.A., “Rich deontic logic: A preliminary study”, Journal of Applied Logic 2 (2004): 19–37.
• Burgess, J.P., “Basic Tense Logic”, pages 89–133 and 1–42 in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 2 and Vol. 7 (2nd Edition), Kluwer Academic Publishers, 1984 and 2002, respectively. DOI: 10.1007/978-94-009-6259-0_2 and 10.1007/978-94-017-0462-5_1
• Carmo, J., and A.J.I. Jones, “Deontic logic and contrary-to-duties”, pages 265–343 in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition, Vol. 8, Kluwer Academic Publishers, 2002. DOI: 10.1007/978-94-010-0387-2_4
• Chellas, B.F., The Logical Form of Imperatives, Stanford, Perry Lane Press, 1969.
• Chellas, B.F., Modal Logic: An Introduction, Cambridge, Cambridge University Press, 1980.
• Chisholm, R.M., “Contrary-to-duty imperatives and deontic logic”, Analysis 24, 2 (1963): 33–36. DOI: 10.1093/analys/24.2.33
• Ciuni, R., and A. Zanardo, “Completeness of a branching-time logic with possible choices”, Studia Logica 96, 3 (2010): 393–420. DOI: 10.1007/s11225-010-9291-1
• Cox, Azizah Al-Hibri, Deontic Logic: A Comprehensive Appraisal and a New Proposal, University Press of America, 1978.
• D’Agostino, M., D.M. Gabbay, R.Hähnle, and J. Posegga (eds.), Handbook of Tableau Methods, Dordrecht, Kluwer Academic Publishers, 1999. DOI: 10.1007/978-94-017-1754-0
• Danielsson, S., Preference and Obligation: Studies in the Logic of Ethics, Uppsala: Filosofiska föreningen, 1968.
• DiMaio, M.C., and A. Zanardo, “A Gabbay-rule free axiomatization of T × W validity”, Journal of Philosophical Logic 27 (1998): 435–487.
• Feldman, F., Doing the Best We Can: An Essay in Informal Deontic Logic, Dordrecht: D. Reidel Publishing Company, 1986.
• Feldman, F., “A simpler solution to the paradoxes of deontic logic”, Philosophical Perspectives 4 (1990): 309–341. DOI: 10.2307/2214197
• Fitting, M., Proof Methods for Modal and Intuitionistic Logics, Dordrecht, D. Reidel Publishing Company, 1983.DOI: 10.1007/978-94-017-2794-5
• Fitting, M., and R.L. Mendelsohn, First-Order Modal Logic, Kluwer Academic Publishers, 1998. DOI: 10.1007/978-94-011-5292-1
• Gabbay, D.M., and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition, Vol. 3, Dordrecht, Kluwer Academic Publishers, 2001. DOI: 10.1007/978-94-017-0454-0
• Gabbay, D.M., A. Kurucz, F. Wolter, M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, Amsterdam, Elsevier, 2003.
• Hansson, B., “An analysis of some deontic logics”, Noûs 3 (1969): 373–398. DOI: 10.2307/2214372
• Hilpinen, R. (ed.), New Studies in Deontic Logic: Norms, Actions, and the Foundation of Ethics, Dordrecht, D. Reidel Publishing Company, 1981. DOI: 10.1007/978-94-009-8484-4
• Horty, J.F., Agency and Deontic Logic, Oxford, Oxford University Press, 2001. DOI: 10.1093/0195134613.001.0001
• Jeffrey, R.C., Formal Logic: Its Scope and Limits, McGraw-Hill, New York, 1967.
• Kracht, M., Tools and Techniques in Modal Logic, Amsterdam, Elsevier, 1999.
• Lenk, H., Normenlogik, Pullach bei München: Verlag Dokumentation, 1974.
• Lewis, D., Counterfactuals, Oxford: Basil Blackwell, 1973.
• Lewis, D., “Semantic analysis for dyadic deontic logic”, pages 1–14 in S. Stenlund (ed.), Logical Theory and Semantical Analysis, D. Reidel Publishing Company, Dordrecht, 1974.
• Loewer, B., and M. Belzer, “Dyadic deontic detachment”, Synthese 54, 2 (1983): 295–318. DOI: 10.1007/BF00869396
• McNamara, P., and H. Prakken (eds.), Norms, Logics and Information Systems: New Studies in Deontic Logic and Computer Science, Amsterdam, IOS Press, 1999.
• Priest, G., An Introduction to Non-Classical Logic, Cambridge, Cambridge University Press, 2008. DOI: 10.1017/CBO9780511801174
• Prior, A., “The paradoxes of derived obligation”, Mind 63, 249 (1954): 64–65. DOI: 10.1093/mind/LXIII.249.64
• Prior, A., Past, Present and Future, Oxford, Clarendon, 1967. DOI: 10.1093/acprof:oso/9780198243113.001.0001
• Rescher, N., “An axiom system for deontic logic”, Philosophical Studies 9, 1–2 (1958): 24–30. DOI: 10.1007/BF00797870
• Rescher, N., and A. Urquhart, Temporal Logic, Wien, Springer-Verlag, 1971. DOI: 10.1007/978-3-7091-7664-1
• Rönnedal, D., “Dyadic deontic logic and semantic tableaux”, Logic and Logical Philosophy 18, 3–4 (2009): 221–252. DOI: 10.12775/LLP.2009.011
• Rönnedal, D., “Temporal alethic-deontic logic and semantic tableaux”, Journal of Applied Logic 10, 3 (2012): 219–237. DOI: 10.1016/j.jal.2012.03.002
• Rönnedal, D., “Extensions of deontic logic: An investigation into some multi-modal systems”, Department of Philosophy, Stockholm University, 2012.
• Rönnedal, D., “Quantified temporal alethic deontic logic”, Logic and Logical Philosophy 24, 1 (2015): 19–59. DOI: 10.12775/LLP.2014.016
• Smullyan, R.M., First-Order Logic, Heidelberg, Springer-Verlag, 1968. DOI: 10.1007/978-3-642-86718-7
• Thomason, R., “Deontic logic as founded on tense logic”, pages 165–176, Chapter 7, in [29]. DOI: 10.1007/978-94-009-8484-4_7
• Thomason, R., “Deontic logic and the role of freedom in moral deliberation”, pages 177–186, Chapter 8, in [29]. DOI: 10.1007/978-94-009-8484-4_8
• Thomason, R., “Combinations of tense and modality”, pages 135–165 and 205–234 in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 2 and Vol. 7 (2nd Edition), 1984 and 2002, respectively. DOI: 10.1007/978-94-009-6259-0_3 and 10.1007/978-94-017-0462-5_3
• van Eck, J., “A system of temporally relative modal and deontic predicate logic and its philosophical applications”, Department of Philosophy, University of Groningen, The Netherlands, 1981.
• van Eck, J., “A system of temporally relative modal and deontic predicate logic and its philosophical applications”, Logique et Analyse 25, 99 (1982): 249–290.
• van Eck, J., “A system of temporally relative modal and deontic predicate logic and its philosophical application”, Logique et Analyse 25, 100 (1982): 339–381.
• van Fraassen, B.C., “The logic of conditional obligation”, Journal of Philosophical Logic 1, 3–4 (1972): 417–438. DOI: 10.1007/BF00255570
• van Fraassen, B.C., “Values and the heart’s command”, The Journal of Philosophy LXX (1973): 5–19. DOI: 10.2307/2024762
• von Kutschera, F., “Normative Präferenzen und bedingte Gebote”, pages 137–165 in [33].
• von Kutschera, F., “T × W completeness”, Journal of Philosophical Logic 26 (1997): 241–250.
• von Wright, G.H., “A new system of deontic logic”, Danish Yearbook of Philosophy 1 (1964): 173–182. DOI: 10.1007/978-94-010-3146-2_4
• Wölfl, S., “Combinations of tense and modality for predicate logic”, Journal of Philosophical Logic 28 (1999): 371–398.
• Zanardo, A., “Branching-time logic with quantification over branches: The point of view of modal logic”, The Journal of Symbolic Logic 61, 1 (1996): 1–39. DOI 10.2307/2275595
• Åqvist, L., “Revised foundations for imperative-epistemic and interrogative logic”, Theoria 37, 1 (1971): 33–73. DOI: 10.1111/j.1755-2567.1971.tb00060.x
• Åqvist, L., “Modal logic with subjunctive conditionals and dispositional predicates”, Journal of Philosophical Logic 2, 1 (1973): 1–76. DOI: 10.1007/BF02115609
• Åqvist, L., “Deontic Logic”, pages 605–714 and 147–264 in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 2 and Vol. 8 (2nd Edition), 1984 and 2002, respectively. DOI: 10.1007/978-94-009-6259-0_11 and 10.1007/978-94-010-0387-2_3
• Åqvist, L., Introduction to Deontic Logic and the Theory of Normative Systems, Naples, Bibliopolis, 1987.
• Åqvist, L., “The logic of historical necessity as founded on two-dimensional modal tense logic”, Journal of Philosophical Logic 28, 4 (1999) 329–369. DOI: 10.1023/A:1004425728816
• Åqvist, L., “Conditionality and branching time in deontic logic: Further remarks on the Alchourrón and Bulygin (1983) Example”, pages 13–37 in K. Segerberg and R. Sliwinski (eds.), Logic, Law, Morality: Thirteen essays in Practical Philosophy in Honour of Lennart Åqvist, Uppsala philosophical studies 51, Uppsala: Uppsala University, 2003.
• Åqvist, L., “Combinations of tense and deontic modality: On the Rt approach to temporal logic with historical necessity and conditional obligation”, Journal of Applied Logic 3 (2005): 421–460.
• Åqvist, L., and J. Hoepelman, “Some theorems about a “tree” system of deontic tense logic”, pages 187–221 in [29]. 10.1007/978-94-009-8484-4_9

Identifiers

DOI

10.12775/LLP.2017.012