One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change.
KeywordsNorms Modal logic Revision Contraction
This research was supported in part by award LogiCCC/0001/2007, project DiFoS, from the European Science Foundation. Thanks to Erich Rast, Choh Man Teng, and three anonymous referees for very helpful comments on earlier drafts.
- Boella, G., Pigozzi, G., van der Torre, L. (2009). Normative framework for normative system change. In D. Sichman, C. Sierra, & C. Castelfranchi (Eds.), Proceedings of the 8th international conference on autonomous agents and multiagent systems (AAMAS 2009), (pp. 169–176).Google Scholar
- Chellas, B. (1980). Model logic. Cambridge: Cambridge University Press.Google Scholar
- Dixon, S., & Wobcke, W. (1993). The implementation of a first-order logic AGM belief revision system. In Proceedings of the fifth IEEE international conference on tools in artificial intelligence, (pp. 40–47). IEEE Computer Society Press.Google Scholar
- Gärdenfors, P., & Makinson, D. C. (1988). Revisions of knowledge systems using epistemic entrenchment. In The 2nd conference on theoretical aspects of reasoning about knowledge (TARK) (pp. 83–96).Google Scholar
- Governatori, G., & Rotolo, A. (2010). Changing legal systems: Legal abrogations and annulments in defeasible logic. Logic Journal of the IGPL.Google Scholar
- Haenni, R., Romeyn, J. -W., Wheeler, & G., Williamson, J. (2010). Probabilistic logic and probabilistic networks. Synthese library. Dordrecht: Springer.Google Scholar
- Jorgensen, J. (1937). Imperatives and logic. Erkenntnis 7, 288–296.Google Scholar
- Katsuno, H., & Mendelzon, A. (1991). On the difference between updating a knowledge base and revising it. In The 2nd international conference on the principles of knowledge representation and reasoning (KR 1991) (pp. 387–394).Google Scholar
- Makinson, D. C., & van der Torre, L. (2007). What is input/output logic? input/output logic, constraints, permissions. In G. Boella, L. van der Torre, & H. Verhagen, (Eds.), Normative multi-agent systems, number 07122 in Dagstuhl seminar proceedings, Dagstuhl, Germany, 2007. Internationales Begegnungs und Forschungszentrum für Informatik (IBFI).Google Scholar
- Nute, D. (1994). Defeasible logic. In G. Dov, C. Hogger, J. Robinson (Eds.), Handbook of logic in artificial intelligence and logic programming (Vol. 3). New York: Oxford University Press.Google Scholar
- Pagnucco, M., & Rott, H. (1999). Severe withdrawal—and recovery. Journal of Philosophical Logic 28, 501–547. (Re-printed with corrections to publisher’s errors in February 2000).Google Scholar
- Spohn, W. (1987). Ordinal conditional functions: A dynamic theory of epistemic states. In W. L. Harper, & B. Skyrms, (Eds.), Causation in decision, belief change and statistics (Vol. 2, pp. 105–134.). Dordrecht: Reidel.Google Scholar
- Wheeler, G. (2010). AGM belief revision in monotone modal logics. In: E. D. Clarke, & A. Voronkov, (Eds.), International conference on logic for programming, artificial intelligence, and reasoning (LPAR-16) short paper proceedings, Dakar, Senegal, 2010.Google Scholar