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OBLIGATION, FREE CHOICE, AND THE LOGIC OF WEAKEST PERMISSIONS

Published online by Cambridge University Press:  28 July 2015

ALBERT J.J. ANGLBERGER ,
NOBERT GRATZL  and
OLIVIER ROY
ALBERT J.J. ANGLBERGER*
Affiliation:
Munich Center for Mathematical Philosophy, LMU Munich
NOBERT GRATZL*
Affiliation:
Munich Center for Mathematical Philosophy, LMU Munich
OLIVIER ROY*
Affiliation:
Universität Bayreuth
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LMU MUNICH FAKULTÄT FÜR PHILOSOPHIE, WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFT MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL-PLATZ 1 D-80539 MÜNCHEN E-mail: [email protected]
†MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LMU MUNICH FAKULTÄT FÜR PHILOSOPHIE, WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFT MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL-PLATZ 1 D-80539 MÜNCHEN E-mail: [email protected]
‡UNIVERSITÄT BAYREUTH DEPARTMENT OF PHILOSOPHY D-95440 BAYREUTH E-mail: [email protected]
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Abstract

We introduce a new understanding of deontic modals that we call obligations as weakest permissions. We argue for its philosophical plausibility, study its expressive power in neighborhood models, provide a complete Hilbert-style axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 807 - 827
Copyright
Copyright © Association for Symbolic Logic 2015 

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References

Anglberger, A., Dong, H., & Roy, O. (2014). Open reading without free choice. In Cariani, F., Grossi, D., Meheus, J., and Parent, X., editors. Deontic Logic and Normative Systems. Heidelberg: Springer, pp. 19–32.CrossRefGoogle Scholar
Asher, N., & Bonevac, D. (2005). Free choice permission is strong permission. Synthese, 145(3), 303–323.Google Scholar
Belnap, N. D., Perloff, M., & Xu, M. (2001). Facing the Future: Agents and Choices in our Indeterminist World. New York: Oxford University Press on Demand.CrossRefGoogle Scholar
van Benthem, J. (1979). Minimal deontic logics. Bulletin of the Section of Logic, 8(1), 36–41.Google Scholar
Blackburn, P., De Rijke, M., & Venema, Y. (2002). Modal Logic. Cambridge, UK: Cambridge University Press.Google Scholar
Brandenburger, A., & Friedenberg, A. (2008). Intrinsic correlation in games. Journal of Economic Theory, 141(1), 28–67.Google Scholar
Brink, D. (1994). Moral conflict and its structure. The Philosophical Review, 103(2), 215–247.CrossRefGoogle Scholar
Broersen, J. (2004). Action negation and alternative reductions for dynamic deontic logics. Journal of Applied Logic, 2, 153–168.CrossRefGoogle Scholar
Brown, F. M. (1987). The Frame Problem in Artificial Intelligence. Los Altos: Morgan Kaufmann Publishers Inc.Google Scholar
Cubitt, R. P., & Sugden, R. (2011). Common reasoning in games: A lewisian analysis of common knowledge of rationality. Technical report, CeDEx discussion paper series.Google Scholar
Czelakowski, J. (1997). Action and deontology. In Ejerhed, E., and Lindström, S., editors. Logic, Action and Cognition. New York: Springer, pp. 47–87.CrossRefGoogle Scholar
Donagan, A. (1984). Consistency in rationalist moral systems. The Journal of Philosophy, 81(6), 291–309.Google Scholar
Dong, H. (2014). A survey between 5wp and dal. Unpublished manuscript, University of Bayreuth.Google Scholar
Gratzl, N. (2013). Sequent calculi for multi-modal logic with interaction. In Grossi, D., Roy, O., and Huang, H., editors. Logic, Rationality, and Interaction. Heidelberg: Springer, pp. 124–134.CrossRefGoogle Scholar
Hansson, S. (2013). The varieties of permissions. 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.Google Scholar
Horty, J. (2012). Reasons as Defaults. Oxford, New York: Oxford University Press.CrossRefGoogle Scholar
Jeffrey, R. (1965). The Logic of Decision. New-York: McGraw-Hill.Google Scholar
Joyce, J. M. (2012). Regret and instability in causal decision theory. Synthese, 187(1), 123–145.CrossRefGoogle Scholar
Kamp, H. (1973). Free choice permission. Proceedings of the Aristotelian Society, 74, 57–74.CrossRefGoogle Scholar
Lellmann, B. (2014). Axioms vs hypersequent rules with context restrictions: Theory and applications. In Demri, S., Kapur, D., and Weidenbach, C., editors. Automated Reasoning, Volume 8562 of Lecture Notes in Computer Science. Springer International Publishing, pp. 307–321. http://dx.doi.org/10.1007/978-3-319-08587-6_23.Google Scholar
Lewis, D. (1979). A problem about permission. In Saarinen, E. et al. , editors. Essays in honour of Jaakko Hintikka. Dordrecht: Reidel, pp. 163–175.CrossRefGoogle Scholar
Makinson, D. (1984). Stenius’ approach to disjunctive permission. Theoria, 50(2–3), 138–147.Google Scholar
McCarty, J. (1980). Circumscription – a form of nonmonotonic reasoning. Artificial Intelligence, 13(1–2), 27–39.CrossRefGoogle Scholar
McNamara, P. (2014). Deontic logic. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Winter 2014 edition). http://plato.stanford.edu/archives/win2014/entries/ logic-deontic/.Google Scholar
Rasmusen, E. (2007). Games and Information (fourth Edition). Oxford: Blackwell.Google Scholar
Roy, O., Anglberger, A., & Gratzl, N. (2014). The logic of best action from a deontic perspective. In Baltag, A., and Smets, S., editors. Johan F.A.K. van Benthem on Logical and Informational Dynamics. Berlin: Springer, pp. 657–676.CrossRefGoogle Scholar
Singer, P. (2011). Practical Ethics (Third ed.). Cambridge: Cambridge University Press.Google Scholar
Trypuz, R., & Kulicki, P. (2009). A systematics of deontic action logics based on boolean algebra. Logic and Logical Philosophy, 18(3–4), 253–270.Google Scholar
Trypuz, R., & Kulicki, P. (2011). A norm-giver meets deontic action logic. Logic and Logical Philosophy, 20, 59–72.Google Scholar
Trypuz, R., & Kulicki, P. (2013). On deontic action logics based on boolean algebra. Journal of Logic and Computation.Google Scholar
Weirich, P. (2012). Causal decision theory. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Winter 2012 edition). http://plato.stanford.edu/archives/win2012/ entries/decision-causal/.Google Scholar
Wright, G. H. v. (1963). Norm and Action - A Logical Enquiry. London: Routledge.Google Scholar
Wright, G. H.v. (1968). An Essay in Deontic Logic and the General Theory of Action. Amsterdam: North-Holland Publishing Company.Google Scholar