Abstract
Normative arrow update logic (NAUL) is a logic that combines normative temporal logic (NTL) and arrow update logic (AUL). In NAUL, norms are interpreted as arrow updates on labeled transition systems with a CTL-like logic. We show that the satisfiability problem of NAUL is decidable with a tableau method and it is in EXPSPACE.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ågotnes, T., van der Hoek, W., Rodríguez-Aguilar, J. A., Sierra, C., Wooldridge, M.: On the logic of normative systems. In Proceedings of 20th IJCAI, pp. 1175–1180 (2007)
Ågotnes, T., van der Hoek, W., Rodríguez-Aguilar, J.A., Sierra, C., Wooldridge, M.: A temporal logic of normative systems. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy. TL, vol. 28, pp. 69–106. Springer, Dordrecht (2009). https://doi.org/10.1007/978-1-4020-9084-4_5
Ågotnes, T., van der Hoek, W., Wooldridge, M.: Robust normative systems and a logic of norm compliance. Logic J. IGPL 18, 4–30 (2010)
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002)
Anderson, A.R., Moore, O.K.: The formal analysis of normative concepts. Am. Sociol. Rev. 22, 9–17 (1957)
Bartha, P.: Conditional obligation, deontic paradoxes, and the logic of agency. Ann. Math. Artif. Intell. 9(1–2), 1–23 (1993)
Chisholm, R.M.: Contrary-to-duty imperatives and deontic logic. Analysis 24, 33–36 (1963)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1981). https://doi.org/10.1007/bfb0025774
Fitoussi, D., Tennenholtz, M.: Choosing social laws for multi-agent systems: minimality and simplicity. Artif. Intell. 119, 61–101 (2000)
Føllesdal, D., Hilpinen, R.: Deontic logic: an introduction. In: Hilpinen, R. (ed.) Deontic Logic: Introductory and Systematic Readings. Synthese Library, vol. 33, pp. 1–35. Springer, Dordrecht (1971). https://doi.org/10.1007/978-94-010-3146-2_1
Herzig, A., Lorini, E., Moisan, F., Troquard, N.: A dynamic logic of normative systems. In: Walsh, T., (ed.), Proceedings of the Twenty-second International Joint Conference on Artificial Intelligence (IJCAI11), pp. 228–233 (2011)
Horty, J.F.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)
Jones, A.J.I., Sergot, M.: On the characterisation of law and computer systems: the normative systems perspective. In: Deontic Logic in Computer Science: Normative System Specification, pp. 275–307 (1993)
Kooi, B., Renne, B.: Arrow update logic. Rev. Symbolic Logic 4(4), 536–559 (2011)
Kuijer, L.B.: An arrow-based dynamic logic of norms. In: 3rd International Workshop on Strategic Reasoning (SR 2015) (2015)
Meyer, J.C.: A different approach to deontic logic: deontic logic viewed as a variant of dynamic logic. Notre Dame J. Formal Logic 29, 109–136 (1988)
Ross, A.: Imperatives and logic. Theoria 7, 53–71 (1941)
Shoham, Y., Tennenholtz, M.: On the synthesis of useful social laws for artificial agent societies. In: Proceedings of the Tenth National Conference on Artificial Intelligence (AAAI 1992), pp. 276–281 (1992)
Shoham, Y., Tennenholtz, M.: On social laws for artificial agent societies: off-line design. Artif. Intell. 73, 231–252 (1995)
van der Meyden, R.: The dynamic logic of permission. J. Log. Comput. 6(3), 465–479 (1996)
van Ditmarsch, H., van der Hoek, W., Kooi, B., Kuijer, L.B.: Arbitrary arrow update logic. Artif. Intell. 242, 80–106 (2017)
Acknowledgement
We thank the LORI reviewers for very detailed and helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
van Ditmarsch, H., Kuijer, L., Liu, M. (2023). An Arrow-Based Dynamic Logic of Normative Systems and Its Decidability. In: Alechina, N., Herzig, A., Liang, F. (eds) Logic, Rationality, and Interaction. LORI 2023. Lecture Notes in Computer Science, vol 14329. Springer, Cham. https://doi.org/10.1007/978-3-031-45558-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-45558-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-45557-5
Online ISBN: 978-3-031-45558-2
eBook Packages: Computer ScienceComputer Science (R0)
