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“Sing and Dance!”

Input/Output Logics without Weakening

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 8554)

Abstract

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe[19,20] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Second, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics.

Keywords

  • Modal Logic
  • Proof System
  • Normative Reasoning
  • Deontic Logic
  • Philosophical Logic

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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  • DOI: 10.1007/978-3-319-08615-6_12
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References

  1. Broome, J.: Rationality Through Reasoning. Wiley-Blackwell, West Sussex (2013)

    CrossRef  Google Scholar 

  2. Chisholm, R.: Contrary-to-duty imperatives and deontic logic. Analysis 24, 33–36 (1963)

    CrossRef  Google Scholar 

  3. Dosen, K.: Negation in the light of modal logic. In: Gabbay, D., Wansing, H. (eds.) What is Negation?, pp. 77–86. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  4. Forrester, J.: Gentle murder, or the adverbial Samaritan. Journal of Philosophy 81, 193–197 (1984)

    CrossRef  MathSciNet  Google Scholar 

  5. Goble, L.: A logic of good, should, and would: Part I. Journal of Philosophical Logic 19, 169–199 (1990)

    MATH  MathSciNet  Google Scholar 

  6. 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)

    CrossRef  Google Scholar 

  7. Goble, L.: Prima facie norms, normative conflicts and dilemmas. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, pp. 241–352. College Publications, London (2013)

    Google Scholar 

  8. Hansen, J.: Imperative logic and its problems. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, pp. 499–544. College Publications, London (2013)

    Google Scholar 

  9. Hansen, J.: Reasoning about permission and obligation. In: Hansson, S.O. (ed.) David Makinson on Classical Methods for Non-Classical Problems, pp. 287–333. Springer (2014)

    Google Scholar 

  10. Hansson, S.O.: Preference-based deontic logic (PDL). Journal of Philosophical Logic 19, 75–93 (1990)

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. Hansson, S.O.: Situationist deontic logic. Journal of Philosophical Logic 26(4), 423–448 (1997)

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. Makinson, D.: On a fundamental problem in deontic logic. In: Namara, P.M., Prakken, H. (eds.) Norms, Logics and Information Systems. Frontiers in Artificial Intelligence and Applications, pp. 29–54. IOS Press, Amsterdam (1999)

    Google Scholar 

  13. Makinson, D., van der Torre, L.: Input/output logics. Journal of Philosophical Logic 29(4), 383–408 (2000)

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. Makinson, D., van der Torre, L.: Constraints for input/output logics. Journal of Philosophical Logic 30(2), 155–185 (2001)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. McLaughlin, R.N.: Further problems of derived obligation. Mind 64(255), 400–402 (1955)

    CrossRef  Google Scholar 

  16. Parent, X., van der Torre, L.: Aggregative deontic detachment for normative reasoning (short paper). In: Eiter, T., Baral, C., Giacomo, G.D. (eds.) Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning, KR 2014. AAAI Press (2014)

    Google Scholar 

  17. Prakken, H., Sergot, M.: Contrary-to-duty obligations. Studia Logica 57, 91–115 (1996)

    CrossRef  MATH  MathSciNet  Google Scholar 

  18. Priest, G.: Paraconsistent logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 6, pp. 287–393. Springer (2002)

    Google Scholar 

  19. Stolpe, A.: Normative consequence: The problem of keeping it whilst giving it up. In: van der Meyden, R., van der Torre, L. (eds.) DEON 2008. LNCS (LNAI), vol. 5076, pp. 174–188. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  20. Stolpe, A.: Norms and Norm-System Dynamics. Ph.D. thesis, Department of Philosophy, University of Bergen, Norway (2008)

    Google Scholar 

  21. von Wright, G.: Norm and Action: A Logical Enquiry. Routledge & Kegan Paul PLC (1963)

    Google Scholar 

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Parent, X., van der Torre, L. (2014). “Sing and Dance!”. In: Cariani, F., Grossi, D., Meheus, J., Parent, X. (eds) Deontic Logic and Normative Systems. DEON 2014. Lecture Notes in Computer Science(), vol 8554. Springer, Cham. https://doi.org/10.1007/978-3-319-08615-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-08615-6_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08614-9

  • Online ISBN: 978-3-319-08615-6

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