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COMPLETENESS OF ÅQVIST’S SYSTEMS E AND F

Published online by Cambridge University Press:  27 November 2014

XAVIER PARENT
XAVIER PARENT*
Affiliation:
Université Aix-Marseille, CNRS, CEPERC UMR 7304
*
*UNIVERSITÉ AIX-MARSEILLE, CNRS, CEPERC UMR 7304, AIX-EN-PROVENCE, 13629, FRANCE E-mail: x.parent.xavier@gmail.com
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Abstract

This paper tackles an open problem posed by Åqvist. It is the problem of whether his dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference-based semantics. It is known that there are two different ways of interpreting what it means for a world to be best or top-ranked among alternatives. This can be understood as saying that it is optimal among them, or maximal among them. First, it is established that, under either the maximality rule or the optimality rule, E is sound and complete with respect to the class of all preference models, the class of those in which the betterness relation is reflexive, and the class of those in which it is total. Next, an analogous result is shown to hold for F. That is, it is established that, under either rule, F is sound and complete with respect to the class of preference models in which the betterness relation is limited, the class of those in which it is limited and reflexive, and the class of those in which it is limited and total.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 1 , March 2015 , pp. 164 - 177
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

BIBLIOGRAPHY

Alchourrón, C. (1993). Philosophical foundations of deontic logic and the logic of defeasible conditionals. In Meyer, J.-J., and Wieringa, R., editors. Deontic Logic in Computer Science, New York: John Wiley & Sons, Inc., pp. 43–84.Google Scholar
Alchourrón, C. (1995). Defeasible logic: Demarcation and affinities. In Crocco, G., Fariñas del Cerro, L., and Herzig, A., editors. Conditionals: From Philosophy to Computer Science, Oxford: Clarendon Press, pp. 67–102.Google Scholar
Åqvist, L. (1987). An Introduction to Deontic logic and the Theory of Normative Systems. Naples: Bibliopolis.Google Scholar
Åqvist, L. (1993). A completeness theorem in deontic logic with systematic frame constants. Logique & Analyse, 36 (141–142), 177–192.Google Scholar
Åqvist, L. (2002). Deontic logic. In Gabbay, D., and Guenthner, F., editors. Handbook of Philosophical Logic (second edition), Vol. 8, Dordrecht, Holland: Kluwer Academic Publishers, pp. 147–264.Google Scholar
Chellas, B. (1975). Basic conditional logic. Journal of Philosophical Logic, 4(2), 133–153.Google Scholar
Chernoff, H. (1954). Rational selection of decision functions. Econometrica, 22(4), 422–443.Google Scholar
Goble, L. (2013). Notes on Kratzer semantics for modality, with application to simple deontic logic. Unpublished.Google Scholar
Goble, L. (2014). Further notes on Kratzer semantics for modality, with application to dyadic deontic logic. Unpublished.Google Scholar
Goldman, H. (1977). David Lewis’s semantics for deontic logic. Mind, 86(342), 242–248.Google Scholar
Halmos, P. (1960). Naive Set Theory. New York: Van Nostrand Reinhold Company.Google Scholar
Hansen, J. (1999). On relations between Åqvist’s deontic system G and van Eck’s deontic temporal logic. In McNamara, P., and Prakken, H., editors. Norms, Logics, and Information Systems, Amsterdam: IOS Press, pp. 127–144.Google Scholar
Hansen, J. (2005). Conflicting imperatives and dyadic deontic logic. Journal of Applied Logic, 3(3–4), 484–511.Google Scholar
Hansson, B. (1969). An analysis of some deontic logics. Noûs, 3(4), 373–398.Google Scholar
Herzberger, H. (1973). Ordinal preference and rational choice. Econometrica, 41(2), 187–237.Google Scholar
Hilpinen, R. (2001). Deontic logic. In Goble, L., editor. The Blackwell Guide to Philosophical Logic, Malden: Blackwell Publishers, pp. 159–182.Google Scholar
Hilpinen, R., & McNamara, P. (2013). Deontic logic: A historical survey and introduction. In Gabbay, D., Horty, J., Parent, X., van der Meyden, R., and van der Torre, L., editors. Handbook of Deontic Logic and Normative Systems, London: College Publications, pp. 3–136.Google Scholar
Jackson, F. (1985). On the semantics and logic of obligation. Mind, 94(374), 177–195.Google Scholar
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1–2), 167–207.Google Scholar
Lehmann, D., & Magidor, M. (1992). What does a conditional knowledge base entail? Artificial Intelligence, 55(1), 1–60.CrossRefGoogle Scholar
Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.Google Scholar
Makinson, D. (1993). Five faces of minimality. Studia Logica, 52(3), 339–379.Google Scholar
McNamara, P. (1995). The confinement problem: How to terminate your mom with her trust. Analysis, 55(4), 310–313.Google Scholar
Parent, X. (2008). On the strong completeness of Åqvist’s dyadic deontic logic G. In van der Meyden, R., and van der Torre, L., editors. Deontic Logic in Computer Science (DEON 2008), Lecture Notes in Artificial Intelligence, vol. 5076, Berlin/Heidelberg: Springer, pp. 189–202.Google Scholar
Parent, X. (2010). A complete axiom set for Hansson’s deontic logic DSDL2. Logic Journal of the IGPL, 18(3), 422–429.Google Scholar
Parent, X. (2014). Maximality vs. optimality in dyadic deontic logic, Journal of Philosophical Logic, 43(6), pp. 1101–1128.Google Scholar
Prakken, H., & Sergot, M. (1997). Dyadic deontic logic and contrary-to-duty obligations. In Nute, D., editor. Defeasible Deontic Logic, Dordrecht: Kluwer Academic Publishers, pp. 223–262.Google Scholar
Schlechta, K. (1995). Preferential choice representation theorems for branching time structures. Journal of Logic and Computation, 5(6), 783–800.Google Scholar
Schlechta, K. (1997). Nonmonotonic Logics: Basic Concepts, Results, and Techniques. Germany: Springer.Google Scholar
Sen, A. (1971). Choice functions and revealed preference. The Review of Economic Studies, 38(3), 307–317.Google Scholar
Sen, A. (1997). Maximization and the act of choice. Econometrica, 65(4), 745–779.Google Scholar
Shoham, Y. (1988). Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence. Cambridge: MIT Press.Google Scholar
Spohn, W. (1975). An analysis of Hansson’s dyadic deontic logic. Journal of Philosophical Logic, 4(2), 237–252.Google Scholar
Stalnaker, R. (1968). A theory of conditionals. In Rescher, N., editor. Studies in Logical Theory, Oxford: Blackwell, pp. 98–112.Google Scholar
Suzumura, K. (1976). Rational choice and revealed preference. The Review of Economic Studies, 43(1), 149–158.Google Scholar
Temkin, L. (1987). Intransitivity and the mere addition paradox. Philosophy and Public Affairs, 16(2), 138–187.Google Scholar