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Abstract

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.

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Notes

  1. Although a full theory of normative systems should be developed for languages containing n \({\mathsf O}_i\) operators, one for each 1 ≤ i ≤ n agents in the normative system, we focus in this paper on the basic case where n = 1 and thus omit the subscript in the remainder.

  2. A formula ϕt taboo is maximal in ϕt (with respect to \(\mathcal{A}_{GO}\)) iff \(\phi^t \vdash \phi^{t}_{taboo}\) and \(\mathcal{A}_{GO} \vdash \phi^{t}_{taboo}\), and for all ϕt* taboo such that \(\phi^t \vdash \phi^{t*}_{taboo}\) and \(\mathcal{A}_{GO} \vdash \phi^{t*}_{taboo}\), then \( \phi^{t*}_{taboo} \not\vdash \phi^t_{taboo}\).

  3. Thanks here to Choh Man Teng for saving our bacon.

  4. Notice that, like normal modal logics but unlike classical (monotone) modal logics, the most general input/output logic, “simple-minded output”, satisfies adjunction as well via the AND rule.

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Acknowledgments

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.

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Correspondence to Marco Alberti.

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Wheeler, G., Alberti, M. NO Revision and NO Contraction. Minds & Machines 21, 411–430 (2011). https://doi.org/10.1007/s11023-011-9243-1

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