NO Revision and NO Contraction
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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: pp. 510-530 CrossRef
- Blackburn, P., Rijke, M., Venema, Y. (2001) Modal logic. Cambridge University Press, New York
- 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 University Press, Cambridge
- Darwiche, A., Pearl, J. (1997) On the logic of iterated belief revision. Artificial Intelligence 89: pp. 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: pp. 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: pp. 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: pp. 157-170 CrossRef
- Haenni, R., Romeyn, J. -W., Wheeler, G., Williamson, J. (2010) Probabilistic logic and probabilistic networks synthese library. Springer, Dordrecht
- Hansson, S. O. (1999) A textbook of belief dynamics: Theory change and database updating. Kluwer Academic Publishers, Berlin
- Jin, Y., Thielscher, M. (2007) Iterated belief revision, revised. Artificial Intelligence 171: pp. 1-18 CrossRef
- Jorgensen, J. (1937) Imperatives and logic. Erkenntnis 7: pp. 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., Teng, C. M., Wheeler, G. (2007) Conditionals and consequences. Journal of Applied Logic 5: pp. 638-650 CrossRef
- Levi, I. (2004) Mild contraction. Clarendon Press, Oxford CrossRef
- Makinson, D. C., Torre, L. (2000) Input-output logics. Journal of Philosophical Logic 30: pp. 155-185 CrossRef
- Makinson, D. C., van der Torre, L. (2001) Constraints for input/output logics. Journal of Philosophical Logic 30: pp. 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. Defeasible logic. In: Gabbay, D., Hogger, C., Robinson, J. eds. (1994) Handbook of logic in artificial intelligence and logic programming (Vol. 3. Oxford University Press, New York
- 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: pp. 27-47 CrossRef
- Reiter, R. (1980) A logic for default reasoning. Artificial Intelligence 13: pp. 81-132 CrossRef
- Rott, H. (2001) Change choice and inference. Oxford University Press, Oxford
- Spohn, W. Ordinal conditional functions: A dynamic theory of epistemic states. In: Harper, W. L., Skyrms, B. eds. (1987) Causation in decision, belief change and statistics (Vol. 2). Reidel, Dordrecht, pp. 105-134
- Stolpe, A. (2010) A theory of permission based on the notion of derogation. Journal of Applied Logic 8: pp. 97-113 CrossRef
- Ditmarsch, H., Hoek, W., Kooi, B. (2008) Dynamic epistemic logic. Synthese Library, Springer, Berlin
- 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
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