Abstract
Åqvist’s dyadic deontic logic G, which aims at providing an axiomatic characterization of Hansson’s seminal system DSDL3 for conditional obligation, is shown to be strongly complete with respect to its intended modelling.
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References
Hansson, B.: An analysis of some deontic logics. Noûs 4, 373–398 (1969)
Mott, P.: On Chisholm’s paradox. Journal of Philosophical Logic 2, 197–211 (1973)
Tomberlin, J.: Contrary-to-duty imperatives and conditional obligation. Noûs 16, 357–375 (1981)
Loewer, B., Belzer, M.: Dyadic deontic detachment. Synthese 54, 295–318 (1983)
Prakken, H., Sergot, M.: Dyadic deontic logic and contrary-to-duty obligation. In: [29], pp. 223–262
van der Torre, L., Tan, Y.H.: The many faces of defeasibility in defeasible deontic logic. In: [29], pp. 79–121
Carmo, J., Jones, A.: Deontic logic and contrary-to-duties. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 8, pp. 265–343. Kluwer Academic Publishers, Dordrecht (2002)
Parent, X.: Remedial interchange, contrary-to-duty obligation and commutation. Journal of Applied Non-Classical Logics 3/4, 345–375 (2003)
Spohn, W.: An analysis of Hansson’s dyadic deontic logic. Journal of Philosophical Logic 4, 237–252 (1975)
Åqvist, L.: An Introduction to Deontic logic and the Theory of Normative Systems, Bibliopolis, Naples (1987)
Åqvist, L.: Deontic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 8, pp. 147–264. Kluwer Academic Publishers, Dordrecht (2002)
Goranko, V., Passy, S.: Using the universal modality: Gains and questions. Journal of Logic and Computation 2, 5–30 (1992)
Sen, A.: Maximization and the act of choice. Econometrica 65, 745–779 (1997)
Makinson, D.: Bridges from Classical to Nonmonotonic logic. King’s College Publications, London (2005)
Schlechta, K.: Coherent Systems. Elsevier, Amsterdam (2004)
Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)
Parent, X.: Non-monotonic Logics and Modes of Argumentation − The Case of Conditional Obligation. PhD thesis, University of Aix-Marseille I, France (2002)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1990)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55, 1–60 (1992)
Goble, L.: A proposal for dealing with deontic dilemmas. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 74–113. Springer, Heidelberg (2004)
Chellas, B.: Modal Logic. Cambridge University Press, Cambridge (1980)
Blackburn, P., de Rijke, M., de Venema, Y.: Modal Logic, vol. 53. Cambrigde University Press, Cambridge (2001)
Åqvist, L.: A completeness theorem in deontic logic with systematic frame constants. Logique & Analyse 36, 177–192 (1993)
Hansen, J.: On relations between Åqvist’s deontic system G and van Eck’s deontic temporal logic. In: Mc Namara, P., Prakken, H. (eds.) Norms, Logics and Information Systems. Frontiers in Artificial Intelligence and Applications, pp. 127–144. IOS Press, Amsterdam (1999)
Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D., Hogger, C., Robinson, J. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 35–110. Clarendon Press, Oxford (1994)
Boutilier, G.: Unifying default reasoning and belief revision in a modal framework. Artificial Intelligence 68, 33–85 (1994)
van der Torre, L., Tan, Y.H.: Contrary-to-duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27(1-4), 49–78 (1999)
Makinson, D.: General theory of cumulative inference. In: Reinfrank, M., Ginsberg, M.L., de Kleer, J., Sandewall, E. (eds.) Non-Monotonic Reasoning 1988. LNCS, vol. 346, pp. 1–18. Springer, Heidelberg (1989)
Nute, D. (ed.): Defeasible Deontic Logic. Kluwer Academic Publishers, Dordrecht (1997)
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Parent, X. (2008). On the Strong Completeness of Åqvist’s Dyadic Deontic Logic G . In: van der Meyden, R., van der Torre, L. (eds) Deontic Logic in Computer Science. DEON 2008. Lecture Notes in Computer Science(), vol 5076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70525-3_15
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DOI: https://doi.org/10.1007/978-3-540-70525-3_15
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