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Open Reading without Free Choice

  • Albert J. J. Anglberger
  • Huimin Dong
  • Olivier Roy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8554)

Abstract

The open reading of permission (OR) states that an action α is permitted iff every execution of α is normatively OK. Free Choice Permission (FCP) is the notorious principle turning permission of disjunction into conjunction of permissions P(ϕψ) → . We start by giving a first-order logic version of OR that defines permission of action types in terms of the legality of action tokens. We prove that implies FCP. Given that FCP has been heavily criticized, this seems like bad news for OR. We disagree. We observe that this implication relies on a debatable principle involving disjunctive actions. We proceed to present alternative views of disjunctive actions which violate this principle, and which so block the undesired implication. So one can have the open reading without free choice and, as we argue towards the end of the paper, there are philosophical reasons why one should.

Keywords

Action Type Free Choice Linear Logic Deontic Logic Mixed Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abramsky, S.: Computational interpretations of linear logic. Theoretical Computer Science 111(1), 3–57 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Anglberger, A., Gratzl, N., Roy, O.: The logic of obligations as weakest permissions (2013) (manuscript)Google Scholar
  3. 3.
    Asher, N., Pelletier, F.: Generics and defaults. In: van Bentham, J., ter Meulen, A. (eds.) Handbook of Logic and Language. Elsevier (1997)Google Scholar
  4. 4.
    Asudeh, A.: Linear logic, linguistic resource sensitivity and resumption, eSSLLI (2006)Google Scholar
  5. 5.
    Belnap, N., Perloff, M., Xu, M.: Facing the future: Agents and choice in our indeterminist world (2001)Google Scholar
  6. 6.
    Broersen, J.: Action negation and alternative reductions for dynamic deontic logics. Journal of Applied Logic 2, 153–168 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Di Cosmo, R., Miller, D.: Linear logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Fall 2010 edn. (2010)Google Scholar
  8. 8.
    Dignum, F., Meyer, J.J., Wieringa, R.: Free choice and contextually permitted actions. Studia Logica 57(1), 193–220 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Dignum, F., Meyer, J.J.: Negations of transactions and their use in the specification of dynamic and deontic integrity constraints. In: Semantics for Concurrency. Workshops in Computing, pp. 61–80. Springer, London (1990)CrossRefGoogle Scholar
  10. 10.
    Girard, J.Y.: Linear logic. Theoretical Computer Science 50(1), 1–102 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Girard, J.Y.: Linear logic: Its syntax and semantics. In: Girard, J.Y., Lafont, Y., Regnier, L. (eds.) Advances in Linear Logic, vol. 222. Cambridge University Press (1995)Google Scholar
  12. 12.
    Hansson, S.: The varieties of permissions. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, vol. 1, College Publication (2013)Google Scholar
  13. 13.
    Van Benthem, J.: Language in Action: categories, lambdas and dynamic logic. MIT Press (1995)Google Scholar
  14. 14.
    Joyce, J.M.: Regret and instability in causal decision theory. Synthese 187(1), 123–145 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Kracht, M., Wolter, F.: Normal monomodal logics can simulate all others. Journal Symbolic Logic 64(1), 99–138 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Makinson, D.: Stenius’ approach to disjunctive permission. Theoria 50, 138–147 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Makinson, D.: Bridges from classical to nonmonotonic logic. College Publications (2005)Google Scholar
  18. 18.
    McCarthy, J.: Epistemological problems of artificial intelligence. In: IJCAI, vol. 77, pp. 1038–1044 (1977)Google Scholar
  19. 19.
    McNamara, P.: Deontic logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Fall 2010 edn. (2010)Google Scholar
  20. 20.
    Meyer, J.J.C.: A different approach to Deontic Logic: Deontic Logic Viewed as a Variant of Dynamic Logic. Notre Dame Journal of Formal Logic 29, 109–136 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Osborne, M.J., Rubinstein, A.: A course in game theory. MIT Press (1994)Google Scholar
  22. 22.
    Roy, O., Anglberger, A.J.J., Gratzl, N.: The logic of obligation as weakest permission. In: Ågotnes, T., Broersen, J., Elgesem, D. (eds.) DEON 2012. LNCS, vol. 7393, pp. 139–150. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Schurz, G.: Relevant Deduction: From Solving Paradoxes Towards a General Theory. Erkenntnis 35, 391–437 (1991)MathSciNetGoogle Scholar
  24. 24.
    Schurz, G., Weingartner, P.: Paradoxes solved by simple relevance criteria. Logique et Analyse 113, 3–40 (1986)MathSciNetGoogle Scholar
  25. 25.
    Simons, M.: Dividing things up: The semantics of or and the modal/or interaction. Natural Language Semantics 13(3), 271–316 (2005)CrossRefGoogle Scholar
  26. 26.
    Trypuz, R., Kulicki, P.: On deontic action logics based on boolean algebra. Journal of Logic and Computation (2013) (forthcoming)Google Scholar
  27. 27.
    von Wright, G.H.: Norm and Action - A Logical Enquiry. Routledge (1963)Google Scholar
  28. 28.
    van Wright, G.H.: An Essay in Deontic Logic and the General Theory of Action. North-Holland Publishing Company (1968)Google Scholar
  29. 29.
    Zimmermann, T.: Free choice disjunction and epistemic possibility. Natural Language Semantics 8(4), 255–290 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Albert J. J. Anglberger
    • 1
  • Huimin Dong
    • 2
  • Olivier Roy
    • 2
  1. 1.Munich Center for Mathematical PhilosophyLMU MunichGermany
  2. 2.Philosophy and EconomicsUniversity of BayreuthGermany

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