NO Revision and NO Contraction
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- Alchourrón, C., Gärdenfors P., & Makinson D. C. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2), 510–530. CrossRef
- Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. New York: Cambridge University Press.
- 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).
- Chellas, B. (1980). Model logic. Cambridge: Cambridge University Press.
- Darwiche, A., & Pearl, J. (1997). On the logic of iterated belief revision. Artificial Intelligence 89, 1–29. CrossRef
- 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.
- Gabbay, D., Rodrigues, O., & Russo, A. (2008). Belief revision in non-classical logics. The Review of Symbolic Logic 1(3), 267–304. CrossRef
- 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).
- Goranko, V., & Passy, S. (1992). Using the universal modality: Gains and questions. Journal of Logic and Computation 2, 5–30. CrossRef
- Governatori, G., & Rotolo, A. (2010). Changing legal systems: Legal abrogations and annulments in defeasible logic. Logic Journal of the IGPL.
- Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic 17, 157–170. CrossRef
- Haenni, R., Romeyn, J. -W., Wheeler, & G., Williamson, J. (2010). Probabilistic logic and probabilistic networks. Synthese library. Dordrecht: Springer.
- Hansson, S. O. (1999). A textbook of belief dynamics: Theory change and database updating. Berlin: Kluwer Academic Publishers.
- Jin, Y., & Thielscher, M. (2007). Iterated belief revision, revised. Artificial Intelligence 171(1), 1–18. CrossRef
- Jorgensen, J. (1937). Imperatives and logic. Erkenntnis 7, 288–296.
- 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).
- Kyburg, H. E. Jr., Teng, C. M., & Wheeler, G. (2007). Conditionals and consequences. Journal of Applied Logic 5(4), 638–650. CrossRef
- Levi, I. (2004). Mild contraction. Oxford: Clarendon Press. CrossRef
- Makinson, D. C., & van der Torre, L. (2000). Input-output logics. Journal of Philosophical Logic 30(2), 155–185. CrossRef
- Makinson, D. C., & van der Torre, L. (2001). Constraints for input/output logics. Journal of Philosophical Logic 30, 155–185. CrossRef
- 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).
- 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.
- 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).
- Poole, D. (1988). A logical framework for default reasoning. Artificial Intelligence 36, 27–47. CrossRef
- Reiter, R. (1980). A logic for default reasoning. Artificial Intelligence 13, 81–132. CrossRef
- Rott, H. (2001). Change choice and inference. Oxford: Oxford University Press.
- 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.
- Stolpe, A. (2010). A theory of permission based on the notion of derogation. Journal of Applied Logic 8, 97–113. CrossRef
- van Ditmarsch, H., van der Hoek, W., B., & Kooi, B. (2008). Dynamic Epistemic Logic. Berlin: Synthese Library, Springer.
- 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.
- NO Revision and NO Contraction
Minds and Machines
Volume 21, Issue 3 , pp 411-430
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Modal logic