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Logic and Logical Philosophy

A Unified Logical Framework for Reasoning about Deontic Properties of Actions and States
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A Unified Logical Framework for Reasoning about Deontic Properties of Actions and States

Authors

  • Piotr Kulicki Catholic University of Lublin, Faculty of Philosophy https://orcid.org/0000-0001-5413-3886
  • Robert Trypuz Catholic University of Lublin, Faculty of Philosophy https://orcid.org/0000-0003-4042-9947
  • Robert Craven Imperial College London, Department of Computing
  • Marek J. Sergot Imperial College London, Department of Computing https://orcid.org/0000-0002-3706-1419

DOI:

https://doi.org/10.12775/LLP.2023.004

Keywords

deontic logic, ought to do, ought to be, deontic action logic, transition system, conditional norms

Abstract

This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms.

References

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Carmo, J., and A. J. I. Jones, “Deontic database constraints, violation and recovery”, Studia Logica, 57, 1 (1996): 139–165. DOI: http://dx.doi.org/10.1007/BF00370673

Craven, R., and M. Sergot, “Agent strands in the action language nC+”, Journal of Applied Logic, 6, 2 (2008): 172–191. DOI: http://dx.doi.org/10.1016/j.jal.2007.06.007

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Hilpinen, R., and P. McNamara, “Deontic logic: A historical survey and introduction”, pages 1–134, chapter 1, in D. Gabbay, J. Horty, R. van der Meyden, X. Parent, and L. van der Torre (eds.), Handbook of Deontic Logic and Normative Systems, Vol. 1, College Publications, London, 2013.

Kulicki, P., and R. Trypuz, “Two faces of obligation”, pages 70–82 in A. Brożek, J. Jadacki, and B. Zarnic (eds.), Theory of Imperatives from Different Points of View (2), “Logic, Methodology and Philosophy of Science at Warsaw University 7”, Wydawnictwo Naukowe Semper, 2013.

Kulicki, P., and R. Trypuz, “Connecting actions and states in deontic logic”, Studia Logica, 105, 5 (2017): 915–942. DOI: http://dx.doi.org/10.1007/s11225-017-9716-1

Meyer, J-J. Ch., “A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic”, Notre Dame Journal of Formal Logic, 29, 1 (1988): 109–136. DOI: http://dx.doi.org/10.1305/ndjfl/1093637776

Sergot, M., “Modelling unreliable and untrustworthy agent behaviour”, pages 161–178 in B. Dunin-Keplicz, A. Jankowski, A. Skowron, and M. Szczuka (eds.), Monitoring, Security, and Rescue Techniques in Multi-agent Systems, Advances in Soft Computing, Springer-Verlag, 2005. DOI: http://dx.doi.org/10.1007/3-540-32370-8_11

Sergot, M., “Action and agency in norm-governed multi-agent systems”, pages 1–54 in A. Artikis, G. M. P. O’Hare, K. Stathis, and G. Vouros (eds.), Engineering Societies in the Agents World VIII. 8th Annual International Workshop, ESAW 2007, Athens, October 2007, Revised Selected Papers, LNCS 4995, Springer, 2008. DOI: http://dx.doi.org/10.1007/978-3-540-87654-0_1

Sergot, M., “Some examples formulated in a ‘seeing to it that’ logic: Il-lustrations, observations, problems”, pages 223–256 in T. Müller (ed.), Nuel Belnap on Indeterminism and Free Action, Vol. 2 of “Outstanding Contributions to Logic”, Springer Open, 2014.

Sergot, M., and R. Craven, “The deontic component of action language nC+”, pages 222–237 in L. Goble and J-J. Ch. Meyer (eds.), Deontic Logic and Artificial Normative Systems. Proc. 8th International Workshop on Deontic Logic in Computer Science (DEON’06), Utrecht, July 2006, LNAI 4048, Springer Verlag, 2006.

Trypuz, R., and P. Kulicki, “On deontic action logics based on Boolean algebra”, Journal of Logic and Computation, 25, 5 (2015): 1241–1260. DOI: http://dx.doi.org/10.1093/logcom/ext057

van der Meyden, R., “The dynamic logic of permission”, Journal of Logic and Computation, 6, 3 (1996): 465–479. DOI: http://dx.doi.org/10.1093/logcom/6.3.465

Logic and Logical Philosophy

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Published

2023-06-02

How to Cite

1.
KULICKI, Piotr, TRYPUZ, Robert, CRAVEN, Robert and SERGOT, Marek J. A Unified Logical Framework for Reasoning about Deontic Properties of Actions and States. Logic and Logical Philosophy. Online. 2 June 2023. Vol. 32, no. 4, pp. 583-617. [Accessed 14 July 2025]. DOI 10.12775/LLP.2023.004.
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Vol. 32 No. 4 (2023): December

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Articles

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Copyright (c) 2023 Piotr Kulicki, Robert Trypuz, Robert Craven, Marek J. Sergot

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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