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Temporal Deontic Logic for the Generalised Chisholm Set of Contrary to Duty Obligations

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7393)

Abstract

We consider a generalised Chisholm set of contrary to duty obligations (CTD) of the form

$$ O q_0 $$

and for i = 0,…, n we have the CTD is

$$ \begin{array} {l} q_i\to O q_{i+1}\\ \neg q_i \to O \neg q_{i+1} \end{array} $$

and the facts ±q j for some j ∈ J ⊆ {0,1,…, n + 1}. Note that for the case of n = 1 and fact ¬q 0 we have the Chisholm paradox.

We also allow for temporal sequencing of the q i in the form that q i + 1 may come temporally before or after q i .

We offer a representation of this problem in a variation of standard deontic logic that we call TSDL, with the standard temporal operator \(\lozenge\), the deontic obligation operator O, and the past operator Y for “yesterday”. This formalism is free of the above paradoxes. We provide an axiomatization and show it to be complete. The logic formalism enjoys the finite tree model property and hence is decidable.

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References

  1. Gabbay, D.M.: Introducing Reactive Kripke Semantics and Arc Accessibility. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Trakhtenbrot/Festschrift. LNCS, vol. 4800, pp. 292–341. Springer, Heidelberg (2008); Earlier version published in Proceeding of CombLog 2004, http://www.cs.math.ist.utl.pt/comblog04/ Carnielli, W., Dionesio, F.M., Mateus, P. (eds.) Centre of Logic and Computation University of Lisbon, pp 7–20 (2004) ftp://logica.cle.unicamp.br/pub/e-prints/comblog04/gabbay.pdf

    CrossRef  Google Scholar 

  2. Prakken, H., Sergot, M.J.: Contrary-to-duty obligations. Studia Logica 57(1), 91–115 (1996)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Carmo, J., Jones, A.J.I.: Deontic Logic and Contrary-to-duties. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 8, pp. 265–343. Springer (2002)

    Google Scholar 

  4. Gabbay, D.M.: Reactive Proof Theory (in preparation)

    Google Scholar 

  5. Gabbay, D.M., Schlechta, K.: Critical analysis of the Carmo–Jones model of contrary to duty obligations. Draft paper, http://arxiv.org/PS_cache_arxiv/pdf/1002/1002.3021v1.pdf

  6. Prakken, H., Sergot, M.: Dyadic deontic logic and contary to duty obligations. In: Nute, D. (ed.) Defeasible Deontic Logic. Synthese Library, pp. 223–262. Kluwer (1997)

    Google Scholar 

  7. de Boer, M., Gabbay, D., Parent, X., Slavkova, M.: Two dimensional deontic logic. In: Synthese, pp. 1–38 (2011), doi:10.1007/s11229-010-9866-4

    Google Scholar 

  8. Gabbay, D.M.: Completeness theorems for reactive modal logics. To appear in AMAI special issue. Paper 392

    Google Scholar 

  9. Chisholm, R.M.: Contrary-to-duty imperatives and deontic logic. Analysis 24 (1963)

    Google Scholar 

  10. Ross, A.: Imperatives and Logic. Theoria 7, 53–71 (1941)

    Google Scholar 

  11. Prior, A.N.: Escapism: The Logical Basis of Ethics. In: Melden, A.I. (ed.) Essays in Moral Philosophy, pp. 135–146. University of Washington Press (1958)

    Google Scholar 

  12. Aqvist, L.: A New Approach to the Logical Theory of Interrogatives, Part I, Analysis, Philosophical Society and Department of Philosophy, University of Uppsala, sect. 6.2 (1965)

    Google Scholar 

  13. Jones, A.J.I., Pörn, I.: Ideality, sub-ideality and deontic logic. Synthese 65 (1985)

    Google Scholar 

  14. Forrester, J.W.: Gentle Murder, or the Adverbial Samartian. The Journal of Philosophy 81(4), 193–197 (1984)

    CrossRef  MathSciNet  Google Scholar 

  15. van der Torre, L., Tan, Y.H.: Contrary to duty reasoning with preference-based dyadic obligations. Annals of Mathematics and Artificial Intelligence 27, 49–78 (1999)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Dignum, F., Broersen, J., Dignum, V., Meyer, J.-J.: Meeting the Deadline: Why, When and How. In: Hinchey, M.G., Rash, J.L., Truszkowski, W.F., Rouff, C.A. (eds.) FAABS 2004. LNCS (LNAI), vol. 3228, pp. 30–40. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  17. Broersen, J., Dignum, F., Dignum, V., Meyer, J.-J.C.: Designing a Deontic Logic of Deadlines. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 43–56. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  18. Dignum, F., Kuiper, R.: Specifying Deadlines with Dense Time Using Deontic and Temporal Logic. International Journal of Electronic Commerce 3(2), 67–86 (winter 1998-1999)

    Google Scholar 

  19. Dignum, F., Meyer, J.-J., Kuiper, R.: An investigation into deontics of durative actions. In: Proceedings 4th Int. Conference on Deontic Logic in Computer Science, Bologna, Italy (January 1998)

    Google Scholar 

  20. Dignum, F., Kuiper, R.: Obligations and Dense Time for Specifying Deadlines. In: Proceedings of Thirty-First HICSS, Hawaii (1998)

    Google Scholar 

  21. Dignum, F., Weigand, H., Verharen, E.: Meeting the Deadline: on the Formal Specification of Temporal Deontic Constraints. In: Michalewicz, M., Raś, Z.W. (eds.) ISMIS 1996. LNCS(LNAI), vol. 1079, pp. 243–252. Springer, Heidelberg (1996)

    CrossRef  Google Scholar 

  22. Broersen, J.: Strategic Deontic Temporal Logic as a Reduction to ATL, with an Application to Chisholm’s Scenario. In: Goble, L., Meyer, J.-J.C. (eds.) DEON 2006. LNCS (LNAI), vol. 4048, pp. 53–68. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  23. Dignum, F., Kuiper, R.: Combining dynamic deontic logic and temporal logic for the specification of deadlines. In: Sprague Jr., R. (ed.) Proceedings of Thirtieth HICSS (1997)

    Google Scholar 

  24. Meyer, C.J.-J.: A simple solution to the “deepest” paradox in deontic logic. Logique et Analyse, 117–118, 81–90 (1987)

    Google Scholar 

  25. Anglberge, A.J.J.: Dynamic Deontic Logic and Its Paradoxes. Studia Logica 89(3), 427–435 (2008)

    CrossRef  MathSciNet  Google Scholar 

  26. Carmo, J.M.C.L.M., Jones, A.J.I.: Completeness and decidability results for a logic of contrary-to-duty conditionals. J. Logic and Computation (2012), doi:10.1093/logcom/exs009

    Google Scholar 

  27. Gabbay, D.: Reactive Standard Deontic Logic. To appear in J. Logic and Computation Special Issue Celebrating 60 Years of Deontic Logic

    Google Scholar 

  28. Gabbay, D.: Reactive Kripke Models and Contrary-to-duty Obligations. Part A: semantics. To appear in Journal of Applied Logic

    Google Scholar 

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Gabbay, D. (2012). Temporal Deontic Logic for the Generalised Chisholm Set of Contrary to Duty Obligations. In: Ågotnes, T., Broersen, J., Elgesem, D. (eds) Deontic Logic in Computer Science. DEON 2012. Lecture Notes in Computer Science(), vol 7393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31570-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-31570-1_7

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