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International Workshop on Logic, Rationality and Interaction

LORI 2019: Logic, Rationality, and Interaction pp 340–354Cite as

A Neutral Temporal Deontic STIT Logic

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11813)

Abstract

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic \(\mathsf {TDS}\). The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic \(\mathsf {TDS}\) sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting.

Keywords

  • Deontic logic
  • Logics of agency
  • Modal logic
  • Multi-agent STIT logic
  • Temporal logic
  • Utilitarianism

Work funded by the projects WWTF MA16-028, FWF I2982 and FWF W1255-N23.

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Fig. 1.

Notes

  1. 1.

    In future work, we aim to study condition (C3) strengthened to equality, as in [14]. In such a setting, completeness is obtained by proving that each \(\mathsf {TDS}\)-frame can be transformed into a frame (satisfying the same formulae) with strengthened (C3); hence, showing that the logic does not distinguish between the two frame classes.

  2. 2.

    The main reason why the grand coalition operator [Ag] is added to our language, is because it will allow us to axiomatize the no choice between undivided histories principle (see A25 of Definition 4). For a discussion of [Ag] we refer to [14].

  3. 3.

    This also holds when all intersections of choices of agents contain both a 1 and a 0.

References

  1. Abarca, A.I.R., Broersen, J.: A logic of objective and subjective oughts. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 629–641. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_41

    CrossRef  Google Scholar 

  2. Arkoudas, K., Bringsjord S., Bello, P.: Toward ethical robots via mechanized deontic logic. In: AAAI Fall Symposium on Machine Ethics, pp. 17–23 (2005)

    Google Scholar 

  3. Balbiani, P., Herzig, A., Troquard, N.: Alternative axiomatics and complexity of deliberative STIT theories. J. Philos. Logic 37(4), 387–406 (2008)

    MathSciNet  CrossRef  Google Scholar 

  4. Belnap, N., Perloff, M., Xu, M.: Facing the Future: Agents and Choices in our Indeterminist World. Oxford University Press on Demand, Oxford (2001)

    Google Scholar 

  5. Bentham, J.: An Introduction to the Principles of Morals and Legislation (1789)

    Google Scholar 

  6. van Berkel, K., Lyon, T.: Cut-free calculi and relational semantics for temporal STIT logics. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 803–819. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_52

    CrossRef  Google Scholar 

  7. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

    CrossRef  Google Scholar 

  8. Gabbay, D.M., Hodkinson, I., Reynolds, M.: Temporal Logic: Mathematical Foundations and Computational Aspects. Oxford University Press, Oxford (1994)

    CrossRef  Google Scholar 

  9. Gerdes, J.C., Thornton, S.M.: Implementable ethics for autonomous vehicles. In: Maurer, M., Gerdes, J.C., Lenz, B., Winner, H. (eds.) Autonomes Fahren, pp. 87–102. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-45854-9_5

    CrossRef  Google Scholar 

  10. Goodall, N.J.: Machine ethics and automated vehicles. In: Meyer, G., Beiker, S. (eds.) Road Vehicle Automation. LNM, pp. 93–102. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-05990-7_9

    CrossRef  Google Scholar 

  11. Herzig, A., Schwarzentruber, F.: Properties of logics of individual and group agency. In: Advances in Modal Logic, vol. 7, pp. 133–149. College Publications, London (2008)

    Google Scholar 

  12. Horty, J.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)

    CrossRef  Google Scholar 

  13. Horty, J., Pacuit, E.: Action types in STIT semantics. Rev. Symbolic Logic 10(4), 617–637 (2017)

    MathSciNet  CrossRef  Google Scholar 

  14. Lorini, E.: Temporal STIT logic and its application to normative reasoning. J. Appl. Non-Classical Logics 23(4), 372–399 (2013)

    MathSciNet  CrossRef  Google Scholar 

  15. Murakami, Y.: Utilitarian deontic logic. In: Advances in Modal Logic, vol. 5, pp. 211–230. King’s College Publications, London (2005)

    Google Scholar 

  16. Nayebpour, M., Koehn, D.: The ethics of quality: problems and preconditions. J. Bus. Ethics 44(1), 37–48 (2003)

    CrossRef  Google Scholar 

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

    MathSciNet  CrossRef  Google Scholar 

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Authors and Affiliations

  1. Institut für Logic and Computation, Technische Universität Wien, Vienna, Austria

    Kees van Berkel & Tim Lyon

Authors
  1. Kees van Berkel
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  2. Tim Lyon
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Corresponding author

Correspondence to Kees van Berkel .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Dr. Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Dr. Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

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van Berkel, K., Lyon, T. (2019). A Neutral Temporal Deontic STIT Logic. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_25

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_25

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